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Solutions Key

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7_MCABESK207233_FMCPindd 2 11713 600 PM

Table of Contents

UNIT 1 The Number System

Module 1Lesson 11 1

Lesson 12 2

Lesson 13 3

Lesson 14 4

Module 2Lesson 21 6

Lesson 22 7

Lesson 23 8

Module 3Lesson 31 10

Lesson 32 14

Lesson 33 15

Lesson 34 17

Lesson 35 18

Lesson 36 20

UNIT 2 Ratios and Proportional

Relationships


Lesson 42 25

Lesson 43 25


Lesson 52 29

Lesson 53 30

UNIT 3 Expressions Equations

and Inequalities


Lesson 62 34

Lesson 63 35

Lesson 64 37


Lesson 72 46

Lesson 73 47

UNIT 4 Geometry


Lesson 82 54

Lesson 83 54

Lesson 84 55


Lesson 92 59

Lesson 93 60

Lesson 94 63

Lesson 95 65

UNIT 5 Statistics


Lesson 102 70

Lesson 103 72


Lesson 112 75

Lesson 113 76

Copyright copy by Houghton Mifflin Harcourt iiiAll rights reserved

Table of Contents

UNIT 6 Probability


Lesson 122 81

Lesson 123 82

Lesson 124 82


Lesson 132 86

Lesson 133 89

Lesson 134 91

Copyright copy by Houghton Mifflin Harcourt ivAll rights reserved

MODULE 1 Adding and Subtracting Integers

Are You Ready

1 an elevator ride down 27 stories -27

2 a $700 profit 700

3 46 degrees below zero -46

4 a gain of 12 yards 12

1 1

5 183

_ + 78

261

261

5 16 17

6 677

_ -288

389

389

1 1

7 1188

_ +902

2090

2090

1 15 14

8 2647

_ -1885

762

762

9

-8-10 -4-6 -2 2 4 6 8 100 10

-8-10 -4-6 -2 2 4 6 8 100 11

-8-10 -4-6 -2 2 4 6 8 100 12

-8-10 -4-6 -2 2 4 6 8 100

LESSON 11

Your Turn

7 -8 + ( -1 ) = -9

8 -3 + ( -7 ) = -10

9 -48 + ( -12 ) = -60

10 -32 + ( -38 ) = -70

11 109 + 191 = 300

12 -40 + ( -105 ) = -145

13 -150 + ( -1500 ) = -1650

14 -200 + ( -800 ) = -1000

Guided Practice

1 a There are 6 counters

b The red counters represent negative numbers

c -5 + ( -1 ) = -6



c -2 + ( -7 ) = -9

3 -5 + ( -2 ) = -7

-8-7-6-5 -2-1 0-4-3 4 -1 + ( -3 ) = -4

-5-4-3-2 1 2 3-1 0 5 -3 + ( -7 ) = -10

-10 -9-8-7 -4-3-2-6-5 6 -4 + ( -1 ) = -5

-5-4-3-2 1 2 3-1 0 7 -2 + ( -2 ) = -4

-5-4-3-2 1 2 3-1 0 8 -6 + ( -8 ) = -14

-16 -12 -4 0-8 9 -5 + ( -4 ) = -9

10 -1 + ( -10 ) = -11

11 -9 + ( -1 ) = -10

12 -90 + ( -20 ) = -110

13 -52 + ( -48 ) = -100

14 5 + ( 198 ) = 203

15 -4 + ( -5 ) + ( -6 ) = -15

16 -50 + ( -175 ) + ( -345 ) = -570

17 Add their absolute values Use the sign of the

integers as the sign of the sum

Solutions KeyThe Number System

UNIT

1

Copyright copy by Houghton Mifflin Harcourt 1 All rights reserved

Independent Practice

18 a

-4

-6

-8

-2

0

2

-5 + (-3)-3 + (-5)

b No -5 + ( -3 ) is -8 and -3 + ( -5 ) is also -8

19 -3 + ( -1 ) + ( -5 ) + ( -2 ) = -11 the golferrsquos total

score is -11

20 -3 + ( -6 ) = -9 the team lost a total of 9 yards

21 -14 + ( -5 ) + ( -12 ) + ( -23 ) = -54 The total

sack yardage was -54

22 a -10 + ( -8 ) = -18

b -6 + ( -2 ) = -8

c -18 lt -8 Jonestown

23 -100 + ( -75 ) + ( -85 ) = -260

Focus on Higher Order Thinking

24 a -25 + ( -45 ) + ( -75 ) = -145 Jan withdrew

$145

b -35 + ( -55 ) + ( -65 ) = -155 Julie withdrew

$155

c Sample answer $45 $55 and $65

25 It is easier to add -80 + ( -20 ) fi rst to get -100

and then add -173 to get -273

26 Disagree there are three pairs of positive integers

1 and 7 2 and 6 and 3 and 5 and three pairs of

negative integers -1 and -7 -2 and -6 -3 and

-5 The absolute value of the sum of any of these

six pairs is 8

LESSON 12

Your Turn

7 -51 + 23

ǀ -51 ǀ - ǀ 23 ǀ = 28

-51 + 23 = -28

8 10 + ( -18 )

ǀ -18 ǀ - ǀ 10 ǀ = 8

10 + ( -18 ) = -8

9 13 + ( -13 )

ǀ 13 ǀ - ǀ -13 ǀ = 0

10 25 + ( -26 )

ǀ -26 ǀ - ǀ 25 ǀ = 1

25 + ( -26 ) = -1

Guided Practice

1 9 + ( -3 ) = 6

2 3 4 5 8 9 106 7 2 -2 + 7 = 5

-3-2-1 0 3 4 51 2 3 -15 + 4 = -11

-18 -16 -12 -10-14 4 1 + ( -4 ) = -3

-5-4-3-2 1 2 3-1 0 5 -4 + 5 = 1

6 -6 + 6 = 0

7 2 + ( -5 ) = -3

8 -3 + 7 = 4

9 -8 + 14 = 6

10 7 + ( -5 ) = 2

11 5 + ( -21 ) = -16

12 14 + ( -14 ) = 0

13 0 + ( -5 ) = -5

14 32 + ( -8 ) = 24

15 To fi nd -4 + 2 start at -4 and move 2 units to the

right to -2 To fi nd the sum -4 + ( -2 ) start at -4

and move 2 units to the left to -6


16 -15 + 71 = 56

17 -53 + 45 = -8

18 -79 + 79 = 0

19 -25 + 50 = 25

20 18 + ( -32 ) = -14

21 5 + ( -100 ) = -95

22 -12 + 8 + 7 = 3

23 -8 + ( -2 ) + 3 = -7


24 15 + ( -15 ) + 200 = 200

25 -500 + ( -600 ) + 1200 = 100

26 9 + ( -22 ) = -13 the team lost 13 yards

27 -55 + 275 = 220 the teamrsquos profi t was $220

28 -47 + 47 = 0 Alexrsquos new balance is $0

29 Sample answer 10 and -2 and 12 and -4

30 Bart won Bartrsquos score = 123 + ( -180 ) = -57

points Samrsquos score = 185 + ( -255 ) = -70 points

-57 gt -70 so Bart has the greater score


31 Start at -4 and move 3 to the right to reach -1

Start at 3 and move 4 to the left to reach -1

The sums are equivalent by the Commutative

Property of Addition

32 The weight is dropped from 4 feet above the surface

Add -12 to represent the distance the weight falls

before it hits the bottom 4 + ( -12 ) = -8 The water

is 8 feet deep

33 Sample answer A model with more positive

counters than negative counters represents a sum of

two integers whose sum is positive

34 The sign of the other integer is positive and its value

is 6 or greater Sample explanation If you start at

-5 on a number line you have to move to the right 6

or more units to get a sum that is positive

LESSON 13

Your Turn

4 -7 - 2 = -7 + ( -2 )

-7 + ( -2 ) = -9

5 -1 - ( -3 ) = -1 + 3

-1 + 3 = 2

6 3 - 5 = 3 + ( -5 )

3 + ( -5 ) = -2

7 -8 - ( -4 ) = -8 + 4

-8 + 4 = -4

Guided Practice

1 5 - 8 = -3 Start with 5 positive counters

Add 3 zero pairs and remove 8 positive counters

3 negative counters are left so the difference is -3

2 -5 - ( -3 ) = -2 Start with 5 negative counters

and remove 3 negative counters 2 negative

counters are left so the difference is -2

3 -4 - 5 = -4 + ( -5 ) = -9

0-1-2-3-4-5-6-7-8-9 4 1 - 4 = 1 + -4 = -3

0 1 2 3 4-1-2-3-4 5 8 - 11 = 8 + ( -11 ) = -3

6 -3 - ( -5 ) = -3 + 5 = 2

7 15 - 21 = 15 + ( -21 ) = -6

8 -17 - 1 = -17 + ( -1 ) = -18

9 0 - ( -5 ) = 0 + 5 = 5

10 1 - ( -18 ) = 1 + 18 = 19

11 15 - 1 = 14

12 -3 - ( -45 ) = -3 + 45 = 42

13 19 - ( -19 ) = 19 + 19 = 38

14 -87 - ( -87 ) = -87 + 87 = 0

15 To subtract an integer add its opposite Sample

example 6 - 8 = 6 + ( -8 ) = -2


16 To fi nd the change to Theorsquos account subtract the

initial balance -$4 from the fi nal balance $25

25 - ( -4 ) = 25 + 4 = 29

The overall change is $29

17 To fi nd the change in elevation subtract the

beginning elevation of -225 feet from the fi nal

elevation of -127 feet

-127 - ( -225 ) = -127 + 225 = 98

The change in elevation was 98 feet

18 Subtract the low temperature -2degF from the high

temperature 90degF

90 - ( -2 ) = 92

The difference between the high and low

temperatures is 92degF

19 Subtract Cheyennersquos score at the end of her turn

from her score at the start of her turn to fi nd the

change in Cheyennersquos score during her turn

-425 - ( -275 ) = -425 + 275 = -150

The change in Cheyennersquos score is -150 points

20 a Final temperature - initial temperature = change

in temperature

Gas A -8 - ( -21 ) = -8 + 21 = 13

13degC increase

Gas B 12 - ( -12 ) = 12 + 12 = 24

24degC increase

Gas C -15 - ( -19 ) = -15 + 19 = 4

4degC increase

b Negative the fi nal temperatures will be less than

the initial temperature because the gas is cooler

So the difference in temperatures will be negative

21 Diet Chow the catrsquos weight changed by

-8 + ( -18 ) = -26 ounces with Diet Chow and

3 + ( -19 ) = -16 ounces with Kitty Diet


22 Sample answer Susanne owed her sister $4 Then

she borrowed $10 more How much does Susanne

owe her sister in all

23 Tom found -11 - 4 instead of -11 - ( -4 ) To

subtract -4 he should add the opposite of -4

-11 + 4 = -7


24 YouranswerwillbegreaterthantheintegeryoustartedwithbecausewhenyousubtractanegativeintegeryouadditsoppositeapositiveintegerForexample-5-( -3)=-5+3=-2-2gt-5

25 -16-21-26subtract5togetthenextterm

LESSON 14

Your Turn

1 Starts-Descends+Ascends-40-13+18=-53+18  =-3535feetbelowthecaveentrance

3 Usenegativeintegersforcheckamountsanduseapositiveintegerforamountdeposited-35+( -45)+180=-80+180  =100$100increase

4 JimJim-10-18+5-12=-10-18-12+5 =-( 10+18+12)+5 =-40+5 =-35Jimrestedat-35feet(35feetbelowthesurface)Carla0-20+5-18=0+5-20-18 =0+5-( 20+18) =5-38 =-33Carlarestedat-33feet(33feetbelowthesurface)

Guided Practice

1 -15+ 9- 12= -6- 12  =-1818feetbelowsealevel

2 -23+5-7=-18-7  =-25-25degF

3 50-40+87-30=10+87-30  =97-30  =6767points

4 -6+15+15=-6+30  =24

5 9- 4- 17= 9- 21  =-12

6 50-42+10=8+10  =18

7 6+13+7-5=19+2  =21

8 65+43-11=108-11  =97

9 -35-14+45+31=-49+76  =27

10 -12+6-4=-6-4  =-10-34-3+39=-37+39  = 2  -10lt2( -12+6-4)lt( -34-3+39)

11 21-3+8=18+8  =26-14+ 31- 6= 17- 6  =11 26gt11( 21-3+8)gt( -14+31-6)

12 SampleanswerAddandsubtractfromlefttoright-5+12+10-7=7+10-7=17-7=10


13 a 5-1+6-1=9

b 9isapositivescoresoitisoverpar

c 9overparislessthan15overparYesCameronbeathisbestgolfscore

14 -6+14-11=-33feetunderground

15 TheCommutativePropertydoesnotapplytosubtraction3-6+5=2and3-5+6=4

16 a -350+275+70-50=-55Leersquosfinalscoreis-55points

b 45gt-55Barry

17 a 300to400

b 75+30-12+14-8+18-30=75+18+6-12=8787customersmustleavebetween400and500

18 100-18+22-53=51$51

19 45-17-22+18=24$24

20 Carlarsquosaccountdecreased$49-18+22-53=-49andLetarsquosaccountonlydecreased$21-17-22+18=-21Carlarsquosaccounthadthegreatestdecreaseinvalue


21 SampleanswerTimoweshisbrother1dollarHeborrows6moredollarsfromhisbrotherHepayshisbrotherback3dollarsHowmuchdoesTimstillowehisbrother-1-6+3=-4$4

22 Nothetotalamountshecouldpayherparentsis10+12+25=47and50-47=3Soshestillneeds$3

23 SampleanswerInthecaseinwhichthefirstnumberispositivethenthesumoftheabsolutevaluesoftheothertwonumbersmustbegreaterthanthevalueofthefirstnumberSampleexample13-5-10=-2ǀ 5ǀ+ǀ 10ǀ=15whichisgreaterthan13

MODULE 1

Ready to Go On

1 -8+( -6)=-14

2 -4+( -7)=-11

3 -9+( -12)=-21

CopyrightcopybyHoughtonMifflinHarcourt 4 Allrightsreserved

DO NOT EDIT--Changes must be made through ldquoFile infordquo CorrectionKey=B


7_MCABESK207233_U1M01indd 4 103113 206 AM

4 5 + ( -2 )

ǀ 5 ǀ - ǀ -2 ǀ = 3

5 + ( -2 ) = 3

5 -8 + 4

ǀ -8 ǀ - ǀ 4 ǀ = 4

-8 + 4 = -4

6 15 + ( -8 )

ǀ 15 ǀ - ǀ -8 ǀ = 7

15 + ( -8 ) = 7

7 2 - 9 = 2 + ( -9 )

2 + ( -9 ) = -7

8 -3 - ( -4 ) = -3 + 4-3 + 4 = 1

9 11 - ( -12 ) = 11 + 12

11 + 12 = 23

10 -15 + 9 - 4 = -6 - 4

= -10

There are 10 fewer people on the bus

11 24 + 8 - 12 - 9 = 24 + 8 - ( 12 + 9 ) = 32 - 21

= 11

There are 11 cards left in the stack

12 Sample answer Tonya owes her sister $10 and

her friend $5 By how much will her savings change

after she pays them

-10 + ( -5 ) = -15 $15 decrease


MODULE 2 Multiplying and Dividing Integers

Are You Ready

1 9 times 3 = 27

2 7 times 10 = 70

3 9 times 8 = 72

4 15 times 10 = 150

5 6 times 9 = 54

6 10 times 23 = 230

7 9 times 9 = 81

8 10 times 20 = 200

9 54 divide 9 = 6

10 42 divide 6 = 7

11 24 divide 3 = 8

12 64 divide 8 = 8

13 90 divide 10 = 9

14 56 divide 7 = 8

15 81 divide 9 = 9

16 110 divide 11 = 10

17 12 + 8 divide 212 + 4

16

18 15 - ( 4 + 3 ) times 2

15 - 7 times 2

15 - 14

1

19 18 - ( 8 - 5 ) 2

18 - ( 3 ) 2

18 - 9

9

20 6 + 7 times 3 - 5

6 + 21 - 5

27 - 5

22

21 9 + ( 2 2 + 3 ) 2 times 2

9 + ( 4 + 3 ) 2 times 2

9 + ( 7 ) 2 times 2

9 + 49 times 2

9 + 98

107

22 6 + 5 - 4 times 3 divide 2

6 + 5 - 12 divide 2

6 + 5 - 6

11 - 6

5

LESSON 21

Your Turn

4 Since the numbers have opposite signs the product

will be negative

ǀ -3 ǀ times ǀ 5 ǀ = 3 times 5 = 15

-3 ( 5 ) = -15

5 Since the numbers have the same sign the product

will be positive

ǀ -10 ǀ times ǀ -2 ǀ = 10 times 2 = 20

( -10 ) ( -2 ) = 20

6 One of the factors is 0 so the product is 0

0 ( -22 ) = 0


will be positive

8 ( 4 ) = 32

Guided Practice

1 -1 ( 9 ) = -9

2 14 ( -2 ) = -28

3 ( -9 ) ( -6 ) = 54

4 ( -2 ) ( 50 ) = -100

5 ( -4 ) ( 15 ) = -60

6 -18 ( 0 ) = 0

7 ( -7 ) ( -7 ) = 49

8 -15 ( 9 ) = -135

9 ( 8 ) ( -12 ) = -96

10 -3 ( -100 ) = 300

11 0 ( -153 ) = 0

12 -6 ( 32 ) = -192

13 7 ( -75 ) = -525 -$525

14 Start at zero and move 5 units to the left 3 times

3 ( -5 ) = -15 the team lost 15 yards

15 6 ( -2 ) = -12 -12degF

16 Multiply the absolute values of the integers If both

integers have the same sign the product is positive

If they have different signs the product is negative


17 No her number line shows the correct result -6

but she modeled 2 ( -3 ) instead of -2 ( 3 )

18 2 ( -3 ) = -6 he went down 6 floors

19 5 ( -4 ) = -20 $20 decrease

20 Adam descended 5 feet a total of 5 times

5 ( -5 ) = -25 Adam is 25 feet below sea level

21 7 ( -6 ) = -42 the cost of the jeans decreased by

$42 over the 7 weeks

22 9 ( -6 ) = -54 -54 ( 2 ) = -108 Casey has $108

less in his savings

23 7 ( -8 ) = -56 7 ( -5 ) = -35

-56 + ( -35 ) = -91 The savings decreased by $91

24 Sample answer Dave plays a video game in which

he loses 20 points every time he misses a goal

He misses 8 goals 8 ( -20 ) = -160 he loses

160 points


25 a 3 ( 3 ) ( -3 ) = 9 ( -3 ) = -27

b 3 ( -3 ) ( -3 ) = -9 ( -3 ) = 27

c -3 ( -3 ) ( -3 ) = 9 ( -3 ) = -27

d 3 ( 3 ) ( 3 ) ( -3 ) = 9 ( 3 ) ( -3 ) = 27 ( -3 ) = -81

e 3 ( 3 ) ( -3 ) ( -3 ) = 9 ( -3 ) ( -3 ) = -27 ( -3 ) = 81

f 3 ( -3 ) ( -3 ) ( -3 ) = -9 ( -3 ) ( -3 ) = 27 ( -3 ) = -81

g When a product of integers has an odd number of

negative factors like -3 ( -3 ) ( -3 ) = -27 and

3 ( 3 ) ( 3 ) ( -3 ) = -81 the sign of the product is

negative

When a product of integers has an even number

of negative factors like ( 3 ) ( -3 ) ( -3 ) = 27 and

3 ( 3 ) ( -3 ) ( -3 ) = 9 ( -3 ) ( -3 ) = 81 the sign of the

product is positive


26 -1 ( 3 ) ( 1 ) 1 ( -3 ) ( 1 ) -1 ( -3 ) ( -1 )

27 Unless one of the factors is 0 whenever the factors

have opposite signs the product will be less than or

equal to both of the two factors

28 The sign of the product is equal to the sign of the

integers The sign of the product of the first two

integers will always be positive Multiplying this

product by the remaining factor will make a positive

product if the factor is positive negative if it is

negative

LESSON 22

Your Turn

2 Since only the dividend is zero the quotient is 0

0 divide ( -6 ) = 0

3 Since the numbers have opposite signs the quotient

will be negative

38 divide ( -19 ) = -2

4 Since the numbers have the same sign the quotient

will be positive

-13 divide ( -1 ) = 13

5 Yolanda received the same number of penalties in

each game -25 divide ( -5 ) = 5 and -35 divide ( -7 ) = 5

Guided Practice

1 -14 ____ 2 = -7

2 21 divide ( -3 ) = -7

3 26 ____ -13

= -2

4 0 divide ( -4 ) = 0

5 -45 ____ -5 = 9

6 -30 divide ( 10 ) = -3

7 -11 ____ -1

= 11

8 -31 divide ( -31 ) = 1

9 0 ___ -7 = 0

10 -121 _____ -11

= 11

11 84 divide ( -7 ) = -12

12 500 ____ -25

= -20

13 -6 divide ( 0 ) = undefined any number divided by 0 is

undefined

14 -63 ____ -21

= 3

15 -40 divide ( 4 ) = -10 $10

16 -22 divide ( 11 ) = -2 2 points

17 -75 divide ( -15 ) = 5 5 targets

18 -99 divide ( -9 ) = 11 11 times

19 In both cases if the signs of the initial numbers are

the same the answer will be positive If the signs are

different the answer will be negative


20 -24 divide ( 12 ) = -2 $2

21 Elisa made a greater number of withdrawals She

made -140 divide ( -20 ) = 7 withdrawals Francis made

-270 divide ( -45 ) = 6 withdrawals and 7 gt 6

22 a -2 - 10 = -12 the temperature decreased 12degF

b -12 divide ( 12 ) = -1 decreased by 1degF each hour

23 The first part the rate of change for the first part

is -200 ft _______ 10 min

= -20 ftmin and the rate of change for

the second part is -300 ft _______ 20 min

= -15 ftmin

20 ftmin gt 15 ftmin

24 Sample answer A football team lost 50 yards due to

5 penalties If the team lost the same number of

yards for each penalty what was the change in field

position for each penalty

25 Sample answer a = - 20 and b = 5 less than

-20 divide 5 = -4 and -20 times 5 = -100

-100 lt -4

26 True if the integers have the same sign the product

and quotient are positive if they have different signs

negative

27 False division by 0 is undefined for any dividend


28 a 100 divide 25 = 4 4 points

b -16 divide ( -4 ) = 4 Fred answered 4 questions

incorrectly

29 a divide ( -3 ) = 8

a = -24

8 divide b = -4

a divide b = -24 divide ( -2 ) = 12


30 Dividing integers with the same sign results in a

positive number Since the original two integers are

negative the quotient is greater than both of these

integers

LESSON 23

Your Turn

1 Reggie earned 110 points

3 ( -30 ) + 200 = -90 + 200

= 110

2 -6 ( 13 ) - 21 = -78 - 21

= -99

4 ( -12 ) divide 6 + 2 = -2 + 2

= 0

5 -87 divide ( -3 ) -9 = 29 - 9

= 20

6 40 divide ( -5 ) + 30 = -8 + 30

= 22

7 -39 divide 3 -15 = -13 - 15

= -28

8 Amber moved 3 ( -3 ) + 5 = -4 or 4 places back

Will moved 2 ( -4 ) + 3 = -5 or 5 places back Will

moved further back

9 ( -10 ) divide 2 - 2 = -5 - 2 = -7

( -28 ) divide 4 + 1 = -7 + 1 = -6

10 42 divide ( -3 ) + 9 = -14 + 9 = -5

( -36 ) divide 9 - 2 = -4 - 2 = -6

Guided Practice

1 -6 ( -5 ) + 12 = 30 + 12

= 42

2 3 ( -6 ) - 3 = -18 - 3

= -21

3 -2 ( 8 ) + 7 = -16 + 7

= -9

4 4 ( -13 ) + 20 = -52 + 20

= -32

5 -4 ( 0 ) - 4 = 0 - 4

= -4

6 -3 ( -5 ) - 16 = 15 - 16

= -1

7 7 ( -5 ) + 20 = -35 + 20

= -15

15 dollars less

8 7 ( -10 ) + ( -100 ) = -70 + ( -100 )

= -170

170 fewer points

9 6 ( -4 ) + 10 = -24 + 10

= -14

Ned lost 14 points

10 4 ( -12 ) + 10 = -48 + 10

= -38

$38 less

11 -3 ( -2 ) + 3 = 6 + 3

= 9

3 ( -4 ) + 9 = -12 + 9

= -3

9 gt -3

-3 ( -2 ) + 3 gt 3 ( -4 ) + 9

12 -8 ( -2 ) -20 = 16 -20

= -4

3 ( -2 ) + 2 = - 6 + 2

= -4

-4 = -4

-8 ( -2 ) -20 = 3 ( -2 ) + 2

13 -7 ( 5 ) - 9 = -35 - 9

= -44

-3 ( 20 ) + 10 = -60 + 10

= -50

-44 gt -50

-7 ( 5 ) -9 gt -3 ( 20 ) + 10

14 -16 ( 0 ) -3 = 0 -3

= -3

-8 ( -2 ) -3 = 16 -3

= 13

-3 lt 13

-16 ( 0 ) -3 lt -8 ( -2 ) -3

15 A negative number usually represents a debt

payment or loss or a change that is a decrease

such as to a savings account


16 -12 ( -3 ) + 7 = 36 + 7

= 43

17 -42 divide ( -6 ) + 5 -8 = 7 + 5 -8

= 12 -8

= 4

18 10 ( -60 ) -18 = -600 -18

= -618

19 ( -11 ) ( -7 ) + 5 - 82 = 77 + 5 - 82

= 82 - 82

= 0

20 35 divide ( -7 ) + 6 = -5 + 6

= 1

21 -13 ( -2 ) - 16 - 8 = 26 - 16 - 8

= 10 - 8

= 2

22 a 5 ( 2 ) -12 + 3 = 10 -12 + 3

= -2 + 3

= 1

b -3 ( 2 ) -1 + 6 + 7 = -6 -1 + 6 + 7

= -7 + 6 + 7

= -1 + 7

= 6

c Rose has more points than Lily so Rose won

the game

23 5 ( -4 ) -8 = -20 - 8 = -28

24 -36 divide ( -4 ) + 9 = 9 + 9 = 18


25 a 4 ( -35 ) -9 = -140 -9

= -149

$149 less

b Yes $200 - $149 = $51 $51 gt $50 so Arleen

has enough money

26 a 2 ( -10 ) + 3 = -20 + 3= -17

b 7 + 2 + ( -7 ) = 2

c Warren since 2 is greater than -17

d Sample answer 2 of clubs 2 of spades

3 of spades king of diamonds 10 of clubs

7 of clubs


27 Sample answer Ann bought three shirts for $7 each

and a pair of pants for $10 Her mother gave her

$25 By how much did the amount of money Ann

had change

28 Disagree the quotient of two integers is positive if

the integers have the same sign So the first two

integers could have been negative integers

29 5 feet equals 60 inches so Lisa is holding the rock

60 inches above the waterrsquos surface The rock will

travel 4 times -5 = -20 inches or 20 inches below the

surface in 4 seconds 60 + 20 = 80 inches

MODULE 2

Ready to Go On


will be negative

( -2 ) ( 3 ) = -6


will be positive

( -5 ) ( -7 ) = 35

3 Since the numbers have the opposite signs the

product will be negative

( 8 ) ( -11 ) = -88

4 ( -3 ) ( 2 ) ( -2 ) = ( -6 ) ( -2 ) = 12

5 5 ( -3 ) = -15 -15degC

6 -63 ____ 7 = -9

7 -15 ____ -3

= 5

8 0 ____ -15

= 0

9 96 ____ -12

= -8

10 -24 divide 6 = -4 -4 Ib

11 ( -4 ) ( 5 ) + 8 = -20 + 8

= -12

12 ( -3 ) ( -6 ) -7 = 18 -7

= 11

13 -27 ____ 9 - 11 = -3 - 11

= -14

14 -24 ____ -3

- ( -2 ) = 8 + 2

= 10

15 Sample answer Maurice lost 3 nickels in the laundry

and found 1 dime in the couch By how much did the

amount of money he had change

( -3 ) ( 5 ) + 10 = -15 + 10 = -5 He had $05 less

than before


MODULE 3 Rational Numbers

Are You Ready

1 9 ___ 14

times 7 __ 6 =

3

2

9 ___ 14

times 7 __ 6 1

2

= 3 __ 4

2 3 __ 5 times 4 __

7 = 12 ___

35

3 11 ___ 8

times 10 ___ 33

= 1

4

11 ___ 8 times 10 ___

33 5

3

= 5 ___ 12

4 4 __ 9 times 3 =

3

4 __ 9 times 3 __

1 1

= 4 __ 3 or 1 1 __

3

5 1 __ 2 divide 1 __

4 = 1 __

2 times 4 __

1

=

1 1 __ 2 times 4 __

1 2

= 2 __ 1 = 2

6 3 __ 8 divide 13 ___

16 = 3 __

8 times 16 ___

13

= 1 3 __ 8 times 16 ___

13 2

= 6 ___ 13

7 2 __ 5 divide 14 ___

15 = 2 __

5 times 15 ___

14

= 1

1 2 __ 5 times 15 ___

14 3

7

= 3 __ 7

8 4 __ 9 divide 16 ___

27 = 4 __

9 times 27 ___

16

= 1

1 4 __ 9 times 27 ___

16 3

4

= 3 __ 4

9 3 __ 5 divide 5 __

6 = 3 __

5 times 6 __

5

= 18 ___ 25

10 1 __ 4 divide 23 ___

24 = 1 __

4 times 24 ___

23

= 1 1 __ 4 times 24 ___

23 6

= 6 ___ 23

11 6 divide 3 __ 5 = 6 __

1 times 5 __

3

= 2

6 __ 1 times 5 __

3 1

= 10 ___ 1 = 10

12 4 __ 5 divide 10 = 4 __

5 times 1 ___

10

= 2

4 __ 5 times 1 ___

10 5

= 2 ___ 25

13 21 - 6 divide 3

21 - 2

19

14 18 + ( 7 - 4 ) times 3

18 + 3 times 3

18 + 9

27

15 5 + ( 8 - 3 ) 2

5 + ( 5 ) 2

5 + 25

30

16 9 + 18 divide 3 + 10

9 + 6 + 10

15 + 10

25

17 60 - ( 3 - 1 ) 4 times 3

60 - ( 2 ) 4 times 3

60 - 16 times 3

60 - 48

12

18 10 - 16 divide 4 times 2 + 6

10 - 4 times 2 + 6

10 - 8 + 6

2 + 6

8

LESSON 31

Your Turn

0 _

571428

4 7 ⟌ _

40000000 Dividing into 40

_ -35

50

_ -49

10

_ -7

30

_ -28

20

_ -14

60

_ -56

40 Second appearance of 40

Because the number 40 repeats during the division

process the answer is a repeating decimal

-0 _

571428 or -0571428571428hellip


0 _ 3

5 3 ⟌ _


_ -3



process the answer is a repeating decimal 0 _ 3 or

0333hellip

045

6 20 ⟌ _

900

_ -8 0

1 00

_ -1 00

0

-045

7 -2 3 __ 4 = -thinsp 4 times 2 + 3

_________ 4 = -11 ____

4

275

4 ⟌ _

1100

_ -8

30

_ -28

20

_ -20

0

-275 terminating

8 7 1 __ 3 =

3 times 7 + 1 _________

3 = 22 ___

3

7 _ 3

3 ⟌ _


_ -21

1 0 Second appearance of 10



7333hellip repeating

Guided Practice

06

1 5 ⟌ _

30

_ -3 0

0

06 terminating

089

2 100 ⟌ _

8900

_ -80 0

9 00

_ -9 00

0

-089 terminating

3 Simplify the fraction

4 ___ 12

= 4 times 1 _____ 4 times 3

= 1 __ 3

0 _ 3

3 ⟌ _


_ -3





0 _

25

4 99 ⟌ _


_ -19 8

520

_ -495



process the answer is a repeating decimal 0 _

25 or


0 _ 7

5 9 ⟌ _


_ -63




-0777hellip repeating

036

6 25 ⟌ _

900

_ -7 5

1 50

_ -1 50

0

-036 terminating

004

7 25 ⟌ _

100

_ -1 00

0

004 terminating

01420 _

45

8 176 ⟌ _

250000000

_ -17 6

7 40

_ -7 04

360

_ -352

80

_ -0

800 First appearance of 800

_ -704

960

_ -880


Because the number 800 repeats during the

division process the answer is a repeating decimal

-01420 _

45 or -014204545hellip repeating

0012

9 1000 ⟌ _

12000

_ -10 00

2 000

_ -2 000

0

0012 terminating


10 -11 1 __ 6 = -thinsp 6 times 11 + 1

_________ 6 = -67 ____

6

111 _ 6

6 ⟌ _

67000

_ -6

07

_ -6

1 0

_ -6


_ -36




- 67 ___ 6

-111 _ 6 or -111666hellip

11 2 9 ___ 10

= 10 times 2 + 9

__________ 10

= 29 ___ 10

29

10 ⟌ _

290

_ -20

9 0

_ -9 0

0

29 ___ 10

29

12 -8 23 ____ 100

= - 100 times 8 + 23

____________ 100

= -823 _____ 100

823

100 ⟌ _

82300

_ -800

23 0

_ -20 0

3 00

_ -3 00

0

-823 _____ 100

-823

13 7 3 ___ 15

= 15 times 7 + 3

__________ 15

= 108 ____ 15

72

15 ⟌ _

1080

_ -105

3 0

_ -3 0

0

108 ____ 15

72

14 54 3 ___ 11

= 11 times 54 + 3

__________ 11

= 597 ____ 11

54 _

27

11 ⟌ _

597000

_ -55

47

_ -44


_ -22

80

_ -77




597 ____ 11

54 _

27 or 542727hellip

15 -3 1 ___ 18

= -thinsp 18 times 3 + 1 __________

18 = -55 ____

18

30 _ 5

18 ⟌ _

55000

_ -54

1 0

_ -0

1 00 First appearance of 100

_ -90




-55 ____ 18

-30 _ 5 or -30555hellip

16 3 2 __ 3 =

3 times 3 + 2 _________

3 = 11 ___

3

3 _ 6

3 ⟌ _

1100

_ -9


_ -1 8




3 _ 6 or 3666hellip lbs of apples

17 -2 7 __ 8 = -

8 times 2 + 7 _________

8 = -23 ____

8

2875

8 ⟌ _

23000

_ -16

7 0

_ -6 4

60

_ -56

40

_ -40

0

-2875 lb

18 Disagree the definition of a rational number is a

number that can be written as the ratio of two

integers with a denominator not equal to zero and

3 ___ 47

is a well-defined ratio of two integers Tom did

not divide long enough to correctly determine that

the quotient is a repeating decimal



19 basketball players

_______________ football players

= 5 ___ 11

0 _

45

11 ⟌ _


_ -4 4

60

_ -55




5 ___ 11

0 _

45 or 04545hellip repeating

20 hockey players

______________ lacrosse players

= 6 ___ 10

06

10 ⟌ _

60

_ -6 0

0

6 ___ 10

06 terminating

21 polo players

_____________ football players

= 4 ___ 11

036

11 ⟌ _


_ -3 3

70

_ -66




4 ___ 11

0 _


22 lacrosse players

______________ rugby players

= 10 ___ 15

= 5 times 2 _____ 5 times 3

= 2 __ 3

0 _ 6

3 ⟌ _


_ -1 8

20 Second appearances of 20



10 ___ 15

0 _ 6 or 0666hellip repeating

23 football players

_____________ soccer players

= 11 ___ 11

= 1

11 ___ 11

1 terminating

24 Agree Sample answer There are 10 players on the

lacrosse team and dividing the number of any other

team by 10 will simply move the decimal point one

digit to the left Therefore the ratio of any team over

the lacrosse team will be a decimal that terminates

one place to the right of the decimal point

25 a -4 7 __ 8 = -thinsp 8 times 4 + 7

_________ 8 = - 39 ___

8

b 4875

8 ⟌ _

39000

_ -32

7 0

_ -6 4

60

_ -56

40

_ -40

0

-4875

c Sample answer 4 7 __ 8 is very close to 5 Therefore

You could estimate that the water level changes

by 5 inches per month The total change in the

water level at the end of the 3-month period

would be approximately -15 inches

26 integer terminating

27 Ben is taller because Benrsquos height of 5 5 ___ 16

is equal

to 85 ___ 16

or 53125 ft while Marcusrsquo height of 5 7 ___ 24

is

equal to 127 ____ 24

or 52916hellip ft

28 The first store has the better deal because they

offer 3 __ 4 or 075 of a bushel for $9 while the second

store offers only 2 __ 3 or 0666hellip of a bushel for $9


29 When the number 1 is the denominator in a fraction

its decimal form is simply the numerator In all other

cases concerning numbers 1 to 10 the division

process stops when either the remainder is 0 or

when the digits begin to repeat When the numbers

2 4 5 or 8 are in the denominator the decimal form

of a fraction will terminate When the numbers


of a fraction will be a repeating decimal

30 Julie made a higher score on her math test since

her math test score of 21 ___ 23

is equal to a repeating

decimal of approximately 0913 while her science

test score of 29 ___ 32

is equal to a terminating decimal of

090625

Sample answer The difference in scores cannot be

determined by simply comparing the numerators of

the two fractions because the denominators are not

the same For Julie to compare her scores she

needs to divide the denominators into their respec-

tive numerators until one of the quotients is found to

be greater than the other

31 No although the digits in the decimal appear to

follow a pattern a repeating decimal must have the

same combination of digits that repeat such as

0121212hellip


LESSON 32

Your Turn

2

50 1 2 3 4

3 + 1 1 __ 2 = 4 1 __

2

3

0-7 -6 -5 -4 -3 -2 -1

-25 + ( -45 ) = -7

6

0 1 2-5-6-7-8 -4 -3-2-1

-8 + 5 = -3

7

10-1

1 __ 2 + ( - 3 __

4 ) = - 1 __

4

8

3 4 5 6 7 80 1 2-3-2-1

-1 + 7 = 6

9

3 4 50 1 2-5-4 -3-2-1

2 1 __ 2 + ( -2 1 __

2 ) = 0

10

3 4 50 1 2-5-4 -3-2-1

-45 + 45 = 0

11

1-1 0

3 __ 4 + ( - 3 __

4 ) = 0

The overall change is 0 cups

12 -15 + 35 + 2

-15 + 55

55 - 15

4

13 3 1 __ 4 + ( -2 ) + ( -2 1 __

4 )

3 1 __ 4 + ( -4 1 __

4 )

3 1 __ 4 - 4 1 __

4

-1

14 -275 + ( 325 ) + 5

-6 + 5

-1

15 15 + 8 + ( -3 )

23 + 3

20

Guided Practice

1

3 4 50 1 2-5-4 -3-2-1

-3 + ( -15 ) = -45

2

0 54321-5-4-3-2-1

15 + 35 = 5

3

0 105-1 -05

1 __ 4 + 1 __

2 = 3 __

4

4

0 54321-5-4-3-2-1

-1 1 __ 2 + ( -1 1 __

2 ) = -3

5

0 54321-5-4-3-2-1

3 + ( -5 ) = -2

6

0 54321-5-4-3-2-1

-15 + 4 = 25

7 -2150 + 2150 = 0 $0

8 -874 + 874 = 0 $0

9 275 + ( -2 ) + ( -525 )

275 + ( -725 )

- ( 725 - 275 )

-45

10 -3 + 1 1 __ 2 + 2 1 __

2 = -3 + 4 = 1

11 124 + 92 + 1

-124 + 102

- ( 124 - 102 )

-22

12 -12 + 8 +13

-12 + 21

21 - 12

9

13 45 + ( -12 ) + ( -45 )

45 + ( -45 ) + ( -12 )

0 + ( -12 )

-12

14 1 __ 4 + ( - 3 __

4 ) = - ( 3 __

4 - 1 __

4 ) = - 2 __

4 = - 1 __

2


15 -4 1 __ 2 + 2 = - ( 4 1 __

2 - 2 ) = -2 1 __

2

16 -8 + ( -1 1 __ 8 ) = -9 1 __

8

17 Start at -4 and move 6 units to the right

The sum is 2


18 The opposite of +19 is -19

19 -$225 + $1500 = $1500 - $225 = $1275

20 -3525 m + ( -85 ) = -4375 m

21 4 3 __ 4 mi + ( -3 1 __

4 mi ) = 1 2 __

4 mi = 1 1 __

2 mi

22 1635 m + ( -05 m ) = 163 m above sea level

23 30 + 15 - 25 = 45 - 25 = 20 pts

24 January

Income - Expenses

$1205 - $129060

- ( $129060 - $1205 ) -$8560

February

Income - Expenses

$1183 - $134544

-($134544 - $1183)

-$16244

Kameh lost $8560 in January and $16244 in

February

25 June

Income - Expenses

$2413 - $210623

$30677

July

Income - Expenses

$2260 - $195850

$30150

August

Income - Expenses

$2183 - $184512

$33788

Kameh gained $30677 in June $30150 in July and

$33788 in August

26 First sum all the values in the Income column Then

sum all the values in the Expenses column Subtract

the total expenses from the total income Finally add

the $250 profit from December (not shown in the

table) to find the total profit or loss of the bakery by

the end of August

Income = $1205 + $1183 + $1664 + $2413

$2260 + $2183 = $10908

Expenses = $129060 + $134544 + $1664 +$210623 + $195850 + $184512

= $1020989

Profit = $10908 - $1020989 + $250

= $94811

27 -2 is the opposite or additive inverse of 2

28 a 7 ( 10 ) + 3 ( -15 ) = 70 - 45 = 25 pts

b 2 ( 10 ) + 8 ( -15 ) = 20 - 120 = -100 pts

c 10 + 10 + 10 + 10 + 10 + ( ndash15 ) + ( ndash15 ) + ( ndash15 ) +

( ndash15 ) + ( ndash15 ) or 5 ( 10 ) + 5 ( ndash15 )


29 The sum of two negative rational numbers is always

negative The sum of a negative rational number and

a positive rational number is negative if the absolute

value of the negative number is greater than that of

the positive number

30 Sample answer The student might have subtracted

the absolute values of the numbers

31 Yes 55 and -55 are opposites and -23 and 23

are opposites so the expression [ 55 + ( -23 ) ] +

( -55 + 23 ) can be viewed as the sum of two

opposites which is always 0

LESSON 33

Your Turn

1

-9 -8 -7 -6 -5 -4

-65 - 2 = -85

2

42 30-1 1

1 1 __ 2 - 2 = - 1 __

2

3

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0

-225 - 55 = -775

6

1 2-1 0

025 - ( -150 ) = 175

7

1-1 0

- 1 __ 2 - ( - 3 __

4 ) = 1 __

4

Guided Practice

1

1312111098765 14 15

5 - ( -8 ) = 13

2

-9 -8 -7 -6 -5 -4 -3

3 1 __ 2 - 4 1 __

2 = -8


3

-15 -13 -11 -9 -5-7

-7 - 4 = -11

4

-6 -5 -4 -3 -2 -1 0 1

-05 - 35 = -4

5 -14 - 22 = -36

6 -125 - ( -48 )

-125 + 48

- ( 125 - 48 )

-77

7 1 __ 3 - ( - 2 __

3 ) = 1 __

3 + 2 __

3 = 1

8 65 - ( -14 ) = 65 + 14 = 79

9 - 2 __ 9

- ( -3 )

- 2 __ 9

+ 3

3 - 2 __ 9

2 9 __ 9 - 2 __

9

2 7 __ 9

10 24 3 __ 8

- ( -54 1 __ 8 )

24 3 __ 8

+ 54 1 __ 8

78 4 __ 8

78 1 __ 2

11 -1 m + ( 105 m ) = -15 m

15 m below sea level

12 -12 1 __ 2 + ( -5 ) = -17 1 __

2

17 1 __ 2

or 175 yards

13 Change in height = Starting height - ending height

533 ft - ( -10 ft ) = 533 ft + 10 ft = 543 ft

14 -4500 + (-3015) = -7515 $7515

15 Explain that she is supposed to start at positive 4 on

the number line then move 12 places to the left

because she is subtracting a positive number She

will end on the number -8 which is the answer


16 -126degC - 75degC = -201degC

17 -2565 ft - 165 ft + 1245 ft = -297 ft

The diver is 297 ft below the surface

18 -9500 ft - ( -26000 ft ) = 16500 ft

19 29035 ft - ( -36198 ft ) = 65233 ft

70000 ft - ( -26000 ft ) = 96000 ft

Mars has the greater difference by

96000 ft - ( 65233 ft ) = 30767 ft

20 a -5degF + 78degF - 32degF

b 78degF - 32degF

c -5degF + 78degF - 32degF 78degF - 5degF - 32degF 78degF - 37degF = 41degF 78degF - 32degF = 46degF

21 a -$1258 + ( -$3072 ) = -$4330

b -$4330 + ( -$25 ) = -$6830

c $6830 since -$6830 + $6830 = 0

22 a No 4 times 52 in = 208 in

b 208 in - 20 in = 08 in more needed

23 a 5 ft - 72 ft + 22 ft

b 5 ft - 72 ft + 22 ft

5 ft + 22 ft - 72 ft

72 ft - 72 ft

= 0 ft because he moved the same distance

backward and forward

24 a Yes

$425 + $089 + $1099

= $1613 lt $20

b $20 - $1613 = $387 left over


25 The Commutative Property of Addition (CPA) could

be used to simplify the two terms that already have

a common denominator first

- 7 ___ 16

- 1 __ 4 - 5 ___

16 = ( - 7 ___

16 ) + ( - 1 __

4 ) + ( - 5 ___

16 )

( - 7 ___ 16

) + ( - 5 ___ 16

) + ( - 1 __ 4 ) by CPA

( -7 + ( -5 ) __________

16 ) + ( - 1 __

4 )

( -12 ____ 16

) + ( - 1 __ 4 )

( - 4 times 3 _____ 4 times 4

) + ( - 1 __ 4 )

( - 3 __ 4 ) + ( - 1 __

4 )

( -3 + ( -1 ) __________

4 )

( -4 ___ 4 ) = -1

26 Lowest -225degF + ( -12degF ) = -345degFHighest -195degF + ( -12degF ) = -315degF

27 Sample answer Yes because both numbers are

rational numbers each can be written as the ratio of

two integers for example a __ b

and c __ d

Both fractions

could be given a common denominator and then

one could then be subtracted from the other The

result would be a fraction which is a rational number

28 No Sample answer It is possible for the

difference of two negative numbers to be negative

[ -4 - ( -1 ) = -3 ] but it is also possible for the

difference to be positive [ -5 - ( -8 ) = 3 ]


LESSON 34

Your Turn

1

-8 -7 -6 -5 -2 -1 0-4 -3

2 ( -35 ) = -7

2

-2 -1 0 1 2 3 4-4 -3

-3 ( -125 ) = 375

4 ( - 3 __ 4 ) ( - 4 __

7 ) ( - 2 __

3 ) = -

13 times 41 times 2 __________ 14 times 7 times 31

= - 1 times 1 times 2 _________ 1 times 7 times 1

= - 2 __ 7

5 ( - 2 __ 3 ) ( - 3 __

4 ) ( 4 __

5 ) = 2 times 31 times 41

__________ 13 times 41 times 5

= 2 times 1 times 1 _________ 1 times 1 times 5

= 2 __ 5

6 ( 2 __ 3 ) ( - 9 ___

10 ) ( 5 __

6 ) = -

12 times 93 times 51

____________ 13 times 210 times 63

= - 1 times 31 times 1 __________ 1 times 2 times 31

= - 1 __ 2

Guided Practice

1

-5 -2 -1 0-4 -3

5 ( - 2 __ 3 ) = 5 __

1 times ( - 2 __

3 )

= - 5 times 2 _____ 1 times 3

= - 10 ___ 3

= -3 1 __ 3

2

-1 -05 0-2 -15

3 ( - 1 __ 4 ) = 3 __

1 times - 1 __

4

= - 3 times 1 _____ 1 times 4

= - 3 __ 4

3

0 1 2-2 -1

-3 ( - 4 __ 7 ) = 3 __

1 times 4 __

7

= 3 times 4 _____ 1 times 7

= 12 ___ 7

= 1 5 __ 7

4

-2 -1 0 1 2 3 4-4 -3

- 3 __ 4 ( -4 ) = 3 __

4 times 4 __

1

= 3 times 41

______ 14 times 1

= 3 times 1 _____ 1 times 1

= 3 __ 1

= 3

5 4 ( -3 ) = -12

6 -18 ( 5 ) = -9

7 -2 ( -34 ) = 68

8 054 ( 8 ) = 432

9 -5 ( -12 ) = 6

10 -24 ( 3 ) = -72

11 1 __ 2 times 2 __

3 times 3 __

4 = ( 1 times 21

______ 12 times 3

) ( 3 __ 4 )

= ( 1 __ 3 ) ( 3 __

4 )

= 1

1 __ 3 times 3 __

4 1

= 1 __ 4

12 - 4 __ 7 ( -thinsp 3 __

5 ) ( - 7 __

3 ) = ( - 4 times 3 _____

7 times 5 ) ( - 7 __

3 )

= 12 ___ 35

( - 7 __ 3 )

= - 4

5 12 times 7 ______ 35 times 3

1

1

= - 4 times 1 _____ 5 times 1

= - 4 __ 5

13 ( - 1 __ 8 ) times 5 times 2 __

3 = ( - 1 __

8 ) times 5 __

1 times 2 __

3

= - 1 times 5 times 21

__________ 48 times 1 times 3


= - 5 ___ 12


14 ( - 2 __ 3

) ( 1 __ 2 ) ( - 6 __


__________ 13 times 21 times 7


= 2 __ 7

15 4 ( -350 ) = -14 or a $14 change in price

16 18 ( -100 ) = -1800 or a $1800 change

17 Sample answer Count the number of times there is

a negative sign If there are an even number of

negative signs then the final product will be positive

If there is an odd number of negative signs then the

final product will be negative


18 a 6 ( -1998 ) Note that the change in her bank

account balance does not depend on the initial

amount

b 200 + 6 ( -1998 )

= 200 - 11988

= 8012 $8012

19 Sample answer Start at 0 then move 15 units to

the left (because 15 is negative in this case) 4 times

You are now on -6 Then because 4 is negative in

this case we want to move to the opposite of -6

which is 6

20 8 ( -3 1 __ 4 ) = -8 ( 13 ___

4 )

= - 1

8 __ 1 times 13 ___

4 1

= - 2 times 13 ______ 1 times 1

= - 26 ___ 1

-26 min At the same rate the watch will be

26 minutes behind after 8 weeks

21 3 ( -325 ) = -975 ft The change in depth is -975 ft

Therefore the submarine will be 975 below sea level

(below the surface)

22 5 + ( -3 ) ( 15 )

= 5 + ( -45 )

= 05 cups left

23 Matthew is incorrect Sample answer Matthew

should have said that multiplying by two negatives

is like multiplying the opposite of a positive twice

The opposite of a positive twice brings you back to

a positive

24 5 ( -15 ) = -75 min Therefore she will be late by

75 minutes or 1 hour and 15 minutes

25 Total score is

2 times ( 6 ) + 16 times ( 05 )

+ 7 times ( -05 ) + 2 times ( -15 )

= 12 + 8 - 35 - 3

= 20 - 65

= 135 pts


26 Temperature at 5 kilometers

= Temp at ground level + change in temp

= 12 + 5 ( -68 )

= 12 + ( -34 )

= -22degC

27 a b c d

+ + + +

+ + - +

+ - + +

- + + +

- - - +

- - + -

- + - -

+ - - -

28 If the product of two numbers is positive then the two

numbers must have the same sign either they are

both positive or both negative If the sum is negative

then at least one of the numbers must be negative

Therefore the two integers that add to -7 and multiply

to 12 must both be negative The negative paired

factors of 12 are -1 and -12 -2 and -6 and -3

and -4 Of those choices only -3 and -4 add to -7

LESSON 35

Your Turn

3 28 ___ -4

= - 28 ___ 4 = -07

4 -664 ______ -04

= 664 ____ 04

= 166

5 - 55 ___ 05

= - 55 ___ 5 = -11

6 -4256 _______ 112

= -38

The divers change in elevation was -38 feet

per minute

7 - 5 __

8 ___

- 6 __ 7 = - 5 __

8 divide - 6 __

7

= - 5 __ 8 times - 7 __

6

= 35 ___ 48

8 - 5 ___

12 ____

2 __ 3 = - 5 ___

12 divide 2 __

3

= - 5 ___ 12

times 3 __ 2

= - 15 ___ 24

= - 5 __ 8


9 -4__5

___1__2 =-4__5divide1__

2

=-4__5times2__1

=-8__5

=-13__5

Guided Practice

1 072_____-09=-72___

9 =-08

2 -1__5

___7__5 =-1__

15times5

1__

7=-1times1_____

1times7=-1__7

3 56___-7=-56___7=-8

4 251____4 divide(-3__

8)=251____

4 times-8__

3

=-251times82________

14times3

=-251times2_______1times3

=-502____3

5 75____-1__5

=-75___1times5__

1=-75times5______

1times1=-375

6 -91____-13=91___

13=7

7 -3__7

___9__4 =-

13__7times4__93

=-1times4_____7times3

=-4___21

8 - 12____003

=-1200_____

3 =-400

9 =changeinwaterlevel_________________

changeindays

=-35L______4day

=-0875 L____day

or-0875Lperday

10 =totalchangeinprice_________________

changeindays

=-$4575________5day

=-$915perdayonaverage

11 totalchangeinaltitude___________________

numberofminutes

=-044mi________08min

=-44mi______8min

=-055mileperminute

12 FirstfindthesignofthenumeratorwhichisnegativeNextfindthesignofthedenominatorwhichisnegativeThereforethequotientwillbepositivebecausethenumeratoranddenominatorbothhavethesamesign


13 5___-2__

8=-5__

1times8__

24

1=-5times4_____

1times1=-20

14 51__3divide(-11__

2)

=-3times5+1_________3 divide2times1+1_________

2

=-16___3divide3__

2

=-16___3times2__

3

=-16times2______3times3

=-32___9

15 -120_____-6 =120____

6 =20

16 -4__5

___-2__

3=

24__5times3__

21=2times3_____

5times1=6__

5

17 103divide(-103)=-103____1 times 1____

103

=-103times1________1times103

=-103____103

=-103____103

=-01

18 -04_____80

=-04___80

=-0005

19 1divide9__5=1__

1times5__

9=5__

9

20 -1___4 ___

23___24

=-1__

14times246

___23


=-6___23

21 -1035_______-23 =1035_____

23 =45

22 totalhours_____________numberofdays

= 21h______7days

=3 h____day

totaltimelost3 h____day

times3days=9hours

Alexusuallyruns21hoursperweeksodivideby7tofindthatheruns3hoursperdaySinceheisunabletorunfor3dayshistimeisdecreasedby9hoursor-9

23 totalchangeinyards

_________________numberofruns

=-4times15+3___________4 times1__

9

yd___run

=-763___4 times1__

91yd

___run

=-153__

4yd______

9runs

=-153__4times1__

9

yd___run

=-7__4or-13__

4yardsperrun



7_MCABESK207233_U1M03indd 19 103113 759 PM

24 -121degC + ( -78degC ) + ( -143degC ) + ( -72degC )

_____________________________________ 4

= 414degC ______ 4

= -1035degC per day

25 a total profit

_____________ number of days

= $1750

______ 7 days

= $250 per day

b $150

_____ day

times 7 days = $1050

c total change


= - $490

______ 7 days

= -$70 per day

26 total meters descended ___________________ number of seconds

= 996 m ______ 12 s

= 83 ms

27 When converting the division equation into a

multiplication problem he forgot to multiply by the

reciprocal and instead multiplied by the fraction in

the denominator The correct answer is given by

- 3 __

4 ___

4 __ 3

= - 3 __

4 times 3 __

4 = - 9 ___

16

28 -37 m _______ year times ( 2012 ndash 1995 ) years

= -37 m _______ year times 17 years

= -629 m


29 Sample answer The average change in temperature

per day would be given by -85 divide 15 if the

temperature were to drop of 85degF over 15 days

-85degF divide 15 d

= - 1785 ____ 315

degF __ d

= - 17 ___ 3 degF __

d or -5 2 __

3 degF __

d asymp -567 degF __

d

On average the temperature changed by -567degF

every day

30 Yes By definition the result of dividing an integer by

a non-zero integer is a rational number

31 Yes The result of dividing an integer by a non-zero

integer always results in a rational number by

definition

LESSON 36

Your Turn

1 Find the total commercial time

3 times 2 1 __ 2 = 7 1 __

2

Find the total entertainment time

30 - 7 1 __ 2 = 22 1 __

2

Find the length of each entertainment segment

22 1 __ 2 divide 4 = 5 5 __

8

Each entertainment segment is 5 5 __ 8 minutes long

2 Find the number of cups of sugar in the bag

454 divide 48 asymp 95

Find the number of 3 __ 4 -cup portions in the bag


12 batches can be made from the bag of sugar

Find the cost of 1 batch


The cost of the sugar is $029 per batch

3 Convert the percent to a decimal

12 3 __ 5 = 126

= 0126

Find the worth after 1 year

750 times 0126 = 945

750 + 945 = 8445

Find the worth after 2 years

8445 times 0126 asymp 10641

8445 + 10641 = 95091


95091 times 0126 asymp 11981

95091 + 11981 = 107072

The stock is worth $107072

Guided Practice

1 45h times 3 1 __ 5 or 32 miles per hour = 144 miles

144 miles divide 3 3 __ 5 or 36 miles per hour = 4 hours

2 2568 inches times -002375 asymp -061 inches

2568 inches - 061 asymp 2507 inches

3 Sample answer Using a calculator to solve a

problem that involves complicated arithmetic can

help you avoid errors It can also help you to check

solutions to any problems you solved by hand


4 Find the total weight

78 times 3 = 234

Find the weight each climber carries

234 divide 4 = 585

Each climber carries 585 kg


5 Find the available width on the page

12 - 3 1 __ 2 = 8 1 __

2

Find half the width

8 1 __ 2 divide 2 = 4 1 __

4

He should put the picture 4 1 __ 4 inches from each side

of the page

6 Find the amount of cereal needed for all the children

11 times 1 __ 3 = 3 2 __

3

10 times 3 __ 4 = 7 1 __

2

3 2 __ 3 + 7 1 __

2 = 11 1 __

6

Compare the total needed with the amount in the

box

11 1 __ 6 lt 12

Yes there is enough Oaties for all the children The

amount needed is 11 1 __ 6 cups and that is less than the

amount in the box 12 cups

7 Find half of the distance that the referee walked

41 3 __ 4 divide 2 = 20 7 __

8

Find how far that distance is from the goal line

50 - 20 7 __ 8 = 29 1 __

8

The referee is 29 1 __ 8 feet from the nearest goal line

8 Donovanrsquos score was 39 ___ 50

= 78 Marcirsquos score was

( 78 + 10 ) = 88

9 Find the number Marci answered correctly

88 = 88 ____ 100

= 44 ___ 50

Find how many more that Marci answered than

Donovan

44 - 39 = 5

Marcie answered 5 more questions correctly than

Donovan

10 Sample answer Donovan got about 40 out of 50

questions right or about 80 Since Marci scored

10 more that is about 90 90 times 50 is 45 So

Marci answered about 45 - 40 or 5 more questions

correctly than Donovan

11 Yes -075 is a reasonable estimate

19 ___ 37

is about 1 __ 2 and 143 is about 15 and

15 times ( - 1 __ 2 ) = -075

12 Sample answer approximately -07343 Use a

calculator Divide -19 by 37 multiply the quotient by

143 then round the product

13 Sample answer Yes -07343 asymp - 075


14 Find the time of the descent

-79 9 ___ 10

divide ( -188 ) = 425

Find the time for the ascent

19 1 __ 8 - 1275 - 425 = 2 1 __

8

Find the distance of the ascent

-28 9 ___ 10

- ( -79 9 ___ 10

) = 51

Find the rate of the ascent

51 divide 2 1 __ 8 = 24

The diverrsquos rate of change in elevation during the

ascent was 24 ftmin

15 Sample answer

(1) Convert the mixed number 27 3 __ 5 to the decimal

276 find the sum of 276 and 159 then multiply

the result by 037


276 Then use the Distributive Property so that

(276 + 159)037 = (276)(037) + (159)(037)

Multiply both 276 and 159 by 037 and add the

products I would use the first method because

there are fewer steps and so fewer chances to

make errors

16 Sample answer You need to know how many

gallons of paint you need to paint a wall Measure

the length and width of the wall with a yardstick

then find the area Use the calculator to divide the

area by the number of square feet a gallon of the

paint covers Round up rather than down to the

nearest gallon so you have enough paint

MODULE 3

Ready to Go On

1 4 1 __ 5 =

5 times 4 + 1 _________

5 = 21 ___

5

42

5 ⟌ _

210

_ -20

1 0

_ -1 0

0

42


2 12 14 ___ 15

= 15 times 12 + 14

___________ 15

= 194 ____ 15

129 _ 3

15 ⟌ _

194000

_ -15

44

_ -30

14 0

_ -13 5

50 first 50

_ -45

50 second 50



129 _ 3 or 12933

3 5 5 ___ 32

= 32 times 5 + 5

__________ 32

= 165 ____ 32

515625

32 ⟌ _

16500000

_ -160

5 0

_ -3 2

1 80

_ -1 60

200

_ -192

80

_ -64

160

_ -160

0

515625

4 45 + 71 = 116

5 5 1 __ 6 + ( -3 5 __

6 ) = 4

6+1 ____

6 -3 5 __

6

= 1 2 __ 6

= 1 1 __ 3

6 - 1 __ 8 -6 7 __

8 = - 1 __

8 + ( -6 7 __

8 )

= -6 8 __ 8

= -7

7 142 - ( -49 ) = 142 + 49

= 191

8 -4 ( 7 ___ 10

) = - 4 __ 1 times 7 ___

10

= - 24 times 7 _______ 1 times 105

= - 2 times 7 _____ 1 times 5

= - 14 ___ 5 or -2 4 __

5

9 -32 ( -56 ) ( 4 ) = 32 times 56 times 4

= 7168

10 - 19 ___ 2 divide 38 ___

7 = -

119 times 7 _______ 2 times 382

= - 1 times 7 _____ 2 times 2

= - 7 __ 4

11 -3201 _______ -33

= 3201 _____ 33

97

33 ⟌ _

3201

_ -297

23 1

_ -23 1

0

97

12 Add the initial stock price with the increase from the

second day

$8360 + $1535 = $9895

Convert the percent decrease to a decimal

-4 3 __ 4 = -475 or -00475

Multiply the price on the second day times the

percent decrease and then subtract the result from

the price on the second day to find the final stock

price

$9895 times -00475 asymp -$47

$9895 - $47 = $9425

The final stock price is $9425 Yes this is

reasonable price on day 1 asymp $85 price on day

2 asymp $100 So the price on day 3 asymp $95

13 Sample answer You can use negative numbers to

represent temperatures below zero or decreases in

prices


MODULE 4 Ratios and Proportionality

Are You Ready

1 3 __ 4 divide 4 __

5 = 3 __

4 times 5 __

4

= 15 ___ 16

2 5 __ 9 divide 10 ___

11 = 5 __

9 times 11 ___

10

= 1

5 __ 9 times 11 ___

10 2

= 11 ___ 18

3 3 __ 8 divide 1 __

2 = 3 __

8 times 2 __

1

= 4

3 __ 8 times 2 __

1 1

= 3 __ 4

4 16 ___ 21

divide 8 __ 9 = 16 ___

21 times 9 __

8

=thinsp 2

7 16 ___ 21

times 9 __ 8 3

1

= 6 __ 7

5 B ( -4 1 )

6 C ( 3 0 )

7 D ( 5 4 )

8 E ( -2 -2 )

9 F ( 0 0 )

10 G ( 0 -4 )

LESSON 41

Your Turn

3 1 __ 6 acre divide ( 1 __

4 hour ) = 1 __

6 times 4 __

1

= 3

1 times 4 _____ 6 times 1

2

= 1 times 2 _____ 3 times 1

= 2 __ 3 acre per hour

4 3 cups divide ( 3 __ 4 cups ) = 3 __

1 divide 3 __

4

= 3 __ 1 times 4 __

3

= 1


1

= 1 times 4 _____ 1 times 1

= 4 cups

5 Jaylan 3 __ 4 divide 1 __

5 = 3 __

4 times 5 __

1 = 15 ___

4 = 3 3 __

4

Wanchen 2 __ 3 divide 1 __

6 = 2 ___

1 3 times 6

2 __

1 = 4 __

1 = 4

Jaylanrsquos unit rate is 3 3 __ 4 cups of water per cup of lime

juice Wanchenrsquos unit rate is 4 cups of water per cup

of lime juice Wanchenrsquos limeade has a weaker lime

flavor because 4 gt 3 3 __ 4 and the limeade with a

greater ratio of water to lime juice will have a weaker

flavor

Guided Practice

1

Distance (mi) 8 1 __ 2 17 25 1 __

2 34 42 1 __

2

Time (h) 1 __ 2 1 1 1 __

2 2 2 1 __

2

2 3 1 __ 2 miles divide ( 1 1 __

4 hours ) = 7 __

2 divide 5 __

4 mi ___ h

= 7 times 4 _____ 2 times 5

= 1 7 times 4 _____ 2 times 5

2

= 7 times 2 _____ 1 times 5

= 14 ___ 5 mi ___

h

= 2 4 __ 5 miles per hour

3 5 __ 8 page divide ( 2 __

3 minute ) = 5 __

8 times 3 __

2

= 15 ___ 16

page per minute

4 1 __ 6 foot divide ( 1 __

3 hour ) = 1 __

6 times 3 __

1

= 2 1 times 3 _____ 6 times 1

1

= 1 times 1 _____ 2 times 1

= 1 __ 2 foot per hour

5 5 __ 8 sq ft divide ( 1 __

4 hour ) = 5 __

8 times 4 __

1

= 2 5 times 4 _____ 8 times 1

1

= 5 times 1 _____ 2 times 1

= 5 __ 2 or 2 1 __

2 square feet per hour

Solutions KeyRatios and Proportional Relationships

UNIT

2


6 240 milligrams divide ( 1 __ 3 pickle ) = 240 ____

1 divide 1 __

3

= 240 ____ 1 times 3 __

1

= 720 ____ 1

Brand Arsquos rate is 720 mg per pickle

325 milligrams divide ( 1 __ 2 pickle ) = 325 ____

1 divide 1 __

2

= 325 ____ 1 times 2 __

1

= 650 ____ 1

Brand Brsquos rate is 650 milligrams per pickle and is

therefore lower than Brand A

7 The unit rate for Ingredient C is

1 __ 4 cup divide ( 2 __

3 serving ) = 1 __

4 times 3 __

2

= 3 __ 8

cup _______

serving

The unit rate for Ingredient D is

1 __ 3 cup divide ( 3 __

4 serving ) = 1 __

3 times 4 __

3

= 4 __ 9

cup _______

serving

To compare 3 __ 8 to 4 __

9 find the least common

denominator of 8 and 9 so that 3 __ 8 = 27 ___

72 and 4 __

9 = 32 ___

72

Therefore ingredient Crsquos unit rate is lower

8 Divide the number in the numerator by the number

in the denominator Write the result with the units of

the rate

For example 1 mile ______

1 __ 2 hour

= 1 __

1 __ 2 = 2 miles per hour


9 a The unit rate in dollars per hour for On Call is

$10 divide ( 35 hours ) = 10 ___ 35

$ __

h asymp $286 per hour

The unit rate in dollars per hour for Talk Time is

$125 divide ( 1 __ 2 hours ) = 125 ____

05 $ __


b Talk Time offers the better deal because its rate in

dollars per hour is lower

c To convert dollars per minute to dollars per hour

multiply by 60

$005 divide ( 1 minute )

= 005 ____ 1

$ ____

min times 60 min ______

1 h

= $3 per hour

d $3 per hour is more expensive than either On Call

or Talk Time so it is not a better deal than either

one

10 a Sample answer 1 __ 2 cup dried fruit to 1 __

8 cup

sunflower seeds in a granola recipe

b The ratio would not change if the recipe were

tripled because both numbers in the ratio would

be multiplied by the same number and therefore

the ratio would still be equivalent to what it was

originally

c 1 __ 2 divide 1 __

8 = 1 ___

1 2 times 8

4 __

1 = 4 __

1 = 4

Sample answer 4 cups dried fruit per 1 cup

sunflower seeds

11 10 songs

____________ 2 commercials

= 5 songs ____________

1 commercials

12 a Terrancersquos rate

6 mi divide ( 1 __ 2 h ) = 6 __

1 times 2 __

1

= 12 miles per hour

Jessersquos rate

2 mi divide ( 15 min ) = 2 __ 1 divide 1 __

4

= 2 __ 1 times 4 __

1 mi ___ h

= 8 miles per hour

b Terrance

50 mi divide ( 12 mi ___ h ) = 50 ___

1 times 1 ___

12

= 50 ___ 12

h

= 4 1 __ 6 h

= 4 10 ___ 60

h

= 4 hours and 10 minutes

Jesse

50 mi divide ( 8 mi ___ h ) = 50 ___

1 times 1 __

8

= 50 ___ 8 h

= 6 1 __ 4 h

= 6 15 ___ 60

h


c 8 mi divide ( 45 min ) = 8 __ 1 divide 3 __

4

= 8 __ 1 times 4 __

3

= 32 ___ 3


Sandrarsquos unit rate is greater than Jessersquos but

lower than Terrancersquos so she runs slower than

Terrance but faster than Jesse

13 1 ___ 10

h = 6 ___ 60

h = 6 min

300 words _________ 6 min

= 50 words per min

1 ___ 12

h = 5 ___ 60

h = 5 min

300 words _________ 5 min

= 60 words per min

Faster Eli typed 50 words per minute in his first test

and 60 words per minute in his second test



14 a For the 10-pack of 21 ounce bars

$1537 divide 10 bars asymp $154 per bar

For the 12-pack of 14 ounce bars


The 12-pack has the better price per bar

b For the 10-pack

$1537 divide ( 10 times 21 oz ) = 1537 divide 21

asymp $073 per ounce

For the 12-pack



The 10-pack has a better price per ounce

c Sample answer Since I always eat them one bar

at a time the 12-pack is the better choice

15 Yes Half a room in half a day corresponds to a unit

rate of 1 __ 2 room divide ( 1 __

2 day ) = 1 room _____

day so at the same

rate the painter could paint 7 rooms in 7 days

16 Sample answer Take the reciprocal of the rate For

example a rate of 7 gallons per hour is equal to

1 hour per 7 gallons

LESSON 42

Your Turn

3 No the rates are not equal and therefore her speed

was not constant

4 Since the ratio of students to adults is constant the

relationship between them is proportional

students ________ adults

= 12 ___ 1 = 36 ___

3 = 60 ___

5 = 12 students per adult

If s = the number of students and a = the number

of adults then a = 1 ___ 12

s or s = 12a

Guided Practice

1 45 ___ 1 = 45 90 ___

2 = 45 135 ____

3 = 45 180 ____

4 = 45

The relationship is proportional

2 k = y __ x = 10 ___

2 = 5 y = 5x

3 k = y __ x = 2 __

8 = 1 __

4 y = 1 __

4 x

4 With the equation y = kx where k is the constant

of proportionality


5 k = y __ x = 74 ___

4 = 1850 y = 1850x

6 $1099

_______ 05 days

= $2198 per day

7 Rent-All because it has the lowest price per day

($1850)

8 100 ft _____ 08 s

= 1000 _____ 8 ft __ s = 125 ft __ s

500 ft _____ 31 s

= 5000 _____ 31

ft __ s asymp 1613 ft __ s

1875 ft ______ 15 s

= 1875 ______ 15


No Emtiaz assumed the relationship is proportional

but it is not The rate of change is not constant and

so his answer is not reasonable

9 $3125

______ 5 h

= $625 per hour and $5000

______ 8 h

= $625 per

hour Because the two unit rates are the same the

relationship between charge and time is proportional

10 The constant rate of change in this context means

that Steven charges $625 per hour

11 y = $625x where x is the number of hours Steven

babysits and y is the amount Steven charges

12 y = $625 ( 3 ) = $1875

13 300 ft _____ 2 min

= 6750

_____ 45

= 150 feet per minute

150 ft _____ min

times 60 min ______ 1 h

= 9000 feet per hour

14 y = 150x

15 Sample answer Feet per minute A submarine may

stay submerged for hours but it would not dive for

hours


16 Yes because there is a proportional relationship

so the distance and the time would increase by the

same factor

17 Sample answer Yes Even though the rates in the

table are not constant per ear of corn due to

rounding there is a constant rate for every 3 ears

of corn

LESSON 43

Your Turn

1 No because 11 ___ 1 ne 16 ___

2 Also the line drawn through

the points does not go through the origin

5 a The point ( 4 60 ) represents that the bicyclist can

ride a distance 60 miles in 4 hours

b k = 60 mi _____ 4 h

= 15 mi ___ h

c y = 15x where x is time in hours and y is

distance in miles

Guided Practice

1

Time (h) 3 5 9 10

Pages 195 325 585 650

Proportional the rate is a constant 65 pages

per hour

2

Time (h) 2 3 5 8

Earnings 15 2250 3750 60

Proportional the rate of is a constant $750 per hour


3 Not proportional the relationship is linear but a line

drawn connecting the points will not pass through

the origin of ( 0 0 )

4 Proportional a line can be drawn that passes

through the points and also the origin of ( 0 0 )

5 k = 28 ft ____ 8 s

= 7 __ 2 ft __ s = 35 ft __ s y = 7 __

2 x or y = 35x where

x = time in seconds and y = height in feet

6 k = $2 ______

8 items = 1 __

4

$ _____

items = 025

$ _____

items so y = 1 __

4 x or

y = 025x where x = number of items and

y = cost in dollars

7 The graph is a straight line passing through the

origin


8 It is the distance ( 0 miles ) that each horse runs in

0 minutes

9 Horse A runs 1 mile in 4 minutes

Horse B runs 1 mile in 25 minutes

10 For Horse A y = 1 __ 4 x

For Horse B y = 1 ___ 25

x or 2 __ 5 x

11 If x is time in minutes and y is distance in miles in

12 minutes Horse A will run 3 miles or 1 __ 4 ( 12 ) = 3

and Horse B will run 48 miles or 2 __ 5 ( 12 ) = 24 ___

5 = 48

12 Students may draw any straight line with a slope

steeper than 2 __ 5 that starts at the origin of ( 0 0 ) An

example is given below

2

2

4

6

8

10

4 6 8 10Time (min)

Dis

tanc

e (m

i)

A

B

O

13 Yes if the train is traveling at a constant speed the

ratio of miles traveled to time in hours will be

constant and therefore a graph comparing miles to

hours will form a straight line that passes through


14 Sample answer When comparing relationships that

may be easier to observe on a graph than in an

equation

15 a

2

8

16

24

32

40

4 6 8 10DVDs

Cost

($)

O

b Sample answer The graph will pass through the

point ( 4 20 ) This point shows that four DVDs will

cost $20

16 The graph passes through the point ( 4 8 ) so

Glenda swam 8 feet in 4 seconds

17 Yes The graph is linear and passes through the

origin and therefore the rate of distance to time is

proportional at each point on the line

18 k = 8 ft ___ 4 s

= 2 ft __ s so y = 2x where x is time in

seconds and y is distance swam in feet It would

take 22 minutes to swim 1 __ 2 mile at this rate


19 Divide the second coordinate by the first to find the

constant of proportionality k Substitute the value of

k into the equation y = kx Then choose a value for x

and solve for y to find the ordered pair

20 Car 3 is not traveling at a constant speed

because 65 ___ 1 ne 85 ___

2

21 Since Car 4 is traveling at twice the speed it will

travel twice the distance as Car 2 in the same

amount of time Therefore the values in Car 4rsquos

distance column will be twice that shown in Car 2rsquos

distance column

MODULE 4

Ready to Go On

1 $140

_____ 18 ft 2

= $778 per square foot

2 $299

_____ 14 lb

asymp $021 per pound

3 $56 ______

25 gal = $224 per gallon

$3205

______ 15 gal

asymp $214 per gallon this is the better deal

4 $160

_____ 5 g

= $3200 per gram this is the better deal

$315

_____ 9 g

asymp $3500 per gram

5 No The ratio of dollars earned to lawns mowed is

not constant 15 ___ 1 ne 48 ___

3


6 k = $9

___ 8euro

= $27 ____

24euro = 9 __

8 $ __

euro or 1125

$ __

euro So y = 9 __

8 x or

y = 1125x where x equals the number of euros

and y equals their value in dollars

7 The graph passes through the point ( 2 5 )

so k = 5 __ 2 servings

_______ pt

or k = 25 servings

_______ pt

Therefore

y = 5 __ 2

x or y = 25x where x equals the number

of pints and y equals the number of servings

8 The new graph will pass through the points ( 0 0 ) and ( 3 2 )

2

2

4

6

8

10

4 6 8 10Pints

Serv

ings

Frozen Yogurt

O

Therefore y = 2 __ 3 x where x equals the number of

pints and y equals the number of servings

9 Sample answer Compare corresponding values of

the variables to determine whether there is a

constant rate


MODULE 5 Proportions and Percent

Are You Ready

1 22 = 22 ____ 100

= 022

2 75 = 75 ____ 100

= 075

3 6 = 6 ____ 100

= 006

4 189 = 100 + 89

= 100 ____ 100

+ 89 ____ 100

= 1 + 089

= 189

5 059 = 59

6 098 = 98

7 002 = 2

8 133 = 133

9 64

_ timesthinsp05

320

32

10 30

_ timesthinsp007

210

21

11 160

_ timesthinsp015

800

_ +1600

2400

24

12 62

_ timesthinsp032

124

_ +thinsp1860

1984

1984

13 4

_ timesthinsp12

8

_ +thinsp40

48

48

14 1000

_ timesthinsp006

6000

60

LESSON 51

Your Turn

2 x = ( $64 - 52 )

__________ $52

x = $12

____ $52

asymp 23

4 x = ( 18 - 12 )

________ 18

x = 6 ___ 18

asymp 33

5 x = ( 16 - 10 )

________ 16

x = 6 ___ 16

= 375

8 010 times $499 = $4990

$499 + $4990 = $54890

9 030 times $499 = $14970

$499 - $14970 = $34930

Guided Practice

1 x = ( $8 - $5 )

_________ $5

x = $3

___ $5

= 60

2 x = ( 30 - 20 )

_________ 20

x = 10 ___ 20

= 50

3 x = ( 150 - 86 )

__________ 86

x = 64 ___ 86

asymp 74

4 x = ( $389 - $349 )

______________ $349

x = $040

_____ $349

asymp 11

5 x = ( 14 - 13 )

________ 13

x = 1 ___ 13

asymp 8

6 x = ( 16 - 5 )

________ 5

x = 11 ___ 5 = 220

7 x = ( 64 - 36 )

_________ 36

x = 28 ___ 36

asymp 78

8 x = ( 80 - 64 )

_________ 80

x = 16 ___ 80

= 20

9 x = ( 95 - 68 )

_________ 95

x = 27 ___ 95

asymp 28


10 x=( 90-45)_________

90

x=45___90

=50

11 x=( 145-132)__________

145

x=13____145

asymp9

12 x=( 64-21)_________

64

x=43___64

asymp67

13 x=( 16-0)________

16

x=16___16

=100

14 x=( 3-1__

2)_______

3

x=21__

2___

3 asymp83

15 010times$900=$090 $900+$090=$990

16 025times48=12 48-12=36cookies

17 020times340=68 $340-68=272pages

18 050times28=14 28+14=42members

19 004times$29000=$1160 $29000-$1160=$27840

20 130times810=1053 810+1053=1863songs

21 030times20=6 20+6=26miles

22 Dividetheamountofchangeinthequantitybytheoriginalamountthenexpresstheanswerasapercent

Independent Practice23

ItemOriginal

PriceNew Price

Percent Change

Increase or

DecreaseBike $110 $96 asympthinsp13 Decrease

Scooter $45 $56 asympthinsp24 Increase

TennisRacket $79 $8295 5 Increase

Skis $580 $435 25 Decrease

24 a 55

x=( 8-3)_______

8 =5__

8=625

x=( 12-7)________

12 =5___

12asymp417

Theamountofchangeisthesamebutthepercentofchangeislessfrom2010to2011

b Changewasgreatestbetween2009and2010

x=( 12-3)________

3

x=9__3=300increase

25 a Amountofchange=( 5-4)=1

Percentdecrease=1__5=20

b $100_____5 =$020each$100_____

4 =$025each

Amountofchange=$025-$020=$005

Percentincrease=$005_____$020

=25

26 Percenterror=( 136-133)___________

136 times100

=03____136

times100asymp2


27 a Theyhavethesame$100+$10=$110and$100+10( $100)=$110

b SylviahasmoreLeroihas$110+$10=$120andSylviahas$110+10( $110)=$121

c BecauseSylviawillhavemoreafterthesecondadditionaldepositandshewillbedepositingincreasingamountsshewillalwayshavemoreinheraccount

28 Thefinalamountisalways0becausea100decreaseofanyamountwouldbe0

29 NoOnlythefirstwithdrawalis$10Eachwithdrawalafterthatislessthan$10becauseitis10oftheremainingbalanceTherewillbemoneyleftafter10withdrawals

LESSON 52

Your Turn

2 a 1c+01c11c

b s=11times$28=$3080

3 a 200

b 1c+2c3c

5 a

1b - 024b

1b024b

b 1b-024b=076b

6 a 1p-005p095p

b 095p=$1425




Guided Practice

1 a 035s

b 1s + 035s 135s

c 135 times $3200 = $4320

d 035 times $3200 = $1120

Item Price Markup MarkupRetail

Price

2 Hat $18 15 $270 $2070

3 Book $2250 42 $945 $3195

4 Shirt $3375 75 $2531 $5906

5 Shoes $7499 33 $2475 $9974

6 Clock $4860 100 $4860 $9720

7 Painting $18500 125 $23125 $41625

8 $4500 - 022 ( $4500 ) = $3510

9 $8900 - 033 ( $8900 ) = $5963

10 $2399 - 044 ( $2399 ) = $1343

11 $27999 - 075 ( $27999 ) = $7000

12 Write the percent of markdown as a decimal

subtract the product of this decimal and the regular

price from the regular price


13 a 046b

b 1b - 046b 054b

c 054 times $2900 = $1566

d 046 times $2900 = $1334

14 Regular Price $329

Sale Price $201

Regular Price $419

Sale Price $245

Regular Price $279

Sale Price $115

Regular Price $309

Sale Price $272

Regular Price $377

Sale Price $224

15 a Sample answer original price $100 final price

$050

b Sample answer original price $100 final price

$9950

c Sample answer original price $100 final price

$350

16 p = 127 ( $7400 ) = $9398

s = 127 ( $4800 ) = $6096

j = 127 ( $32500 ) = $41275

2 ( 9398 ) + 3 ( $6096 ) + $41275 = $78359

17 Either buy 3 get one free or 1 __ 4 off Either case would

result in a discount of 25 which is better than 20


18 No she is taking a loss Her cost for the tea is t so

the retail price is 12t The discounted price is

08 ( 12t ) or 096t which is less than t

19 No first change 201 decrease second change

251 increase The second percent change is

greater

20 Rafael can purchase the coat after 11 or 12 weeks

after 11 weeks the price is $10932 after 12 weeks

the price is $10385 and after that Danielle donates

the coat

LESSON 53

Your Turn

1 005 times $2000 = $100 $100 + $2000 = $2100

3 005 times $40000 = $2000

$2000 times 4 years = $8000

$40000 + $8000 = $48000

4 Commission $4500 times 00375 = $16875

Total $2200 + $16875 = $236875

Guided Practice

1 005 times $3000 = $150

2 015 times $7000 = $1050

3 0004 times $10000 = $040

4 15 times $2200 = $3300

5 001 times $8000 = $080

6 20 times $500 = $1000

7 a 007 times $4399 = $308

b $4399 + $308 = $4707

8 115 times $7550 = $8683

9 007 times $2000 = $140

$140 times 5 years = $700

10 003 times $550 = $1650

$1650 times 10 years = $165

$550 + $165 = $715

11 a 090 times $20 = $18

b 1085 times $18 = $1953

12 020 times $2999 = $600 tip

00625 times $2999 = $187 tax

$2999 + $600 + $187 = $3786 total

13 Write the tax rate as a decimal Then multiply the

decimal by the price of the item and add the result

to the price


14 $3275 + $3988 = $7263 total meal cost

014 times $7263 = $1017 tip

$7263 + $1017 = $8280 total with tip

15 $7865 times 015 = $1180 meal discount

$7865 times 020 = $1573 tip

$7865 + $1573 - $1180 = $8258 total

16 $125 times 235 = $29375 retail ring cost

0075 times $29375 = $2203 tax

$29375 + $2203 = $31578 total with tax


17 $7999 times 012 = $960 discount

$7999 - $960 = $7039 price before tax

$7039 times 10675 = $7514 total with tax

18 4 times $999 times 020 = $799 discount

4 times $999 - $799 = $3197 price before tax


19 $4500 + 00725 = $32625 commission

$750 + $32625 = $107625 total income

20 $700 times 0055 = $3850 commission

$475 + $3850 = $51350 total income

21 a Multiply Sandrarsquos height by 010 and add the

product to 4 to get Pablorsquos height Then multiply

Pablorsquos height by 008 and add the product to

Pablorsquos height to get Michaelarsquos height

b Using 48 inches for 4 feet

48 inches times 01 = 48 inches so Pablorsquos height is

53 inches or 4 feet 5 inches to the nearest inch

53 inches times 008 = 42 inches so Michaelarsquos

height is 57 inches or 4 feet 9 inches to the

nearest inch

22 a $4998 times 05 = $2499 50 discount

$2499 - $1000 = $1499 $10 discount

b $4998 - $1000 = $3998 $10 discount

$3998 times 05 = $1999 50 discount

23 a $95 times 09 = $8550 discounted camera

$8550 + $1599 = $10149 total

b $1599 times 09 = $1439 discounted battery

$95 + $1439 = $10939 total

c Eric should apply the discount to the digital

camera he can save $8

d $10149 times 008 = $812 tax

$10149 + $812 = $10961 total

24 a Store 1 $22 divide 2 = $11

Store 2 $1299 times 09 = $1169

Store 1 charges $11 per shirt and Store 2

charges $1169 Therefore I would save

$069 per shirt at Store 1

b Store 3 $2098 times 045 = $944

Yes It is selling shirts at $944


25 Marcus should choose the option that pays $2400

plus 3 of sales He would make $2550 to $2700

per month The other option would pay only $1775

to $2050 per month

26 Percent error = ǀ 132 - 137 ǀ

____________ 137

times 100 = 05 ____ 137

asymp 36

MODULE 5

Ready to Go On

1 x = ( 63 - 36 )

_________ 36

x = 27 ___ 36

= 75 increase

2 x = ( 50 - 35 )

_________ 50

x = 15 ___ 50

= 30 decrease

3 x = ( 72 - 40 )

_________ 40

x = 32 ___ 40

= 80 increase

4 x = ( 92 - 69 )

_________ 92

x = 23 ___ 92

= 25 decrease

5 $60 times 015 = $9

$60 + $9 = $69

6 $32 times 0125 = $4

$32 + $4 = $36

7 $50 times 022 = $11

$50 - $11 = $39

8 $125 times 030 = $3750

$12500 - $3750 = $8750


$325 + $312 = $637 total income

10 $5310

______ $1735

asymp 31

11 Find the amount per hour that Priya makes if she

makes 20 more than James

$700 times 020 = $140

$700 + $140 = $840

Next find the amount Slobhan makes if he makes

5 less than Priya

$840 times 005 = $042

$840 - $042 = $798

Slobhan makes $798 per hour

12 Both the 6 tax and the 20 tip are applied to the

initial cost of the meal so the two percents can be

added together and multiplied by the cost

$45 times 026 = $1170

$45 + $1170 = $5670

The total cost of the meal is $5670

13 Sample answer sales tax increase discount

decrease tip increase


MODULE 6 Expressions and Equations

Are You Ready

1 5 + x

2 11 - n

3 -9 ___ y

4 2x - 13

5 2x + 3

= 2 ( 3 ) + 3

= 6 + 3

= 9

6 -4x + 7

= -4 ( 1 ) + 7

= -4 + 7

= 11

7 15x - 25

= 15 ( 3 ) - 25

= 45 - 25

= 2

8 04x + 61

= 04 ( -5 ) + 61

= -20 + 61

= 41

9 2 __ 3 x - 12

= 2 __ 3

( 18 ) - 12

= 2 __ 3

times ( 18 ___ 1 ) - 12

= 36 ___ 3 - 12

= 0

10 - 5 __ 8

x + 10

= - 5 __ 8 ( -8 ) + 10

= - 5 __ 8 times- 8 __

1 + 10

= - 5 ___ 1 8

times- 8 1 __

1 + 10

= - 5 __ 1 times- 1 __

1 + 10

= 5 + 10

= 15

11 1 __ 2 divide 1 __

4

= 1 times 4 _____ 2 times 1

= 1 times 4 2 ______

1 2 times 1

= 1 times 2 _____ 1 times 1

= 2

12 3 __ 8 divide 13 ___

16

= 3 __ 8 times 16 ___

13

= 3 times 16 2 _______

1 8 times 13

= 3 times 2 ______ 1 times 13

= 6 ___ 13

13 2 __ 5 divide 14 ___

15

= 2 __ 5 times 15 ___

14

= 1 2 times 15

3 ________

1 5 times 14 7

= 1 times 3 _____ 1 times 7

= 3 __ 7

14 4 __ 9 divide 16 ___

27

= 4 __ 9 times 27 ___

16

= 1 4 times 27

3 ________

1 9 times 16 4

= 1 times 3 _____ 1 times 4

= 3 __ 4

LESSON 61

Your Turn

2 ( 3x + 1 __ 2 ) + ( 7x - 4 1 __

2 )

= 3x + 7x + 1 __ 2 - 4 1 __

2

= 10x - 4

3 ( -025x - 3 ) - ( 15x + 14 ) = -025x - 3 - 15x - 14

= -175x - 44

4 02(3b - 15c) + 6c

= 06b - 3c + 6c

= 06b + 3c

5 2 __ 3 (6e + 9f - 21g) - 7f

= 4e + 6f - 14g - 7f

= 4e - f - 14g

6 5x - 3(x - 2) - x

= 5x - 3x + 6 - x

= x + 6

7 83 + 34y - 05(12y - 7)

= 83 + 34y - 6y + 35

= 118 - 26y

Solutions KeyExpressions Equations and Inequalities

UNIT

3


Guided Practice

1 baseballs 14 + (12)n tennis balls 23 + (16)n

14 + 12n + 23 + 16n

14 + 23 + 12n + 16n

37 + 28n

So the total number of baseballs and tennis balls is

37 + 28n

2 37 + 28n

37 + 28 ( 9 )

= 37 + 252

= 289

3 14 + 5(x + 3) - 7x = 14 + 5x + 15 - 7x

= 29 - 2x

4 3 ( t - 4 ) - 8 ( 2 - 3t ) = 3t - 12 - 16 + 24t

= 27t - 28

5 63c - 2 ( 15c + 41 ) = 63c - 3c - 82

= 33c - 82

6 9 + 1 __ 2 ( 7n - 26 ) - 8n = 9 + 35n - 13 - 8n

= -4 - 4 1 __ 2 n

7 2x + 12

2 ( x + 6 )

8 12x + 24

12 ( x + 2 )

9 7x + 35

7 ( x + 5 )

10 You multiply numbers or expressions to produce a

product You factor a product into the numbers or

expressions that were multiplied to produce it


11 Let d = number of days

Fee for 15 food booths 15 ( 100 + 5d ) Fee for 20 game booths fee 20 ( 50 + 7d ) Amount the company is paid for the booths

15 ( 100 + 5d ) + 20 ( 50 + 7d ) = 15 ( 100 ) + 15 ( 5d ) + 20 ( 50 ) + 20 ( 7d )

= 1500 + 75d + 1000 + 140d

= 1500 + 1000 + 75d + 140d

= 2500 + 215d

12 New length 96 + l

New width 60 + w

Perimeter of new pattern

2(96 + l) + 2(60 + w)

=2(96) + 2l + 2(60) + 2w

192 + 2l + 120 + 2w

192 + 120 + 2l + 2w

312 + 2l + 2w

13 Width 3

Length 1 x-tile and 2 +1-tiles

Factors 3 and x + 2

Product 3 ( x + 2 ) = 3x + 6

14 Width 4

Length 2 x-tiles and 1 -1-tile

Factors 4 and 2x - 1

Product 4 ( 2x - 1 ) = 8x - 4

15 The area is the product of the length and width

( 6 times 9 ) It is also the sum of the areas of the

rectangles separated by the dashed line ( 6 times 5

and 6 times 4 ) So 6 ( 9 ) = 6 ( 5 ) + 6 ( 4 )

16 Perimeter of triangle ( x + 3 ) + ( 2x + 4 ) +

6x = ( x + 3 ) + ( 2x + 4 ) +

6x = 3x + 7 +

-3x = _ -3x

3x = 7 +

_ -7 = _ -7

3x - 7 =

The length of the side is 3x - 7

17 Perimeter of rectangle 2 ( 3x - 3 ) + 2 ( )

10x + 6 = 2 ( 3x - 3 ) + 2 ( )

10x + 6 = 6x - 6 + 2

_ -6x = _ -6x

4x + 6 = - 6 + 2

_ + 6 = _ + 6

4x + 12 = 2

( 4x + 12 ) divide 2 = ( 2 ) divide 2

2x + 6 =

The length of the side is 2x + 6

18 a P = 2l + 2w

Perimeter of tennis court T

2(2x + 6) + 2(x)

= 4x + 12 + 2x

= 6x + 12

Perimeter of basketball court B

2(3x - 14) + 2( 1 __ 2 x + 32)

= 6x - 28 + x + 64

= 7x + 36

b (7x + 36) - (6x + 12)

= 7x + 36 - 6x - 12

= x + 24

c Find the length of tennis court

Let x = 36

2x + 6 = 2 ( 36 ) + 6

= 72 + 6

= 78

Find the width of the basketball court

Let x = 36

1 __ 2 x + 32 = 1 __

2 ( 36 ) + 32

= 18 + 32

= 50

Find the length of the basketball court

Let x = 36

3x - 14 = 3 ( 36 ) - 14

= 108 - 14

= 94

The tennis court is 36 ft by 78 ft The basketball

court is 50 ft by 94 ft


19 Find the area of each small square and rectangle

( x ) ( x ) = x 2

( x ) 1 = x

( 1 ) 1 = 1


x

x

1

11

1 1

x2 x x x

x 1 1 1x 1 1 1

Area =

x 2 + x + x + x + x + x + 1 + 1 + 1 + 1 + 1 + 1

= x 2 + 5x + 6

( x + 3 ) ( x + 2 ) = x 2 + 5x + 6

20 Agree To find 58 times 23 let 23 = 3 + 20 Then find

the product 58 ( 3 + 20 ) First step 58 ( 3 ) = 174

Second step 58 ( 20 ) = 1160 Third step 174 +

1160 = 1334 So 58 ( 23 ) = 58 ( 3 ) + 58 ( 20 )

21 ( 1 ) Think of 997 as 1000 - 3 So 8 times 997 = 8 ( 1000 - 3 ) By the Distributive Property

8 ( 1000 - 3 ) = 8000 - 24 = 7976

( 2 ) Think of 997 as 900 + 90 + 7 By the Distributive

Property 8 ( 900 + 90 + 7 ) = 7200 + 720 + 56 =

7976

LESSON 62

Your Turn

1 49 + z = -9

_ -49 _ -49

z = -139

2 r - 171 = -48

_ +171 _ +171

r = 123

3 -3c = 36

-3c ____ -3

= 36 ___ -3

c = -12

5 x - 15 = 525

_ +15 _ +15

x = 675

The initial elevation of the plane is 675 miles

6 x ___ 35

= -12

x ___ 35

( 35 ) = -12 ( 35 )

x = -42

The decrease in the value of the stock was $420

7 25x = 75

25x ____ 25

= 75 ___ 25

x = 3

The power was restored in 3 hours

Guided Practice

1 Let x represent the number of degrees warmer the

average temperature is in Nov than in Jan

x + ( -134 ) = -17 or x - 134 = -17

x - 134 = -17

_ +134 _ +134

x = 117

The average temperature in November is 117degF

warmer

2 Let x represent the number of days it takes the

average temperature to decrease by 9degF

-1 1 __ 2 x = -9

( - 2 __ 3 ) ( - 3 __

2 x ) = ( - 2 __

3 ) ( -9 )

x = 18 ___ 3

x = 6

It took 6 days for the temperature to decrease by 9degF

3 -2x = 34

-2x ____ -2

= 34 ___ -2

x = -17

4 y - 35 = -21

_ + 35 _ + 35

y = 14

y = 14

5 2 __ 3 z = -6

( 3 __ 2 ) 2z ___

3 = ( 3 __

2 ) ( -6 )

z = -9

6 Sample answer It helps me describe the problem

precisely and solve it using inverse operations


7 Let x equal the elevation of Mt Everest

x - 870737 = 203215

_ +870737 _ +870 737

x = 2902887

The elevation of Mt Everest is 2902887 ft

8 Let x equal the number of feet Liam descended

2825131 - x = 2320106

_ -2825131 _ -2825131

-x = - 505025

x = 505025

Liam descended 505025 ft

His change in elevation was -505025 ft

9 Let x equal the elevation of Mt Kenya

2825131 - x = 1119421

_ -2825131 _ -2825131

-x = -1705710

x = 1705710

The elevation of Mt Kenya is 170571 ft

10 Find the change in elevation

1250 - 935 = 315

Use an equation

Let x = the number of minutes the balloon

descends

( -22 1 __ 2 ) x = -315

( - 45 ___ 2 ) x = -315

( - 2 ___ 45

) ( - 45 ___ 2 ) x = -315 ( - 2 ___

45 )

x = 14

It will take the balloon 14 minutes to descend


4106 - 3205 = 901

Use an equation to find the rate of descent


Let x = rate of descent

34x = 901

34x ____ 34

= 901 ____ 34

x = 265 = 26 1 __ 2

The rate of descent was 26 1 __ 2 feet per minute

12 Let x = the number of degrees warmer Montanarsquos

average temperature is than Minnesotarsquos

- 25 + x = -07

_ + 25 _ + 25

x = 18

Montanarsquos average 3-month temperature is 18degC

warmer than Minnesotarsquos

13 Let x = the number of degrees warmer Floridarsquos

average temperature is than Montanarsquos

181 - x = -07

_ - 181 _ -181

-x = -188

x = 188

Floridarsquos average 3-month temperature is 188degC

warmer than Montanarsquos

14 Let x = the number of degrees the average

temperature in Texas would have to change

125 + x = 181

_ -125 _ -125

x = 56

It would have to increase by 56degC

15 Let x = the number of yards the team must get on

their next play

-26 1 __ 3

+ x = 10

+26 1 __ 3

______

+26 1 __ 3

______

x = 36 1 __ 3

The team needs to get 36 1 __ 3 yards on their next play

16 Let x = the number of seconds

( -2 1 __ 2 ) x = -156

( -25 ) x = -156

( -25 _____ -25

) x = -156 ______ -25

x = 624

It takes the diver 624 seconds to reach -156 feet

17 Sample answer The elevation is the product of the

rate and the time

18 Let x = the total amount withdrawn

x __ 5 = 455

( 5 ) x __ 5 = 455 ( 5 )

x = 2275

The total amount she withdrew was $22750

Sample answer

$4550 asymp $50 and $50 times 5 = $250 which is close

to $22750


19 ( 1 ) The elevations of the diver and the reef both are

below sea level

( 2 ) The change in the planersquos elevation the plane

descends the plane is moving from a higher to a

lower elevation

20 -4x = -48

( -4x ____ -4

) = -48 _____ -4

x = 12

- 1 __ 4 x = -48

( -4 ) ( - 1 __ 4 ) x = -48 ( -4 )

x = 192

192 ____ 12

= 16

In the first case -4x = -48 you divide both sides

by -4 In the second - 1 __ 4 x = -48 you multiply

both sides by -4 The second solution (192) is

16 times the first (12)

21 Add the deposits and the withdrawals Let x repre-

sent the amount of the initial deposit Write and

solve the equation x + deposits - withdrawals =

$21085

LESSON 63

Your Turn

4 Let x represent the number of video games Billy

purchased

Original balance on gift card $150

Cost for x video games $35 middot x

Final balance on gift card $45

Original balance minus $35 times number of games equals $45

darr darr darr darr darr darr darr $150 - $35 middot x = $45

Equation 150 - 35x = 45

5 Sample answer You order x pounds of coffee from

Guatemala at $10 per pound and it costs $40 to

ship the order How many pounds can you order so

that the total cost is $100

Guided Practice

1

+ + ++ ++

+++ + +

+++

2

----

+ ++ ++

- - -


3 Let a represent the number of adults that attend

Ticket cost for 1 child = $6

Ticket cost for a adults = $9 middot a

Total cost for movie = $78

cost for child plus $9 times number of adults equals $78

darr darr darr darr darr darr darr $6 + $9 middot a = $78

Equation 6 + 9a = 78

4 x is the solution of the problem

2x is the quantity you are looking for multiplied by 2

+ 10 means 10 is added to 2x

= 16 means the result is 16

5 Sample answer A department store is having a sale

on recliners buy two and get a discount of $125

Sanjay purchases two recliners and the total cost

(before taxes) is $400 What is the price of a single

recliner not including any discounts

6 Choose a variable to represent what you want to

find Decide how the items of information in the

problem relate to the variable and to each other

Then write an equation tying this all together


7 On one side of a line place three negative variable

tiles and seven +1-tiles and then on the other side

place 28 +1-tiles

8 Let d represent the number of days Val rented the

bicycle

Flat rental fee $5500

Cost for d days of rental $850 middot dTotal cost $123

$850 times number of days plus flat fee equals total cost

darr darr darr darr darr darr darr $850 bull d + $55 = $123

Equation 85d + 55 = 123

9 Let r represent the number of refills

Refill mug cost $675

Cost for r refills $125 middot r Total cost $3175

$125 times number of refills plus refill mug cost equals total cost

darr darr darr darr darr darr darr $125 bull r + $675 = $3175

Equation 125r + 675 = 3175

10 Let n represent the number of weekday classes

The Saturday class lasts 60 minutes

The length of time for the weekday classes is 45 middot n

The total number of minutes for all classes in a week

is 28545 minutes times number of plus minutes for equals total minutes

weekday classes Saturday class

darr darr darr darr darr darr darr45 bull n + 60 = 285

Equation 45n + 60 = 285

11 Let n represent the number of African animals

Half the number of African animals is 1 __ 2 n

45 more than the number of African animals

means + 45

The total number of animals is 172

half times number of and 45 more than number equals total number

African animals of African animals of animals

darr darr darr darr darr darr

1 _ 2

bull n + 45 = 172

Equation 1 __ 2 n + 45 = 172

12 Let u represent the number of uniforms

Cost for basketball equipment $548

Cost for u uniforms $2950 middot uTotal cost $2023

$2950 times number of plus cost for basketball equals total cost

uniforms equipment

darr darr darr darr darr darr darr $2950 bull u + $548 = $2023

Equation 295u + 548 = 2023

13 Let x represent the number of weeks

Initial amount in account $500

$20 per week 20 middot xFinal amount in account $220

initial amount minus 20 times number of equals final amount

weeks

darr darr darr darr darr darr darr 500 - 20 bull x = 220

Equation 500 - 20x = 220

14 a The equation adds 25 but Deenarsquos scenario

involves subtracting 25

b Let x represent the number of shirts

Cost of shirts before discount 9 middot xDiscount means subtract

Amount of discount $25

Total bill $88

9 times number of minus discount equals total

shirts bill

darr darr darr darr darr darr darr 9 bull x - 25 = 88

Equation 9x - 25 = 88

c Sample answer I bought some shirts at the store

for $9 each and a pair of jeans for $25 making

my bill a total of $88 How many shirts did I buy

15 a Let c represent the number of children

Flat fee for Sandy $10

Cost per child for Sandy $5 middot cTotal charge for Sandy $10 + $5c

Total charge for Kimmi $25

To compare the two costs set these values equal

Equation 10 + 5c = 25

b Solve the equation to find c the number of

children a family must have for Sandy and Kimmi

to charge the same amount

10 + 5c = 25

10 - 10 + 5c = 25 - 10

5c = 15

5c ___ 5 = 15 ___

5

c = 3

3 children

c They should choose Kimmi because she charges

only $25 If they chose Sandy they would pay

10 + 5 ( 5 ) = $35



16 To get Andresrsquo equation you can multiply every

number in Peterrsquos equation by 4 To get Peterrsquos

equation you can divide every number in Andrewrsquos

equation by 4 or multiply by 1 __ 4

17 Part of the equation is written in cents and part in

dollars All of the numbers in the equation should be

written either in cents or dollars

18 Sample answer Cici has a gift card with a balance

of 60 She buys several T-shirts for $8 each Her new

balance is $28 after the purchases Write an

equation to help find out how many T-shirts Cici

bought

LESSON 64

Your Turn

1 Model the equation

+ ++ +

+ ++ ++ +

+ ++ ++ +

++

Remove 5 +1-tiles from each side of the mat

+ ++ +

+ ++ ++ +

+ ++ ++ +

++

Divide each side into two equal groups

++

+ ++ +

++

The solution is x = 3

++ ++


+ + ++ + ++ +

+++

+++

__

Add 1 +1-tile to each side of the mat Note that

a negative-positive tile pair results in zero

+ + ++ + ++

++ +

+++

+++

__


+ + ++++ + +++

The solution is n = 3

+ + +++


++++

______

______

____

Add 3 +1-tiles to each side of the mat Note that


++++

+

++

+

++

______

______

____


++++

____

The solution is a = -1

++ __



____

________

++

Add 2 -1-tiles to each side of the mat Note that


________

________

++

____


________

________

We get -y = -1

____

In order to change -y to y add a positive y-variable

tile to each side

++

__ ++ __

Add 1 +1-tile to each side of the mat

++++

__

The solution is y = 1

+++

6 3n + 10 = 37

Solve the equation for n

3n + 10 = 37

-10 ____

-10 ____

3n = 27

3n ___ 3 = 27 ___

3

n = 9

The triplets are 9 years old

7 n __ 4 - 5 = 15


n __ 4 - 5 = 15

+5 ___

+5 ___

n __ 4 = 20

n __ 4 ( 4 ) = 20 ( 4 )

n = 80

The number is 80

8 -20 = 5 __ 9 ( x - 32 )

Solve the equation for x

-20 = 5 __ 9 ( x - 32 )

-20 = 5 __ 9 x - 160 ____

9

+ 160 ____ 9

______

+ 160 ____ 9

______

- 20 ___ 9 = 5 __

9 x

- 20 ___ 9 divide ( 5 __

9 ) = 5 __

9 x divide ( 5 __

9 )

4 20 times 9

1 _______

9 1 times 5

1 = x

- 4 __ 1 = x

-4 = x

The temperature in the freezer is -4degF

9 120 - 4x = 92


120 - 4x = 92

-120 _____

-120 _____

- 4x = -28

-4x ____ -4

= -28 ____ -4

x = 7

She had 7 incorrect answers


Guided Practice

1 To solve the equation with algebra tiles first remove

one +1-tile from both sides Then divide each side

into two equal groups

2 Remove 1 +1-tile from each side

++++

+ +++++++++


++++

++++++++


++ + + + +

3 Let w = the width of the frame

2 times height plus 2 times width equals perimeter

darr darr darr darr darr darr darr darr darr2 bull 18 + 2 bull w = 58

Solve the equation

2 ( 18 ) + 2w = 58

36 + 2w = 58

36 - 36 + 2w = 58 - 36

2w = 22

2w ___ 2 = 22 ___

2

w = 11

The width is 11 inches

4 1200 minus 25x = 500


1200 - 25x = 500

_ -1200 _ -1200

-25x = -700

-25x _____ -25

= -700 _____ -25

x = 28

The manager will reorder in 28 days

5 Use the inverse operations of the operations

indicated in the problem If the equation does

not involve parentheses use addition or subtraction

before multiplication or division to solve the

equation


6 9s + 3 = 57

9s + 3 - 3 = 57 - 3

9s = 54

9s ___ 9 = 54 ___

9

s = 6

7 4d + 6 = 42

4d + 6 - 6 = 42 - 6

4d = 36

4d ___ 4 = 36 ___

4

d = 9

8 115 - 3y = -485

115 - 115 - 3y = -485 - 115

thinsp-3y = -60

-3y

____ -3

= -60 ____ -3

y = 20

9 k __ 2 + 9 = 30

k __ 2 + 9 - 9 = 30 - 9

k __ 2 = 21

2 sdot k __ 2 = 2 sdot 21

k = 42

10 g

__ 3 - 7 = 15

g

__ 3 - 7 + 7 = 15 + 7

g

__ 3 = 22

3 sdot g

__ 3 = 3 sdot 22

g = 66

11 z __ 5 + 3 = -35

z __ 5 + 3 - 3 = -35 - 3

z __ 5 = -38

5 sdot z __ 5 = 5 ( -38 )

z = -190

12 -9h - 15 = 93

-9h - 15 + 15 = 93 + 15

-9h = 108

-9h ____ -9 = 108 ____

-9

h = -12

13 - 1 __ 3 (n + 15) = -2

- 1 __ 3 n - 5 = -2

- 1 __ 3 n - 5 + 5 = -2 + 5

- 1 __ 3 n = 3

-3 sdot - 1 __ 3 n = -3 sdot 3

n = -9

14 -17 + b __ 8 = 13

-17 + 17 + b __ 8 = 13 + 17

b __ 8 = 30

8 sdot b __ 8 = 8 sdot 30

b = 240


15 7 ( c - 12 ) = -21

7c - 84 = -21

_ +84 _ +84

7c = 63

7c ___ 7 = 63 ___

7

c = 9

16 -35 + p

__ 7 = -52

-35 + 35 + p

__ 7 = -52 + 35

p

__ 7 = -17

7 sdot p

__ 7 = -17 sdot 7

p = -119

17 46 = -6t - 8

46 + 8 = -6t - 8 + 8

54 = -6t

54 ___ -6

= -6t ____ -6

t = -9

18 Let a = the original amount in the account

Double the (original plus 26) equals new

sum of amount amount


2 (a + $26) = $264

Solve the equation

2 ( a + 26 ) = 264

2 ( a + 26 )

_________ 2 = 264 ____

2

a + 26 = 132

a + 26 - 26 = 132 - 26

a = 106

Puja originally had $106 in the account

19 Let t = the temperature 6 hours ago

Twice temperature less 6 degrees equals current

6 hours ago temperature

darr darr darr darr darr darr 2middot t - 6 = 20

Solve the equation

2t - 6 = 20

2t - 6 + 6 = 20 + 6

2t = 26

2t __ 2 = 26 ___

2

t = 13

Six hours ago it was 13 degF in Smalltown

20 -35 = 5 __ 9 ( x - 32 )

-35 = 5 __ 9 x - 160 ____

9

+ 160 ____ 9

______

+ 160 ____ 9

- 155 ____ 9 = 5 __

9 x

thinsp- 155 ____ 9 divide ( 5 __

9 ) = 5 __

9 x divide ( 5 __

9 )

-thinsp 31

155 times 9

1

= x

9 1

times 5

1

- 31 ___ 1 = x

-31 = x

The temperature is -31degF

21 Let a = Artaudrsquos ageopposite of Artaudrsquos age add 40 equals 28

darr darr darr darr darr darr(-) a + 40 = 28

Solve the equation

-a + 40 = 28

-a + 40 - 40 = 28 - 40

-a = -12

-a ___ -1

= -12 ____ -1

a = 12

Artaud is 12 years old

22 Let c = number of customers when Sven startedtwice number of

customers when Sven started

plus 11 more equals present number of customers

darr darr darr darr darr2 middot c +11 = 73

Solve the equation

2c + 11 = 73

2c + 11 - 11 = 73 - 11

2c = 62

2c ___ 2 = 62 ___

2

c = 31

Sven had 31 customers when he started

23 Let p = original price of the jacket

half original less $6 equals amount

price paid

darr darr darr darr darr

1 __ 2

middot p -6 = 88

Solve the equation

1 __ 2 p - 6 = 88

1 __ 2 p - 6 + 6 = 88 + 6

1 __ 2 p = 94

2 sdot 1 __ 2 p = 2 sdot 94

p = 188

The original price was $188


24 115 minus 8n = 19


115 - 8n = 19

_ -115 _ -115

-8n = -96

-8n _____ -8

= -96 _____ -8

n = 12

They had 19 apples left after 12 days

25 -55x + 056 = -164

-55x + 056 - 056 = -164 - 056

-55x = -22

-55x ______ -22

= -22 _____ -22

x = 04

26 -42x + 315 = -651

-42x + 315 - 315 = -651 - 315

-42x = -966

-42x ______ -42

= -966 ______ -42

x = 23

27 k ___ 52

+ 819 = 472

k ___ 52

+ 819 - 819 = 472 - 819

k ___ 52

= -347

52 sdot k ___ 52

= 52 ( -347 )

k = -18044

28 Sample answer -3x - 5 = -26

29 Sample answer x __ 5 + 10 = 5

30 When dividing both sides by 3 the student forgot to

divide 2 by 3

3x + 2 = 15

3x ___ 3 + 2 __

3 = 15 ___

3

x + 2 __ 3 = 5

- 2 __ 3

___

- 2 __ 3

___

x = 5 - 2 __ 3

x = 5 times3

___ 1

times3 - 2 __

3

x = 15 ___ 3 - 2 __

3

x = 13 ___ 3 or 4 1 __

3

The solution should be x = 4 1 __ 3

31 a 2(x + 40) = 234


2x + 80 = 234

2x + 80 - 80 = 234 - 80

2x = 154

2x ___ 2 = 154 ____

2

x = 77

Trey saved $77

b Sample answer In both solutions you would

divide $234 by 2 then subtract 40 234 divide 2 ndash 40

= 77 These are the same operations applied in

the same order as when solving the equation


32 F = 18c + 32

F - 32 = 18c + 32 - 32

F - 32 = 18c

F - 32 ______ 18

= 18c ____ 18

F - 32 ______ 18

= c

33 P = 2 ( ℓ + w ) P = 2ℓ + 2w

P - 2ℓ = 2ℓ - 2ℓ + 2w

P - 2ℓ = 2w

P - 2ℓ ______ 2 = 2w ___

2

P - 2ℓ ______ 2 = w

34 ax + b = c

ax + b - b = c - b

ax = c - b

ax ___ a = c - b ______ a

x = c - b ______ a

MODULE 6

Ready to Go On

1 Add the amounts for the cost of first day of the field

trip with the second day of the field trip where n is

the number of members in the club

15n + 60 + 12n + 95

Therefore the total cost of the two-day field trip can

be written as the expression 27n + 155

2 h + 97 = -97

_ -97 _ -97

h = -194

3 - 3 __ 4 + p = 1 __

2

+ 3 __ 4 + 3 __

4

p = 1 __ 2 + 3 __

4

p = 1 times2

___ 2

times2 + 3 __

4

p = 2 __ 4 + 3 __

4

p = 5 __ 4

4 -15 = -02k

-15 _____ -02

= -02k ______ -02

75 = k


5 y ___

-3 = 1 __

6

y ___

-3 ( -3 ) = 1 __

6 ( -3 )

y = 1 __ 6 times -3 ___

1

y = -3 ___ 6

y = -1 ___ 2

6 - 2 __ 3

m = -12

- 2 __

3 m _____

- 2 __ 3 = -12 ____

- 2 __ 3

m = -12 divide - 2 __ 3

m = -12 ____ 1 divide - 2 __

3

m = -12 ____ 1 times - 3 __

2

m = -36 ____ -2

m = 18

7 24 = - t ___ 45

24 ( 45 ) = - t ___ 45

( 45 )

108 = -t

-108 = t

8 Let d represent the number of the day after the first

day for example d = 1 means the first day after the

day he started number of number number

2 times day after plus of sit-ups equals of sit-ups

first day first day today

darr darr darr darr darr darr darr

2 middot d + 15 = 33

Equation 2d + 15 = 33

9 5n + 8 = 43

5n + 8 - 8 = 43 - 8

5n = 35

5n ___ 5 = 35 ___

5

n = 7

10 y __

6 - 7 = 4

y __

6 - 7 + 7 = 4 + 7

y __

6 = 11

6 sdot y __

6 = 6 sdot 11

y = 66

11 8w - 15 = 57

8w - 15 + 15 = 57 + 15

8w = 72

8w ___ 8 = 72 ___

8

w = 9

12 g

__ 3 + 11 = 25

g

__ 3 + 11 - 11 = 25 - 11

g

__ 3 = 14

3 sdot g

__ 3 = 3 sdot 14

g = 42

13 f __ 5 - 22 = -25

f __ 5 - 22 + 22 = -25 + 22

f __ 5 = -03

5 sdot f __ 5 = 5 ( -03 )

f = -15

14 - 1 __ 4 (p + 16) = 2

- 1 __ 4 p - 4 = 2

- 1 __ 4 p - 4 + 4 = 2 + 4

- 1 __ 4 p = 6

-4 sdot - 1 __ 4 p = 6 sdot -4

p = -24

15 Sample answer Analyze the situation to determine

how to model it using a two-step equation Solve

the equation Interpret the solution in the given

situation


MODULE 7 Inequalities

Are You Ready

1 9w = -54

9w ___ 9 = -54 ____

9

w = -6

2 b - 12 = 3

thinsp _ + 12 = _ + 12

b = 15

3 n __ 4

= -11

4 times n __ 4

= 4 ( -11 )

n = -44

4-7

ndash5ndash10 0 5 10

75 4 6

8 3 - (-5)

3 + 5

8

9 -4 - 5

-9

10 6 - 10

-4

11 -5 - (-3)

-5 + 3

-2

12 8 - (-8)

8 + 8

16

13 9 - 5

4

14 -3 - 9

-12

15 0 - (-6)

0 + 6

6

LESSON 71

Your Turn

4 y minus 5 ge minus7

_ +5 _ +5

y ge minus2

-4-5 -3 -2-1 0 1 2 3 4 5

Check Substitute 0 for y

minus1 ge -8

minus1(minus2) le -8(minus2)

2 le 16

5 21 gt 12 + x

_ -12 _ minus12

9 gt x

x lt 9

10 2 3 4 5 6 7 8 9 10

Check Substitute 8 for x

21 gt 12 + 8

21 gt 12 + 8

21 gt 20

6 -10y lt 60

-10y

_____ -10

lt 60 ____ -10

y gt -6

-10-9 -8 -7 -6 -5 -4 -3 -2-1 0 1

Check Substitute -5 for y

-10y lt 60

-10(-5) lt 60

50 lt 60

7 7 ge - t __ 6

7(-6) le - t __ 6 (-6)

-42 le t

t ge -42

-46 -45 -44 -43 -42 -41 -40-47

Check Substitute -36 for t

7 ge - t __ 6

7 ge - ( -36 ____

6 )

7 ge 6

8 Write and solve an inequality

Let m = the number of months

35m le 315

35m ____ 35

le 315 ____ 35

m le 9

Tony can pay for no more than 9 months of his gym

membership using this account

Guided Practice

1 -5 le -2

_ +7 _ +7

2 le 5

2 -6 lt -3

-6 ___ -3

gt -3 ___ -3

2 gt 1

3 7 gt -4

_ -7 _ -7

0 gtthinsp -11


4 -1 ge -8

-1 ( -2 ) le -8 ( -2 )

2 le 16

5 n - 5 ge -2

_ +5 _ +5

n ge 3

-5 -4 -3 -2-1 0 3 4 51 2

Check Substitute 4 for n

n - 5 ge -2

4 - 5 ge -2

-1 ge -2

6 3 + x lt 7

_ -3 _ -3

x lt 4

-2-1 0 3 4 5 6 7 81 2


3 + x lt 7

3 + 3 lt 7

6 lt 7

7 -7y le 14

-7y

____ -7 ge 14 ___ -7

y ge -2

-5-6-7 -4 -3 -2-1 0 1 2 3


-7y le 14

-7 ( -1 ) le 14

7 le 14

8 b __ 5 gt -1

b __ 5 ( 5 ) gt -1 ( 5 )

b gt -5

-5-6-7-8 -4 -3 -2-1 0 1 2

Check Substitute 0 for b

b __ 5 gt -1

0 __ 5 gt

-1

0 gt -1

9 a -4t ge -80

b -4t ge -80

-4t ____ -4

le -80 ____ -4

t le 20

It will take the physicist 20 or fewer hours to change

the temperature of the metal

c The physicist would have to cool the metal for

more than 20 hours for the temperature of the

metal get cooler than -80deg C

10 You reverse the inequality symbol when you divide

or multiply both sides of an inequality by a negative

number


11 x - 35 gt 15

_ + 35 _ +35

x gt 50

100 20 30 40 50 60 70 80 90100


x - 35 gt 15

51 minus 35 gt 15

16 gt 15

12 193 + y ge 201

_ -193 _ minus193

y ge 8

10 2 3 4 5 6 7 8 9 10


193 + y ge 201

193 + 9 ge 201

202 ge 201

13 - q

__ 7 ge -1

- q

__ 7 ( -7 ) le -1 ( -7 )

q le 7

8 9 105 6 70 1 2 3 4

Check Substitute ndash14 for q

- q

__ 7 ge -1

- -14 ____ 7 ge

-1

2 ge -1

14 -12x lt 60

-12x _____ -12

gt 60 ____ -12

x gt -5

0-10-9 -8 -7 -6 -5 -4 -3 -2-1

Check Substitute -4 for x

-12x lt 60

-12 ( -4 ) lt 60

48 lt 60

15 5 gt z -3

_ +3 _ +3

8 gt z

z lt 8

10 2 3 4 5 6 7 8 9 10

Check Substitute 7 for z

5 gt z - 3

5 gt 7 - 3

5 gt 4


16 05 le y __

8

05 ( 8 ) le y __

8 ( 8 )

4 le y

y ge 4

8 9 105 6 70 1 2 3 4


05 le y __

8

05 le 8 __

8

05 le 1


Let x = the number of inches

12 + x le 28

_ -12 _ -12

x le 16

The puppy will grow at most 16 inches more


Let w = the total weight of the kittens

w __ 7 lt 35

w __ 7 ( 7 ) lt 35 ( 7 )

w lt 245

The possible combined weights of the kittens is any

weight less than 245 ounces but greater than 0


Let s = the number of sides

6s le 42

6s ___ 6 le 42 ___

6

s le 7

The length of a side is at most 7 inches


Let x = the amount Tom needs to spend

3025 + x ge 50

_ -3025 _ -3025

x ge 1975

Tom needs to spend at least $1975


Let w = the width of the region

155w ge 1705

155w ______ 155

ge 1705 _____ 155

w ge 11

The possible width of the region is at least 11 feet


Let t = the number of seconds

thinsp-12t lt -120

-12t _____ -12

gt -120 _____ -12

t gt 10

No let t be the number of seconds the descent

takes the inequality is ndash12t lt -120 so t gt 10 so

the submarinersquos descent takes 10 seconds or more


Let s = the amount of spinach

3s le 10

3s ___ 3 le 10 ___

3

s le 3 1 __ 3

The greatest amount of spinach she can buy is 3 1 __ 3

pounds


Let m = the amount of money Gary has

m ___ 05

le 55

m ___ 05

( 05 ) le 55 ( 05 )

m le 275

Gary has at most $275


Let x = the number of pounds of onions

125x le 3

125x _____ 125

le 3 ____ 125

x le 24

No 125x le 3 x le 24 so 24 pounds of onions is

the most Florence can buy 24 lt 25 so she cannot

buy 25 pounds


26 If you divide both sides of -7z ge 0 by -7 and do

not reverse the inequality symbol you get z ge 0

This is incorrect because if you choose a value from

the possible solutions such as z = 1 and substitute

it into the original equation you get -7 ge 0 which is

not true

27 x gt 9 for each inequality in each case the number

added to x is 9 less than the number on the right

side of each inequality so x gt 9 is the solution

28 Find the formula for the volume of a rectangular

prism

V = lwh

Write and solve an inequality

Let h = the height in inches

( 13 ) ( 1 __ 2 ) h lt 65

65h lt 65

65h ____ 65

lt 65 ___ 65

h lt 10

All heights greater than 0 in and less than 10 in

( 13 ) ( 1 __ 2 ) h lt 65 65h lt 65 h lt 10 A height cannot

be 0 or less than 0 so h gt 0 and h lt 10


LESSON 72Your Turn

3 Let a represent the amount each member must

raise

Number of members 45

Starting amount $1240

Target amount $6000

starting number amount each is greater target

amount plus of members times member than or amount

must raise equal to

darr darr darr darr darr darr darr $1240 + 45 middot a ge $6000

Equation 1240 + 45a ge 6000

4 Let n represent the greatest number of rides Ella

can go on

Starting amount $40

Admission price $6

Cost for each ride $3

admission cost for number is less starting

price plus each ride times of rides than or amount

equal to

darr darr darr darr darr darr darr $6 + $3 middot n le $40

Equation 6 + 3n le 40

5 x is the solution of the problem the quantity you

are looking for

3x means that for a reason given in the problem

the quantity you are looking for is multiplied by 3

+ 10 means that for a reason given in the problem

10 is added to 3x

gt 30 means that after multiplying the solution x by

3 and adding 10 to it the result must be greater

than 30

Sample answer An exam consists of one essay

question worth 10 points and several multiple choice

questions worth 3 points each If Petra earns full

points on the essay question how many multiple

choice questions must she get right in order to get

a score greater than 30 points

6 x is the solution of the problem the quantity you are

looking for



-50 means that for a reason given in the problem

50 is subtracted from 5x

le 100 means that after multiplying the solution x by

5 and subtracting 50 from it the result must be less

than or equal to 100

Sample answer Miho has $100 to spend on her

garden She spends $50 on gardening supplies

Vegetable plants cost $5 each What is the greatest

number of plants she can buy

Guided Practice

1

- -- -

-

lt

++++++

+ + ++ + +

+

2

---

gt

+ + ++ + +

+ + ++ + +

+ + +


raise

Amount to be raised $7000

Amount already raised $1250

Number of members 92 amount number of amount each is greater target

already plus members times member than or amount

raised raises equal to

darr darr darr darr darr darr darr 1250 + 92 times a ge 7000

The inequality that represents this situation is

1250 + 92a ge 7000

4 x is the solution of the problem 7x is the solution

multiplied by 7 -18 means that 18 is subtracted

from 7x le 32 means that the result can be no

greater than 32

5 Sample answer Alexa has $32 to spend on T-shirts

for her friends She has a gift card worth $18 T-shirts

cost $7 each How many T-shirts can Alexa buy

6 Sample answer Choose a variable to represent

what you want to find Decide how the information in

the problem is related to the variable Then write an

inequality


7 number possible amount is

of times amount each minus for more $200

friends friend earns supplies than

darr darr darr darr darr darr darr 3 middot a - $28 gt $200

3a + 28 gt 200

Let a = possible amount each friend earned

8 cost of number cost of less than amount

bagel times of bagels plus cream or equal Nick

cheese to has

darr darr darr darr darr darr darr $075 middot n + $129 le $700

075n + 129 le 700

Let n = the number of bagels Nick can buy

9 number max amount amount less than total amount

of shirts times each shirt minus of gift or equal Chet can

can cost certificate to spend

darr darr darr darr darr darr darr 4 sdot a - 25 le 75

4a - 25 le 75Let a = the maximum amount each shirt can cost


10 number of number number of is less total

seats in plus of rows on times seats in than equal number

balcony ground floor one row equal to of people

darr darr darr darr darr darr darr 120 + 32 middot n le 720

120 + 32n le 720

Let n = the number of people in each row

11 amount commission amount greater than earning

earned per plus rate times of sales or equal to for this

month month

darr darr darr darr darr darr darr 2100 + 005 middot s ge 2400

2100 + 005s ge 2400

Let s = the amount of her sales

12 number number average greater

of cans plus of days times number of than goal

collected cans per day

darr darr darr darr darr darr darr 668 + 7 n gt 2000

668 + 7n gt 2000

Let n = the average number of cans collected each

day

13 cost per cost per number of less than total amount

month plus CD times CDs she or equal spent in

buys to a month


$7 + $10 middot c le $100

7 + 10c le 100

Let c = the number of CDs Joanna buys

14 cost of cost for number of less than total amount

belt plus each times shirts he or equal of money

shirt can buy to Lionel has


$22 + $17 middot n le $80

22 + 17n le 80

Let n = the number of shirts he can buy

15 Sample answer Mr Craig is buying pizzas for the

7th grade field day He can spend up to $130 and

needs 15 pizzas He has a $20 coupon How much

can he spend per pizza $10 or less per pizza

16 ldquoat leastrdquo in this case means m ge 25

17 ldquono greater thanrdquo in this case means k le 9

18 ldquoless thanrdquo in this case means p lt 48

19 ldquono more thanrdquo in this case means b le -5

20 ldquoat mostrdquo in this case means h le 56

21 ldquono less thanrdquo in this case means w ge 0

22 The average score of the three tests Marie has

already taken and the three she will still take

is given by

95 + 86 + 89 + 3s

________________ 6

where s is the average score on the three remaining

tests

This value needs to be greater than or equal to 90

so the inequality can be written as

95 + 86 + 89 + 3s

________________ 6 ge 90 or

95 + 86 + 89 + 3s ge 540 or

270 + 3s ge 540


23 5 + 10 lt 20 Sample answer If the combined length

of two sides of a triangle is less than the length of

the third side the two shorter sides will not be long

enough to form a triangle with the third side Here

the combined length of 5 ft and 10 ft is 15 ft not

enough to make a triangle

24 -m gt 0 Sample answer Since m is less than 0 it

must be a negative number -m represents the

opposite of m which must be a positive number

since the opposite of a negative number is positive

So -m gt 0

25 n gt 1 __ n if n gt 1

n lt 1 __ n if n lt 1

n = 1 __ n if n = 1

LESSON 73

Your Turn

1 Model the inequality

++

++++

+++

++++

++++

+++

gt

Add seven -1-tiles to both sides of the mat

++

++++

+++

++++

++++

+++

gt

- -- -- --

- -- -- --

Remove zero pairs from both sides of the mat

++

++++

gt

Divide each side into equal groups

++

++++

gt


The solution is x gt 2

+ + +gt


+++++

----

+++++

+ +++++

ge

Add four +1-tiles to both sides of the mat

+++++

----

+++++

+ ++

++++

+++

++++

ge

Remove zero pairs from the left side of the mat

+++++

+++++

+ +++++

++++

ge


+++++

+++++

+ +++++

++++

ge

The solution is h ge 3

+ + + +ge

3 Use inverse operations to solve the inequality

5 - p

__ 6 le 4

5 - 5 - p

__ 6 le 4 - 5

thinsp- p

__ 6 le -1

thinsp-6 ( - p

__ 6 ) ge -6 ( -1 )

p ge 6

Graph the inequality and interpret the circle and

arrow

0 1 4 5 72 3 6 8 9 10

Joshua has to run at a steady pace of at least 6 mih

4 Substitute each value for v in the inequality

3v - 8 gt 22

v = 9 v = 10 v = 11

3 ( 9 ) - 8 gt 22 3 ( 10 ) - 8 gt 22 3 ( 11 ) - 8 gt 22

Evaluate each expression to see if a true inequality

results

3 ( 9 ) - 8 gt 22 3 ( 10 ) - 8 gt

22 3 ( 11 ) - 8 gt

22

27 - 8 gt 22 30 - 8 gt

22 33 - 8 gt

22

19 gt 22 22 gt

22 25 gt

22

not true not true true

v = 11

5 Substitute each value for h in the inequality

5h + 12 le -3

h = -3 h = -4 h = -5

5 ( -3 ) + 12 le -3 5 ( -4 ) + 12 le -3 5 ( -5 ) + 12 le -3


results

5 ( -3 ) + 12 le -3 5 ( -4 ) + 12 le

-3 5 ( -5 ) + 12 le

-3

-15 + 12 le -3 -20 + 12 le

-3 -25 + 12 le

-3

-3 le -3 -8 le

-3 -13 le

-3

true true true

h = -3 h = -4 h = -5


Guided Practice

1 Remove 4 +1-tiles from both sides then divide each

side into 3 equal groups the result is x lt 3


5d - 13 lt 32

5d - 13 + 13 lt 32 + 13

5d lt 45

5d ___ 5 lt 45 ___

5

d lt 9

Graph the inequality

20 6 84 10 12 14 16 18 20


-4b + 9 le -7

-4b + 9 - 9 le -7 - 9

-4b le -16

-4b ____ -4

ge -16 ____ -4

b ge 4


20 6 84 10 12 14 16 18 20

4 Substitute each value for m in the inequality

2m + 18 gt - 4

m = -12 m = -11 m = -10

2 ( -12 ) + 18 gt -4 2 ( -11 ) + 18 gt -4 2 ( -10 ) + 18 gt -4


results

2 ( -12 ) + 18 gt -4 2 ( -11 ) + 18 gt

- 4 2 ( -10 ) + 18 gt

- 4

- 24 + 18 gt -4 - 22 + 18 gt

- 4 - 20 + 18 gt

- 4

- 6 gt - 4 - 4 gt

- 4 - 2 gt

- 4


m = -10

5 Substitute each value for y in the inequality

- 6y + 3 ge 0

y = 1 y = 1 __ 2 y = 0

-6 ( 1 ) + 3 ge 0 -6 ( 1 __ 2 ) + 3 ge 0 -6 ( 0 ) + 3 ge 0


results

-6 ( 1 ) + 3 ge 0 - 6 ( 1 __

2 ) + 3 ge

0 - 6 ( 0 ) + 3 ge

0

-6 + 3 ge 0 -3 + 3 ge

0 0 + 3 ge

0

-3 ge 0 0 ge

0 3 ge

0

not true true true

y = 1 __ 2

y = 0

6 Solve the inequality

65 - 4t ge 15

65 - 65 - 4t ge 15 - 65

-4t ge -5

-4t ____ -4

le -5 ___ -4

t le 125


0 05 1 15 2 25

Lizzy can spend from 0 to 125 h with each student

No 15 h per student will exceed Lizzyrsquos available

time

7 Sample answer Apply inverse operations until you

have isolated the variable If you multiply or divide

both sides of the inequality by a negative number

reverse the direction of the inequality symbol


8 2s + 5 ge 49

2s + 5 - 5 ge 49 - 5

2s ge 44

2s ___ 2 ge 44 ___

2

s ge 22

10 14 1612 18 20 22 24 26 28 30

9 -3t + 9 ge -21

-3t + 9 - 9 ge -21 -9

-3t ge -30

-3t ____ -3

le -30 ____ -3

t le 10

ndash2ndash4ndash6ndash8ndash10 0 2 4 6 8 10

10 55 gt -7v + 6

55 - 6 gt -7v + 6 - 6

49 gt - 7v

49 ___ -7 lt -7v ____ -7

v gt -7

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0

11 21 1 __ 3 gt 3m - 2 2 __

3

21 1 __ 3 + 2 2 __

3 gt 3m - 2 2 __

3 + 2 2 __

3

24 gt 3m

24 ___ 3 gt 3m ___

3

8 gt m or m lt 8

0 1 4 5 72 3 6 8 9 10

12 a ___ -8

+ 15 gt 23

a ___ -8

+ 15 - 15 gt 23 - 15

a ___ -8

gt 8

-8 ( a ___ -8

) lt -8 ( 8 )

a lt -64

-70 -68 -66 -64 -62 -60


13 f __ 2 - 22 lt 48

f __ 2 - 22 + 22 lt 48 + 22

f __ 2 lt 70

2 ( f __ 2 ) lt 2 ( 70 )

f lt 140

100 110 120 130 140 150

14 -25 + t __ 2 ge 50

-25 + 25 + t __ 2 ge 50 + 25

t __ 2 ge 75

2 ( t __ 2 ) ge 2 ( 75 )

t ge 150

130 140 150 160 170 180

15 10 + g ___

-9 gt 12

10 - 10 + g ___

-9 gt 12 - 10

g ___

-9 gt 2

-9 ( g ___

-9 ) lt -9 ( 2 )

g lt -18

-20 -18 -14 -12 -10-16

16 252 le -15y + 12

252 - 12 le -15y + 12 - 12

24 le - 15y

24 ____ -15

ge -15y

_____ -15

y le -16

-20 -18 -14 -12 -10-16

17 -36 ge -03a + 12

-36 - 12 ge -03a + 12 - 12

-48 ge -03a

-48 _____ -03

le -03a ______ -03

a ge 16

10 11 12 13 14 16 17 18 19 2015

18 80 - 2w ge 50

80 - 80 - 2w ge 50 - 80

- 2w ge -30

-2w ____ -2

le -30 ____ -2

w le 15

The width is a positive number no greater than

15 inches the possible widths in inches will be 10

11 12 13 14 and 15

19 Inequality 7n - 25 ge 65

7n - 25 ge 65

7n - 25 + 25 ge 65 + 25

7n ge 90

7n ___ 7 ge 90 ___

7

n ge 12 6 __ 7

Grace must wash at least 13 cars because n must

be a whole number


20 No Sample answer If x lt x - 1 then subtracting

x from both sides of the inequality 0 lt -1 That is

untrue so no value of x can be less than x - 1

21 a

10 3 42 5 6 7 8 9 10

b

10 3 42 5 6 7 8 9 10

c A number cannot simultaneously be less than 2

and greater than 7 Therefore there is no number

that satisfies both inequalities

d Consider the graph of x gt 2 and x lt 7

The solution includes all the numbers on the

number line so the solution set is all numbers

22 Sample answer Joseph might have reasoned that n

was first multiplied by 2 then increased by 5 to give

a result less than 13 Working backward he would

have subtracted 5 from 13 ( to get 8 ) then divided by

2 ( to get 4 ) giving n lt 4 Shawnee would have

followed these same steps but would have used a

variable and invers operations

MODULE 7

Ready to Go On

1 n + 7 lt -3

thinsp _ -7

_ -7

n lt -10

2 5p ge -30

5p

___ 5 ge -30 ____

5

p ge -6

3 14 lt k + 11

_ -11 _ -11

3 lt k

4 d ___ -3

le minus6

( -3 ) ( d ) ge ( -3 ) ( -6 )

d ge 18


5 c - 25 le 25

_ +25 _ +25

c le 5

6 12 ge -3b

12 ___ -3

le -3b _____ -3

-4 le b

7 Let n be the number of minimum points Jose must

score 562 + n ge 650

Solve the inequality

562 + n ge 650

_ -562 _ -562

n ge 88

8 Let t be the number of minutes Lainey can descend

-20 - 20t ge -100

9 2s + 3 gt 15

_ -3 _ -3

2s gt 12

2s ___ 2

gt 12 ___ 2

s gt 6

10 - d ___ 12

- 6 lt 1

_ +6 _ +6

- d ___ 12

lt 7

12 ( - d ___ 12

) lt 12 ( 7 )

-d lt 84

d gt -84

11 -6w - 18 ge 36

_ +18 _ +18

thinsp-6w ge 54

-6w _____ -6

le 54 ___ -6

w le -9

12 z __ 4 + 22 le 38

_ -22 _ -22

z __ 4 le 16

4 ( z __ 4 ) le 4 ( 16 )

z le 64

13 b __ 9 - 34 lt -36

_ +34 _ +34

b __ 9 lt -2

9 ( b __ 9 ) lt 9 ( -2 )

b lt -18

14 -2p + 12 gt 8

-12 ____

-12 ____

-2p gt -4

-2p

____ -2 lt -4 ___

-2

p lt 2

15 Sample answer Look for key words or phrases

that indicate inequality such as ldquogreater thanrdquo

ldquoless thanrdquo ldquoat mostrdquo or ldquoat leastrdquo


MODULE 8 Modeling Geometric Figures

Are You Ready

1 3x + 4 = 10

3x + 4 - 4 =10 - 4

3x = 6

3x ___ 3 = 6 __

3

x = 2

2 5x - 11 = 34

5x - 11 + 11 = 34 + 11

5x = 45

5x ___ 5 = 45 ___

5

x = 9

3 -2x + 5 = -9

-2x + 5 - 5 = -9 - 5

-2x = -14

-2x ____ -2

= -14 ____ -2

x = 7

4 -11 = 8x + 13

-11 - 13 = 8x + 13 - 13

-24 = 8x

-24 ____ 8 = 8x ___

8

-3 = x

5 4x - 7 = -27

4x - 7 + 7 = -27 + 7

4x = -20

4x ___ 4 = -20 ____

4

x = -5

6 1 __ 2 x + 16 = 39

1 __ 2 x + 16 - 16 = 39 - 16

1 __ 2 x = 23

( 2 ) 1 __ 2 x = ( 2 ) 23

x = 46

7 12 = 2x - 16

12 + 16 = 2x - 16 + 16

28 = 2x

28 ___ 2 = 2x ___

2

14 = x

8 5x - 15 = -65

5x - 15 + 15 = -65 + 15

5x = -50

5x ___ 5 = -50 ____

5

x = -10

9 x __ 5 = 18 ___

30

x times 30 = 5 times 18

30x = 90

30x ____ 30

= 90 ___ 30

x = 3

10 x ___ 12

= 24 ___ 36


36x = 288

36x ____ 36

= 288 ____ 36

x = 8

11 3 __ 9 = x __

3

3 times 3 = 9 times x

9 = 9x

9 __ 9 = 9x ___

9

1 = x

12 14 ___ 15

= x ___ 75


1050 = 15x

1050 _____ 15

= 15x ____ 15

70 = x

13 8 __ x = 14 ___ 7

8 times 7 = x times 14

56 = 14x

56 ___ 14

= 14x ____ 14

4 = x

14 14 ___ x = 2 __ 5


70 = 2x

70 ___ 2 = 2x ___

2

35 = x

15 5 __ 6 = x ___

15


75 = 6x

75 ___ 6 = 6x ___

6

125 = x

Solutions KeyGeometry

UNIT

4


16 81 ___ 33

= x ____ 55


4455 = 33x

4455 _____ 33

= 33x ____ 33

135 = x

LESSON 81

Your Turn

6 Length 132 in times 5 ft ____ 3 in

= 22 ft

Width 6 in times 5 ft ____ 3 in

= 10 ft

Area 10 ft ( 22 ft ) = 220 square feet

Guided Practice

1

Blueprint

length (in)3 6 9 12 15 18

Actual

length (ft)5 10 15 20 25 30

a The wall is 30 feet long

b 25 ft times 3 in ____ 5 ft

= 15 in

2 The width is 7 in times 4 ft ____ 2 in

= 14 ft and the length is

14 in times 4 ft ____ 2 in

= 28 ft and the area is

28 ft ( 14 ft ) = 392 square feet

3 Length 10 cm times 5 m _____ 2 cm

= 25 m

Width 6 cm times 5 m _____ 2 cm

= 15 m

Area 25 m ( 15 m ) = 375 square meters

4 a

b Length is 36 m and width is 24 m using both

scales

5 If the scale drawing is complete and accurate you

can use it to find any length or area of the object of

the drawing


6 a 2 in times 40 cm ______ 1 in

= 80 cm

15 in times 40 cm ______ 1 in

= 60 cm

The dimensions of the painting are 80 cm by 60 cm

b 80 cm times 60 cm = 4800 c m 2

c 80 cm times 1 in _______ 254 cm

asymp 315 in

60 cm times 1 in _______ 254 cm

asymp 236 in

The dimensions of the painting are approximately

315 in by 236 in

d 315 in times 236 in asymp 743 i n 2

7 120 ft times 1 unit _____ 5 ft

= 24 units

75 ft times 1 unit _____ 5 ft

= 15 units

The dimensions of the drawing are 24 units by

15 units

8 Sample answer 2 in6 ft 1 in3 ft and 1 in1 yd

9 Because the scale is 10 cm1 mm and because

10 cm is longer than 1 mm the drawing will be

larger

10 a Let r represent the scale

54 ft times r = 810 m

r = 810 m ______ 54 ft

r = 150 m ______ 1 ft

The scale is 1 ft = 150 m

b 54 ft times 12 in _____ 1 ft

= 648 in

Let b represent the number of tiny bricks

b = 648 in times 1 brick ______ 04 in

b = 162 bricks

The model is 162 tiny bricks tall

11 a Let h represent the height of the model

h = 30 ft times 126 cm _______ 1 ft

h = 378 cm

Let n represent the number of toothpicks

n = 378 cm times 1 toothpick

_________ 63 cm

n = 6 toothpicks

The model will be 6 toothpicks tall

b 378 cm times 1 swab ______ 76 cm

asymp 5 swabs

The model will be about 5 cotton swabs tall


12 If the area of the scale drawing is 100 square cm

then one side is 10 cm Let s represent the side

length of the actual floor

s = 10 cm times 2 ft _____ 1 cm

s = 20 ft

So the area is 20 ft(20 ft) = 400 ft 2

The ratio of areas is 100 square cm 400 square feet

or 1 square cm 4 square feet


13 Decide on the new scale yoursquod like to use Then find

the ratio between the old scale and the new scale

and redraw the scale drawing accordingly For

example the ratio could be 13 In that case you

would redraw the dimensions at three times the

original size

14 Sample answer 1 __ 4 in 8 ft 40 ft by 24 feet 960 f t

2

LESSON 82

Guided Practice

1 The two angles 45deg and a right angle or 90deg with

the included side 8 cm determine the point at which

the sides meet so a unique triangle is formed

2 The sum of the measures of the two short sides

4 + 3 = 7 The sum is less than the measure of the

long side 11 so no triangle is formed

3 The two angles 40deg and 30deg with the included side

7 cm determine the point at which the sides meet

so a unique triangle is formed


6 + 7 = 13 The sum is greater than the measure of

the long side 12 so a unique triangle is formed

5 Sample answer Segments with lengths of 5 in

5 in and 100 in could not be used to form a

triangle


6 A figure with side lengths of 3 centimeters and 6

centimeters and an included angle of 120deg deter-

mine the length of the third side of a triangle and so

produce a unique triangle

6 cm

3 cm120˚

7 The side lengths proposed are 15 ft 21 ft and 37 ft

The sum of the measures of the two shorter sides

15 + 21 = 36 So the sum is less than the measure

of the long side 37 No such triangle can be created

8 The three angle measures can be used to form

more than one triangle The sign and the scale

drawing are two different-sized triangles with the

same angle measures


9 More than one triangle can be formed Two triangles

can be created by connecting the top of the 2-in

segment with the dashed line once in each spot

where the arc intersects the dashed line The

triangles are different but both have side lengths of

2 in and 1 1 __ 2 in and a 45deg angle not included

between them

10 The third side has a length of 15 in The third side

must be congruent to one of the other two sides

because the triangle is isosceles The third side

cannot measure 6 in because 6 + 6 is not greater

than 15 So the third side must measure 15 in

LESSON 83

Guided Practice

1 triangle or equilateral triangle

2 rectangle

3 triangle

4 rainbow-shaped curve

5 Sample answer Draw the figure and the plane


6 Sample answer A horizontal plane results in cross

section that is a circle A plane slanted between

horizontal and vertical results in an oval cross

section A vertical plane through the cylinder results

in a rectangle A vertical plane along an edge of the

cylinder results in a line cross section

7 You would see circles or ovals with a cone but not

with a pyramid or prism


8 The plane would pass through the cube on a

diagonal from the top to the bottom of the cube

9 a It is a circle with a radius of 12 in

b The cross sections will still be circles but their

radii will decrease as the plane moves away from

the spherersquos center

10 The dimensions of two faces are 12 in by 8 in two

are 8 in by 5 in and two are 12 in by 5 in the

volume is 480 in 3

11 Sample answer If you think of a building shaped like

a rectangular prism you can think of horizontal

planes slicing the prism to form the different floors


LESSON 84

Your Turn

5 Supplementary angles sum to 180deg Sample answer angFGA and angAGC

6 Vertical angles are opposite angles formed by two

intersecting lines

Sample answer angFGE and angBGC

7 Adjacent angles are angles that share a vertex and

one side but do not overlap Sample answer

mangFGD and mangDGC

8 Complementary angles are two angles whose

measures have a sum of 90deg Sample answer

mangBGC and mangCGD

9 Because mangFGE = 35deg and angFGE and angBGC are

vertical angles that means mangBGC = 35deg also

Because lines _

BE and _

AD intersect at right angles

mangBGD = 90deg so mangBGC + mangCGD = 90deg which means

mangBGC + mangCGD = 90deg 35deg + x = 90deg 35deg minus 35deg + x = 90deg minus 35deg x = 55deg

mangCGD = 55deg

10 angJML and angLMN are supplementary so their

measures sum to 180deg mangJML + mangLMN = 180deg 3x + 54deg = 180deg 3x + 54deg - 54deg = 180deg - 54deg 3x = 126deg

3x ___ 3 = 126deg ____

3

x = 42deg

mangJML = 3x = 3 ( 42deg ) = 126deg

11 Sample answer You can stop at the solution step

where you find the value of 3x because the measure

of angJML is equal to 3x

Guided Practice

1 angUWV and angUWZ are complementary angles

2 angUWV and angVWX are adjacent angles

3 angAGB and angDGE are vertical angles

so mangDGE = 30deg

4 mangCGD + mangDGE + mangEGF = 180deg 50deg + 30deg + 2x = 180deg 80deg + 2x = 180deg 2x = 100deg mangEFG = 2x = 100deg

5 mangMNQ + mangQNP = 90deg 3x - 13deg + 58deg = 90deg so 3x + 45deg = 90degThen 3x = 45deg and x = 15deg mangMNQ = 3x - 13deg = 3 ( 15deg ) - 13deg = 45deg - 13deg = 32deg

6 Sample answer Let mangS = x Write and solve an

equation ( x + 3x = 180deg ) to find x then multiply the

value by 3


7 Sample answer angSUR and angQUR are adjacent

They share a vertex and a side

8 Sample answer angSUR and angQUP

9 Sample answer angTUS and angQUN

10 mangQUR = 139deg Sample answer angSUR and angSUP

are supplementary so mangSUP = 180deg - 41deg = 139deg angSUP and angQUR are vertical angles so they are

congruent and mangQUR = mangSUP = 139deg

11 mangRUQ is greater Sample answer angSUR and

angNUR are complementary so

mangNUR = 90deg - 41deg = 49deg mangTUR = 41deg + 90deg which is less than

mangRUQ = 49deg + 90deg

12 Because angKMI and angHMG are vertical angles their

measures are equal

mangKMI = mangHMG

84 = 4x

84 ___ 4 = 4x ___

4

x = 21deg

13 Because angKMH and angKMI are supplementary

angles the sum of their measures is 180deg mangKMH + mangKMI = 180deg x + 84 = 180

x + 84 - 84 = 180 - 84

x = 96

mangKMH = 96deg

14 Because angCBE and angEBF are supplementary

angles the sum of their measures is 180deg mangCBE + mangEBF = 180deg x + 62 = 180

x + 62 - 62 = 180 - 62

x = 118

mangCBE = 118deg

15 Because angABF and angFBE are complementary

angles the sum of their measures is 90deg mangABF + mangFBE = 90deg x + 62 = 90

x + 62 - 62 = 90 - 62

x = 28

mangABF = 28deg

16 Because angCBA and angABF are supplementary

angles the sum of their measures is 180deg mangABF = 28deg so

mangCBA + mangABF = 180deg x + 28 = 180 - 28

x + 28 - 28 = 152

mangCBA = 152deg


17 If the two angles are complementary the sum of

their angles is 90degmangA + mangB = 90deg ( x + 4deg ) + x = 90deg 2x + 4deg = 90deg _ -4deg _ -4deg 2x = 86deg

2x ___ 2 = 86deg ___

2

x = 43degBecause x = mangB then mangB = 43deg and

mangA = 43deg + 4deg so mangA = 47deg

18 If the two angles are supplementary the sum of their

angles is 180degmangD + mangE = 180deg 5x + x = 180deg 6x = 180deg

6x ___ 6 = 180deg ____

6

x = 30degBecause x = mangE then mangE = 30deg and

mangD = 30deg x 5 so mangD = 150deg


their angles is 90deg When angles are divided into

minutes and seconds one apostrophe signifies a

minute and two apostrophes signifies a second

mangJ + mangK = 90deg0000

48deg268+ mangK = 90deg0000

_ -48deg268 _ -48deg268

mangK = 41deg3352

mangK = 41deg3352 or mangK = 41 degrees

33 minutes 52 seconds


20 Yes a parking lot can be built because the measure

of angle K is 180deg - ( 50deg + 90deg ) or 40deg which is

greater than 38deg

21 Disagree the sum of the measures of a pair of

complementary angles is 90deg So the measure of

each angle must be less than 90deg 119deg gt 90deg

22 a The sum of mangA and its complement will be 90deg Let x represent the complement

mangA + x = 90deg 77deg + x = 90deg _ -77deg = _ -77deg x = 13deg The complement of mangA has a measure of 13deg

and a complement of a complement of mangA

would have an angle equal to mangA or 77deg b A complement of a complement of an angle has

the same measure of the angle itself Let xdeg be

the measure of an angle The measure of a

complement of the angle is ( 90 - xdeg ) A complement of that angle has a measure of

( 90 - ( 90 - xdeg ) ) = ( 90 - 90 + xdeg ) = xdeg

MODULE 8

Ready to Go On

1

Living

roomKitchen Office Bedroom Bedroom Bathroom

Actual

ℓ times w ( ft ) 16 times 20 12 times 12 8 times 12 20 times 12 12 times 12 6 times 8

Blueprint

ℓ times w ( in ) 4 times 5 3 times 3 2 times 3 5 times 3 3 times 3 15 times 2

2 No The side lengths proposed are 8 cm 4 cm and

12 cm The sum of the measures of the two shorter

sides 4 + 8 = 12 So no such triangle can be

created

3 The longest side could be 15 cm because 20 cm is

too long given the lengths of the other sides

4 A circle is a possible cross section of a sphere

A point is another

5 A circle rectangle oval and line are possible cross

sections of a cylinder

6 mangBGC and mangFGE are vertical angles so

mangFGE = 50deg


their angles is 90deg mangS + mangY = 90deg

( 2 ( mangY ) - 30deg ) + mangY = 90deg 3 ( mangY ) - 30deg = 90deg _ +30deg = _ +30deg 3 ( mangY ) = 120deg

3 ( mangY ) ________ 3 = 120deg ____

3

mangY = 40deg

mangY = 40deg

8 Sample answer You can use scale drawings to plan

rooms or gardens


MODULE 9 Circumference Area and Volume

Are You Ready

1 416

_ times 13

1248

_ +thinsp4160

5408

5408

2 647

_ times thinsp04

2588

2588

3 705

_ times thinsp94

2820

_ +thinsp63450

66270

6627

4 256

_ timesthinsp049

2304

_ +thinsp10240

12544

12544

5 1 __ 2 ( 14 ) ( 10 )

7 ( 10 )

70 i n 2

6 ( 35 ) ( 35 )

1225 ft 2

7 ( 8 1 __ 2 ) ( 6 )

17 ___ 1 2 sdot 6 3 __

1

51 i n 2

8 1 __ 2 ( 125 ) ( 24 )

1 __ 2 ( 24 ) ( 125 )

( 12 ) ( 125 )

15 m 2

LESSON 91

Your Turn

3 d = 11 cm

C = πd

C asymp 314 ( 11 )

C asymp 3454

The circumference is about 3454 cm

6 C = πd

44 asymp 314d

44 ____ 314

asymp d

d asymp 1401 yards

Divide the diameter of the garden by the digging

rate

1401 divide 7 = 2001

It takes Lars about 2 hours to dig across the garden

Guided Practice

1 d = 9 in

C asymp 314 ( 9 )

C asymp 2826 in

2 r = 7 cm

C = 2πr

C asymp 2 ( 22 ___ 7 ) ( 7 )

C asymp 44 cm

3 d = 25 m

C = πd

C asymp 314 ( 25 )

C asymp 785 m

4 r = 48 yd

C = 2πr

C asymp 2 ( 314 ) ( 48 )

C asymp 3014 yd

5 r = 75 in

C = 2πr

C asymp 2 ( 314 ) ( 75 )

C asymp 471 in

6 Find the diameter

C = πd

66 asymp 314d

66 ____ 314

asymp 314d _____ 314

21 asymp d

Find the cost

Carlos needs 21 + 4 = 25 feet of rope

25 times $045 = $1125

Carlos will pay $1125 for the rope

7 Because C = π yd and C = πd d = 1 yd then

r = 05 yd

d = 1 yd

8 Because C = 788 ft and C = 2πr

2πr = 788

2πr ___ 2π

= 788 ____ 2π

r asymp 788 _______ 2 ( 314 )

r asymp 1255 ft

d = 2r asymp 2 ( 1255 ft )

d asymp 2510 ft

9 d = 2r so r = d __ 2 asymp 34 ___

2

r asymp 17 in

C = πd asymp 314 ( 34 )

C = 1068 in


10 Use the formula C = πd and substitute

314 for π and 13 for the diameter


11 d = 59 ft

C = πd

C asymp 314 ( 59 )

C asymp 1853 ft

12 r = 56 cm

C = 2πr

C asymp 2 ( 22 ___ 7 ) ( 56 )

C asymp 352 cm

13 d = 35 in

C = πd

C asymp ( 22 ___ 7 ) ( 35 )

C asymp 110 in

14 Sample answer In exercises 12 and 13 the radius

or diameter is a multiple of 7

15 r = 94 ft

d = 2r = 2 ( 94 )

d = 188 ft

C = πd

C asymp 314 ( 188 )

C asymp 590 ft

16 d = 475 in

r = d __ 2 = 475 ____

2

r = 2375 in

C = πd

C asymp 314 ( 475 )

C asymp 14915 in

17 d = 18 in

r = d __ 2 = 18 ___

2

r = 9 in

C = πd

C asymp 314 ( 18 )

C asymp 5652 in

18 r = 15 ft

C = 2πr

C asymp 2 ( 314 ) ( 15 ) = 942 ft

The cost for edging is C times $075 per foot

so ( 942 ) ( 075 ) = 7065 or about $707

19 C = πd

C asymp ( 22 ___ 7 ) ( 63 )

C asymp 198 ft

The distance traveled is 12 times the

circumference of the Ferris wheel so

distance = 12 ( 198 ) or about 2376 ft

20 C = πd asymp 314 ( 2 )

C asymp 628 ft

Converting km to ft

2 km sdot ( 3280 ft _______

1 km ) = 6560 ft

6560 ft

_______ 628 ft

= 104459

The wheel makes about 1045 revolutions

21 The distance your friend walks is half the

circumference of the pond

1 __ 2 C = 1 __

2 πd asymp 1 __

2 sdot 314 ( 025 ) = 03925

Your friend walks approximately 03925 mi

The difference is 03925 - 025 = 01425

Your friend walks about 014 mi farther

22 Capitol Rotunda Dimensions

Height 180 ft

Circumference 3015 ft

Radius r = C ___ 2π asymp 3015

_______ 2 ( 314 )

asymp 48 ft

Diameter d = 2r = 2 ( 48 ) = 96 ft


23 The length of the fence is half the circumference

plus the diameter

1 __ 2 C = 1 __

2 πd asymp 1 __

2 sdot 314 ( 30 ) = 471

The total distance is 471 + 30 = 771 ft

The total cost is the length of fence times the cost

per linear foot

( 771 ft ) ( $925 _____

ft ) = $71318

It will cost about $71318

24 The circumference of the patio is

C = πd asymp 314 ( 18 ) = 5652 ft

Converting the length of one strand of lights from

inches to feet

( 54 in ) ( 1 ft _____ 12 in

) = 45 ft

To find the number of strands of lights divide the

circumference by the length of one strand

5652 ft _______ 45 ft

= 1256

Because Sam cannot buy a fraction of a strand he

must buy 13 strands

25 The distance is the difference in the circumferences

C inner

= πd asymp 314 ( 150 ) = 471 ft

The outer diameter is 150 ft + 2 ( 2 ft ) = 154 ft

C outer

= πd asymp 314 ( 154 ) = 48356 ft

The difference is 48356 - 471 = 1256 ft

It is about 1256 ft farther

26 No The circumference of the larger gear is about

πd asymp 314 ( 4 ) = 1256 inches The circumference of

the smaller gear is about πd asymp 314 ( 2 ) = 628

inches So the circumference of the larger gear is

628 inches more than the circumference of the

smaller gear


27 Pool B about 057 m or 184 ft Sample answer

24 feet asymp 732 m so the diameter of Pool B is

greater and the circumference is greater

314 ( 75 ) - 314 ( 732 ) = 314 ( 018 ) asymp 057

057 m asymp 187 ft

LESSON 92

Your Turn

4 A = π r 2 A = π ( 10 ) 2

A asymp 314 ( 10 ) 2

A asymp 314 sdot 100

A asymp 314 f t 2

Guided Practice

1 r = d __ 2 = 14 ___

2 = 7 m

A = π r 2 A = π ( 7 ) 2

A asymp 314 ( 7 ) 2

A asymp 314 sdot 49

A asymp 1539 m 2

2 A = π r 2 A = π ( 12 ) 2

A asymp 314 ( 12 ) 2


A asymp 4522 m m 2

3 r = d __ 2 = 20 ___

2 = 10 yd

A = π r 2 A = π ( 10 ) 2

A asymp 314 ( 10 ) 2


A asymp 314 y d 2

4 A = π r 2 A = π ( 8 ) 2

A asymp 314 ( 8 ) 2

A asymp 314 sdot 64

A asymp 20096 i n 2

5 r = d __ 2 = 12 ___

2 = 6 cm

A = π r 2 A = π ( 6 ) 2

A asymp 314 ( 6 ) 2

A asymp 314 sdot 36

A asymp 11304 c m 2

6 r = d __ 2 = 13 ___

2 = 65 in

A = π r 2 A = π ( 65 ) 2

A asymp 314 ( 65 ) 2


A asymp 13267 i n 2

7 C = 4π = 2πr

4π ___ 2π

= 2πr ___ 2π

r = 2

A = π r 2 A = π ( 2 ) 2

A = 4π square units

8 C = 12π = 2πr

12π ____ 2π

= 2πr ___ 2π

r = 6

A = π r 2 A = π ( 6 ) 2


9 C = π __ 2 = 2πr

π __ 2 divide 2π = 2πr ___

2π

π __ 2 sdot 1 ___

2π = r

1 __ 4 = r

A = π r 2

A = π ( 1 __ 4 ) 2 = π ( 1 ___

16 )

A = π ___ 16

square units

10 A = π r 2 = 64π

π r 2 ___ π = 64π ____ π

r 2 = 64

r = 8

C = 2πr

= 2π ( 8 )

=16π yd

11 A = π r 2


12 r = d __ 2 = 10 ___

2 = 5 in

A = π r 2 A = π ( 5 ) 2

A asymp 314 ( 5 ) 2

A asymp 314 sdot 25

A asymp 785 i n 2

13 A = π r 2 A = π ( 16 ) 2

A asymp 314 ( 16 ) 2


A asymp 80384 c m 2

14 The area of the window is half the area of a circle of

diameter 36 in

r = d __ 2 = 36 ___

2 = 18 in

A semicircle

= 1 __ 2 π r 2

A semicircle

= 1 __ 2 π ( 18 ) 2

A semicircle

asymp 1 __ 2 ( 314 ) ( 18 ) 2

A semicircle

asymp 05 sdot 314 sdot 324

A asymp 50868 i n 2


15 If the point ( 3 0 ) lies on the circle and the origin is

its center the radius of the circle is 3 units

A = π r 2 A = π ( 3 ) 2

A asymp 314 ( 3 ) 2

A asymp 314 sdot 9A asymp 2826 square units

16 The difference in areas is given by

A r = 75 mi

- A r = 50 mi

π ( 75 ) 2 - π ( 50 ) 2

= π ( 7 5 2 minus 5 0 2 ) = π ( 5625 minus 2500 ) = π ( 3125 ) asymp 98125

The area of the relayed signal is about 9813 mi 2

greater

17 The area of the field which is not reached by the

sprinkler is the area of the field minus the area

reached by the sprinkler or s 2 minus π r 2 where

s = 12 m and r is the radius of the circular area The

diameter of the circle is equal to a side of the field

12 m so the radius is 12 ___ 2 = 6 m So

s 2 minus π r 2 = 1 2 2 minus π ( 6 ) 2

= 144 minus π ( 36 )

asymp 144 minus 11304 = 3096

The area not reached by the sprinkler is

approximately 3096 m 2

18 No the area of the regular pancake is 4π in 2 and the

area of the silver dollar pancake is π in 2 so the area

of the regular pancake is 4 times the area of the

silver dollar pancake

19 No the top of the large cake has an area 9 times

that of the small cake The area of the top of the

large cake is 144π in 2 and that of the small cake is

16π in 2

20 Sample answer First find the radius of the circle by

using the formula C = 2πr Then substitute the

radius into the formula for the area of a circle

21 The 18-inch pizza is a better deal because it costs

about $20

_____ π ( 9 ) 2

asymp $008 or 8 cents per square inch

while the 12-inch pizza costs about $10

_____ π ( 6 ) 2

asymp $009

or 9 cents per square inch

22 a Because the bear can walk at a rate of 2 miles

per hour and was last seen 4 hours ago the

radius of the area where the bear could be found

is given by ( 2 miles per hour ) ( 4 hours ) = 8 miles

A = π r 2 = π ( 8 ) 2

= π ( 64 )

asymp 20096

The searchers must cover an area of about

201 mi 2

b The additional area is the difference in areas of

circles with radii ( 2 miles per hour ) ( 5 hours )

= 10 miles and the original 8 miles

A new

minus A old

= π ( 10 ) 2 - π ( 8 ) 2

= π ( 1 0 2 - 8 2 ) = π ( 100 - 64 )

= π ( 36 ) asymp 11304

The searchers would have to cover about 113 mi 2

more area


23 No the combined area is 2π r 2 while the area of a

circle with twice the radius is 4π r 2

24 The area is multiplied by a factor of n 2

25 To find the part that is the bullrsquos-eye take the ratio of

the area of the bullrsquos-eye to that of the whole target

The radius of the bullrsquos-eye is 3 __ 2 = 15 in and

the radius of the whole target is 15 ___ 2 = 75 in

A

bullrsquos-eye ________

A whole target

=

π ( 15 ) 2 ______

π ( 75 ) 2

= ( 15 ) 2

_____ ( 75 ) 2

= 225 _____ 5625

= 004

The bullrsquos-eye is 004 or 4 of the whole target

LESSON 93

Your Turn

2 The figure can be separated into a rectangle and

two right triangles

The dimensions of the large rectangle are

length = 8 + 3 = 11 ft width = 4 ft

The dimensions of the two small triangles are

base = 3 ft height = 2 ft ( upper triangle ) base = 3 ft height = 3 ft ( lower triangle ) The area of the rectangle is

A = ℓw = 11 sdot 4 = 44 f t 2

The area of the upper triangle is

A = 1 __ 2 bh = 1 __

2 sdot 3 sdot 2 = 3 f t 2

The area of the lower triangle is

A = 1 __ 2 bh = 1 __

2 sdot 3 sdot 3 = 45 f t 2

Therefore the total area of the figure is

44 + 3 + 45 = 515 f t 2

3 The figure can be separated into a square and a

semicircle

Each side of the square is equal to 10 m

The radius of the semicircle is half the diameter

or 10 ___ 2 = 5 m

The area of the square is

A = s 2 = 1 0 2 = 100 m 2

The area of the semicircle is

A = 1 __ 2 π r 2

A asymp 1 __ 2 sdot 314 sdot ( 5 ) 2

A asymp 1 __ 2 sdot 314 sdot 25

A asymp 3925 m 2

Therefore the approximate total area of the figure is

100 + 3925 = 13925 m 2


4 The composite figure is made up of a rectangle and two

semicircles which can be combined to form one circle

The dimensions of the rectangle are

length = 5 ft width = 4 ft

The diameter of the circle is 4 ft so the radius is

4 __ 2 = 2 ft

The area of the rectangle is

A = ℓw = 5 sdot 4 = 20 f t 2

The area of the circle is

A = π r 2 A asymp 314 sdot ( 2 ) 2

A asymp 314 sdot 4A asymp 1256 f t 2

The approximate total area is the sum of these

two areas

20 + 1256 = 3256 f t 2

Because the glass costs $28 per square foot

multiply the total area by the cost per square foot

( 3256 f t 2 ) ( $28 ____

f t 2 ) = $91168

It will cost about $91168 to replace the glass

Guided Practice

1 Separate the figure into a triangle a rectangle and

a parallelogram

Find the area of each figure

For triangle A = 1 __ 2 bh = 1 __

2 ( 4 ) ( 2 ) = 4

For rectangle A = ℓw = ( 5 ) ( 3 ) = 15

For parallelogram A = bh = ( 5 ) ( 3 ) = 15

Triangle 4 cm 2 rectangle 15 cm

2 parallelogram

15 cm 2

Step 3 Find the area of the composite figure

4 + 15 + 15 = 34 cm 2

The area of the irregular shape is 34 cm 2

2 Method 1

A 1 = ℓw A

2 = ℓw

= 12 sdot 9 = 20 sdot 9 = 108 = 180

Total area = 288 c m 2

Method 2

A 1 = ℓw A

2 = ℓw

= 9 sdot 8 = 12 sdot 8 = 72 = 216


3 Separate the figure into a trapezoid with h = 5 ft

b 1 = 7 ft and b 2 = 4 ft and a parallelogram with

base = 4 ft and height = 4 ft

For trapezoid A = 1 __ 2 h ( b

1 + b

2 )

A = 1 __ 2 ( 5 ) ( 7 + 4 )

A = 1 __ 2 ( 5 ) ( 11 ) = 275 f t 2

For parallelogram A = bh = ( 4 ) ( 4 ) = 16 f t 2

Find the area of the composite figure

275 + 16 = 435 ft 2

Multiply the total area by the cost per square foot to

find the cost

( 435 f t 2 ) ( $225 _____

f t 2 ) = $9788

4 The first step is separating the composite figure into

simpler figures


5 Area of square A = s 2 = 2 6 2 = 676 i n 2

Area of semicircle A = 1 __ 2 π r 2

A asymp 1 __ 2 sdot 314 sdot ( 13 ) 2


A asymp 26533 i n 2

The approximate total area is the sum

676 + 26533 = 94133 in 2

6 a The floor of the closet is a composite of a

rectangle with length = 10 ft and width = 4 ft and

a triangle with base = 6 ft and height = 3 + 4 = 7 ft

Area of rectangle A = ℓw = 10 sdot 4 = 40 f t 2

Area of triangle A = 1 __ 2 bh

A = 1 __ 2 sdot 6 sdot 7

A = 1 __ 2 sdot 42

A = 21 f t 2

The total area is the sum

40 + 21 = 61 f t 2

b The cost is the area multiplied by the cost per

square foot

( 61 f t 2 ) ( $250 _____

f t 2 ) = $15250

7

O 42-2-4

2

-4

y

A (-2 4) B (0 4)

C (2 1)D (5 1)

E (5 -2)F (-2 -2)

The area can be thought of as a composite of a

trapezoid and a rectangle

For trapezoid Let b 1 of the trapezoid be the

segment from the point ( -2 1 ) point C with length

4 units b 2 be from point A to point B with length

2 units and height equal to 3 units

For rectangle The corners of the rectangle are

( -2 1 ) D E and F Let the length of the rectangle

be 7 units and the width be 3 units

Area of trapezoid

A = 1 __ 2 h ( b

1 + b

2 )

A = 1 __ 2 ( 3 ) ( 4 + 2 )

A = 1 __ 2 ( 3 ) ( 6 ) = 9 square units


Area of rectangle A = ℓw

A = 7 sdot 3 A = 21 square units


9 + 21 = 30 square units

8 The field is a composite of a square with side = 8 m

a triangle with base = 8 m and height = 8 m and a

quarter of a circle with radius = 8 m

Area of square A = s 2 = 8 2 = 64 m 2


A = 1 __ 2 sdot 8 sdot 8

A = 1 __ 2 sdot 64

A = 32 m 2

Area of quarter circle A = 1 __ 4 π r 2

A asymp 1 __ 4 sdot 314 sdot ( 8 ) 2


A asymp 5024 f t 2


64 + 32 + 5024 = 14624 m 2

9 The bookmark is a composite of a rectangle with

length = 12 cm and width = 4 cm and two

semicircles which combine to form a full circle with

diameter = 4 cm so radius = 4 __ 2 = 2 cm

Area of rectangle A = ℓw = 12 sdot 4 = 48 c m 2

Area of circle A = π r 2 A asymp 314 sdot ( 2 ) 2

A asymp 314 sdot 4 A asymp 1256 c m 2


48 + 1256 = 6056 cm 2

10 The pennant is a composite of a rectangle with

length = 3 ft and width = 1 ft and a triangle with




A = 1 __ 2 sdot 1 sdot 1

A = 1 __ 2 sdot 1

A = 05 f t 2

The area of one pennant is the sum

3 + 05 = 35 ft 2

Alex is making 12 pennants so the total area of all

12 pennants is 12 sdot 35 = 42 ft 2

The cost for the pennants will be the total area times

the fabric cost per square foot

( 42 f t 2 ) ( $125 _____

f t 2 ) = $5250

11 The area of the square is the total area minus the

area of triangle

325 ft 2 - 75 ft 2 = 25 ft 2

The area of a square is A = s 2 so s 2 = 25 f t 2

Because 5 sdot 5 = 25 the length of each side of the

square is 5 ft


12 The area of the garden can be found from counting

squares there are 18 full squares and 4 half-squares

for a total of 20 square units Each square unit will

grow about 15 carrots So Christina will grow about

20 ( 15 ) or 300 carrots

13 To find the length of the three sides of the square

subtract the lengths of the two sides of the triangle

from the perimeter The total length of three sides of

the square is 56 - 20 = 36 in Divide by 3 to find

that the length of one side and the base of the

triangle is equal to 12 in The total area of the figure

is the area of the square plus the area of the

triangle

Area of square A = s 2 = 1 2 2 = 144 i n 2


A = 1 __ 2 sdot 12 sdot 8

A = 1 __ 2 sdot 96

A = 48 i n 2


144 + 48 = 192 in 2

14 Think of the scarf as a rectangle minus two

semicircles The rectangle has length = 28 in and

width = 15 in The circle has diameter = 15 in so

its radius is 15 ___ 2 = 75 in

Area of rectangle A = ℓw = 28 sdot 15 = 420 i n 2



A asymp 176625 i n 2

The total area is the difference

420 - 176625 = 243375 in 2 or 243 3 __

8 i n 2

15 a The window is a composite of a square and a

semicircle Because each square in the window

has an area of 100 in 2 the length of each side is

10 in So each side of the square portion of the

entire window has length 10 sdot 4 = 40 in The

diameter of the semicircle is also 40 in so

the radius is 40 ___ 2 = 20 in



A asymp 1 __ 2 sdot 314 sdot ( 20 ) 2


A asymp 628 i n 2


1600 + 628 = 2228 in 2


b The shade is a composite of a rectangle and

a semicircle The length of the rectangle is equal

to the length of one side of the square portion

of the window plus 2 sdot 4 inches for a total of

40 + 2 sdot 4 = 48 in

The height of the rectangular portion of the shade

is equal to 4 times the length of one side of the

square portion of the window plus 4 inches for a

total of 40 + 4 = 44 in

The diameter of the semicircle at the top is the

same as the length of the bottom of the shade

48 in so the radius = 48 ___ 2 = 24 in



A asymp 1 __ 2 sdot 314 sdot ( 24 ) 2


A asymp 90432 i n 2

The approximate total area of the shade is

the sum

2112 + 90432 asymp 3016 in 2

LESSON 94

Your Turn

3 Find the area of a base

B = l times w

= 9 times 2

= 18 square inches

Find the perimeter of the base

P = 2 ( 9 ) + 2 ( 2 )

= 18 + 4 = 22 inches

Find the surface area

S = Ph + 2B

S = 22 ( 1 1 __ 2 ) + 2 ( 18 )

= 33 + 36

= 69

The surface area of the box is 69 square inches

4 Find the area of the base of the larger prism

B = times w

= 12 times 12

= 144 square inches


P = 4 ( 12 )

= 48 inches

Find the surface area of the larger prism

S = Ph + 2B

S = 48 ( 12 ) + 2 ( 144 )

= 576 + 288

= 864 square inches

Find the area of the base of the smaller prism

B = l times w

= 8 times 8

= 64 square inches


P = 4 ( 8 )

= 32 inches

Find the surface area of the smaller prism

S = Ph + 2B

S = 32 ( 8 ) + 2 ( 64 )

= 256 + 128

= 384 square inches

Add the surface areas of the two prisms and

subtract the areas not stained (the bottom of the

larger prism and the smaller prism and an equal

area of the top of the larger prism where the smaller

prism sits) Surface area = 864 + 384 - 144 - 64

- 64 = 976 The surface area of the part of the plant

stand that she will stain is 976 square inches

Guided Practice

1 Perimeter of base = 5 + 5 + 8 = 18

Perimeter of base = 18 ft

Height = 7 ft

Base area = 1 __ 2 ( 3 ) ( 8 ) = 12 ft 2

Surface area

S = ( 18 ft ) ( 7 ft ) + 2 ( 12 ft 2 ) = 150 ft 2

2 Find the area of a base of the cube

B = l times w

= 25 times 25

= 625 m 2

Find the perimeter of the base of the cube

P = 4 ( 25 )

= 10 m

Find the surface area of the cube

S = Ph + 2B

S = 10 ( 25 ) + 2 ( 625 )

= 25 + 125

= 375

Surface area of cube

S = 375 m 2

Find the area of a base of the rectangular prism

B = l times w

= 11 times 9

= 99 m 2

Find the perimeter of the base of the rectangular

prism

P = 2 ( 11 ) + 2 ( 9 )

= 22 + 18

= 40 m

Find the surface area of the rectangular prism

S = Ph + 2B

S = 40 ( 7 ) + 2 ( 99 )

= 280 + 198

= 478

Surface area of rectangular prism

S = 478 m 2

Find the overlapping area the bottom of the cube

A = ( 25 ) ( 25 ) = 625

Overlapping area A = 625 m 2

Surface area of composite figure

= 375 + 478 -2 ( 625 ) = 503 m 2

3 Find the surface area of each of the prisms that

make up the solid Add the surface areas and

subtract the areas of any parts that are not on the

surface




B = l times w

= 10 times 3

= 30 in 2


P = 2 ( 10 ) + 2 ( 3 )

= 20 + 6

= 26 in


S = Ph + 2B

S = 26 ( 4 ) + 2 ( 30 )

=104 + 60

= 164 in 2

She needs 164 in 2 of wrapping paper

5 Find the area of the base

B = l times w

= 20 times 15

= 300 cm 2


P = 2 ( 20 ) + 2 ( 15 )

= 40 + 30

= 70 cm

Find the surface area of the box

S = Ph + 2B

S = 70 ( 9 ) + 2 ( 300 )

= 630 + 600

= 1230 cm 2

Find the surface area of the top and sides

1230 - 300 = 930 cm 2

Find the area of a glass tile

Area of tile = 5 times 5 = 25 mm 2

Convert cm 2 to mm

2

930 cm 2 times 100 mm

2 ________

1 cm 2 = 93000 mm

2

Find the number of tiles needed

93000 divide 25 = 3720

3720 tiles are needed

6 Find the area of the L-shaped base

Area of L-shape = 2 times 1 + 3 times 1

= 2 + 3 = 5 in 2

Find the perimeter of the L-shaped base

Perimeter = 3 + 3 + 1 + 2 + 2 + 1

= 12 in


S = Ph + 2B

S = 12 ( 3 ) + 2 ( 5 )

= 36 + 10

= 46 in 2

The surface area of each brace is 46 in 2

7 Find the area of the triangular prism

Perimeter = 25 + 25 + 3 = 8 ft

Base area = 1 __ 2 ( 2 ) ( 3 ) = 3 ft 2

Surface area = Ph + 2B

= 8 ( 4 ) + 2 ( 3 )

= 32 + 6 = 38 ft 2

Find the area of the rectangular prism

Perimeter = 2 ( 3 ) + 2 ( 4 ) = 14 ft

Base area = 3 times 4 = 12 ft 2


= 14 ( 2 ) + 2 ( 12 )

= 28 + 24 = 52 ft 2


subtract the parts not on the surface

Surface area = 38 + 52 - 12 - 12 = 66 ft 2

The total surface area of the doghouse is 66 ft 2

8 Treat the figure as ( 1 ) a composite of two triangular

prisms and one rectangular prism or ( 2 ) a prism

with a base that is a trapezoid

9 Find the area of the trapezoid base

Area of trapezoid = 1 __ 2 ( b

1 + b

2 ) h

1 __ 2 ( 16 + 48 ) 12 = 384 in

2


P = 48 + 20 + 16 + 20 = 104 in


S = Ph + 2B

S = 104 ( 24 ) + 2 ( 384 )

= 2496 + 768

= 3264 in 2

The surface area of the ramp is 3264 in 2


B = l times w

= 7 times l

= 7 ft 2


P = 2 ( 7 ) + 2 ( 1 )

= 14 + 2

= 16 ft


S = Ph + 2B

S = 16 ( 2 ) + 2 ( 7 )

= 32 + 14

= 46 f t 2


B = l times w

= 1 times 1

= 1 ft 2


P = 2 ( 1 ) + 2 ( 1 )

= 2 + 2 = 4 ft


S = Ph + 2B

S = 4 ( 3 ) + 2 ( 1 )

= 12 + 2

= 14 ft 2



Surface area = 46 + 14 - 1 - 1 = 58 ft 2

The surface area of the stand is 58 ft 2

11 Find the number of cans of paint needed

58 divide 25 = 232

It takes 2 full cans and 1 partial can so 3 cans are

needed

Find the cost of 3 cans of paint

3 times 679 = 2037

No they need 3 cans which will cost $2037


12 Find the area of the base of the box

B = l times w

= 27 times 24

= 648 cm 2


P = 2 ( 27 ) + 2 ( 24 )

= 54 + 48

= 102 cm


S = Ph + 2B

S = 102 ( 10 ) + 2 ( 648 )

= 1020 + 1296

= 2316 cm 2

2316 cm 2 will be covered with paper

13 Area of the original base B = l times w

Area of the new base = 2l times 2w = 4lw = 4B

Perimeter of the original = 2l + 2w

Perimeter of the new = 2 ( 2l ) + 2 ( 2w ) =

2 ( 2l + 2w ) = 2P

Original S = Ph + 2B

New S = 2Ph + 2 ( 4B )

No Ph doubles and 2B quadruples S more than

doubles


14 Find the area of the base of the prism

B = l times w

= 25 times 25

= 625 ft 2


P = 4 ( 25 )

= 10 ft

Find the surface area of the prism

S = Ph + 2B

S = 10 ( 35 ) + 2 ( 625 )

= 35 + 135

= 485 ft 2

Find the surface area less the area of the bottom

surface of the prism

485 - 625 = 4225 ft 2

Find what percent of the surface area less the area

of the bottom is compare to the total surface area

4225 _____ 485

times 100 asymp 87

Sample answer She would be painting about 87

of the total surface area so she will use about 87

of the total amount of paint

15

Circumference ofcircle πd = πtimes4

r = 2 in

9 in

Find the area of the circle base

A = πr 2

asymp 31 4 ( 2 ) 2 = 1256 in 2

Find the circumference of the circle

C = πd

asymp 314 ( 4 ) = 1256 in 2

Find the area of the rectangle

Area asymp 9 times 1256 = 11304 in 2

Find the surface area of the cylinder

S = Ch + 2B

asymp 1256 ( 9 ) + 2 ( 1256 ) = 13816 in 2

Round to the nearest tenth 1382 in 2

The surface area of the oatmeal box is

approximately 1382 in 2

Find the amount of cardboard for 1500 boxes

1500 times 1382 = 207300 in 2

Convert square inches to square feet and round to

the nearest whole number

( 207300 in 2 ) 1 ft 2 _______

144 in 2 asymp 1440 ft 2

It would take about 1440 ft 2 of cardboard

16 Each face has 9 squares 1 cm by 1 cm so S =

54 cm 2 The surface area stays the same when one

or more corner cubes are removed ( Fig 2 3 ) because the number of faces showing is still the

same In Fig 4 S increases because 2 more faces

show

LESSON 95

Your Turn

2 Find the base area B of the triangular prism

B = 1 __ 2 bh

= 1 __ 2 ( 24 ) 7

= 84 m 2

Find the volume of the prism

V = Bh

= ( 84 ) ( 22 )

= 1848 m 3

The volume of the prism is 1848 m 3

5 Find the base area B of the trapezoidal prism

B = 1 __ 2 ( b 1 + b 2 ) h

= 1 __ 2 ( 8 + 12 ) 10

= 1 __ 2 ( 20 ) 10 = 100 cm

2


V = Bh

= ( 100 ) ( 22 )

= 2200 cm 3

The volume of the prism is 2200 cm 3

7 Find the volume of each prism

Find the base area B of the rectangular prism

B = bh

= ( 13 ) 13

= 169 in 2

Find the volume of the rectangular prism

V = Bh

= ( 169 ) ( 30 )

= 5070 in 3


Find the base area B of the triangular prism

B = 1 __ 2 bh

= 1 __ 2 ( 9 ) 13

= 585 in 2

Find the volume of the triangular prism

V = Bh

= ( 585 ) ( 30 )

= 1755 in 3

Find the sum of the volumes

5070 + 1755 = 6825 in 3

The volume of the composite figure is 6825 in 3

Guided Practice

1 B = 1 __ 2 bh = 1 __

2 ( 8 ) ( 3 ) = 12 ft 2

V = Bh = ( 12 times 7 ) ft 3 = 84 ft 3

2 B = 1 __ 2 ( b 1 + b 2 ) h = 1 __

2 ( 15 + 5 ) 3 = 30 m

2

V = Bh = ( 30 times 11 ) m 3 = 330 m 3

3 Find the base area B of the rectangular prism

B = bh

= ( 4 ) 6 = 24 ft 2


V = Bh

= ( 24 ) ( 12 ) = 288 ft 3

The volume of the rectangular prism = 288 ft 3


B = 1 __ 2 bh

= 1 __ 2 ( 6 ) 4 = 12 ft 2


V = Bh

= ( 12 ) ( 6 ) = 72 ft 3

The volume of the triangular prism = 72 ft 3


288 + 72 = 360 ft 3

The volume of the composite figure = 360 ft 3


B = bh

= ( 40 ) ( 50 ) = 2000 ft 2


V = Bh

= ( 2000 ) ( 15 ) = 30000 ft 3


B = 1 __ 2 bh

= 1 __ 2 ( 40 ) ( 10 ) = 200 ft 2


V = Bh

= ( 200 ) ( 50 ) = 10000 ft 3


30000 + 10000 = 40000 ft 3

The volume of the barn is 40000 ft 3


B = 1 __ 2 ( b 1 + b 2 ) h

= 1 __ 2 ( 10 + 12 ) 5

= 1 __ 2 ( 22 ) 5 = 55 cm

2

Find the volume of the trapezoidal prism

V = Bh

= ( 55 ) ( 7 ) = 385 cm 3

The volume of the container is 385 cm 3

6 Find the volume of each prism using the formula

V = Bh Then add the volumes of all the prisms


7 The area of the base of the prism is given 35 in 2


V = Bh

= ( 35 ) ( 5 ) = 175 in 3

The volume of the trap is 175 in 3

8 The shape of the ramp is triangular prism


B = 1 __ 2 bh

= 1 __ 2 ( 7 ) ( 6 ) = 21 in

2


V = Bh

= ( 75 ) ( 7 ) = 525 in 3

The volume of the ramp is 525 in 3


B = 1 __ 2 bh

= 1 __ 2 ( 8 ) ( 4 ) = 16 ft 2


V = Bh

= ( 16 ) ( 24 ) = 384 ft 3

The space contained within the goal is 384 ft 3


B = 1 __ 2 ( b 1 + b 2 ) h

= 1 __ 2 ( 7 + 5 ) 4

= 1 __ 2 ( 12 ) 4 = 24 in

2


V = Bh

= ( 24 ) ( 8 ) = 192 in 3

The volume of the gift box is 192 in 3

11 Find the volume of the triangular prism

V = Bh

= ( 20 ) ( 15 ) = 300 in 3

The units for volume are incorrect the volume is

300 cubic inches

12 The area of the base of the hexagonal prism is

given B = 234 in 3

Find the volume of the hexagonal prism

V = Bh

= ( 234 ) ( 3 ) = 702 in 3



B = bh

= ( 3 ) ( 3 ) = 9 in 2


V = Bh

= ( 9 ) ( 3 ) = 27 in 3


702 + 27 = 972 in 3

The volume of the figure is 972 in 3

13 Find the base area B of the larger rectangular prism

B = bh

= ( 75 ) 375 = 28125 m 2

Find the volume of the larger rectangular prism

V = Bh

= ( 28125 ) ( 75 ) asymp 21094 cm 3

Find the base area B of the smaller rectangular

prism

Find the measure of the base

15 - 75 = 75

Find the base area B of the larger rectangular prism

B = bh

= ( 75 ) 375 = 28125 m 2

Find the volume of the smaller rectangular prism

V = Bh

= ( 28125 ) ( 375 ) asymp 10547 cm 3

Find the sum of the volumes of the prisms

21094 + 10547 = 31641 m 3

The volume of the figure rounded to the nearest

hundredth is 31641 m 3

14 Find the volume of the hexagonal candle

V = Bh

= ( 21 ) ( 8 ) = 168 cm 3

Find the amount of wax Josie would have after

making the hexagonal candle

260 - 168 = 92 cm 3

Find the volume of the triangular candle

V = Bh

= ( 7 ) ( 14 ) = 98 cm 3



260 - 168 = 92 cm 3

Find the area of the base of a triangular candle with

a height of 14 cm

V = Bh

92 = B ( 14 )

92 ___ 14

= B ( 14 ) _____ 14

6 8 ___ 14

= B asymp 657

No the area of the base of the triangular candle

must be less than or equal to about 657 cm 2

15 The base of trapezoidal prism is given 36 in 2 Find

the volume of the trapezoidal prism

V = Bh

= ( 36 ) ( 5 ) = 180 in 3

The base of triangular prism is given 32 in 2

Find the volume of the trapezoidal

prism V = Bh

= ( 32 ) ( 6 ) = 192 in 3

Triangular prism you get 192 in 3 for the same price

you would pay for 180 in 3 with the trapezoidal prism


16 Find the area of the base of the trapezoidal prism

V = Bh

286 = B ( 8 )

286 ____ 8 = B ( 8 )

3575 = B

Find the missing dimension of the base of the

trapezoidal prism

1 __ 2 ( 2 + b 2 ) 13 = 3575

1 __ 2 ( 2 + b 2 ) ( 13 ___

13 ) = 3575 _____

13

( 2 ) 1 __ 2 ( 2 + b 2 ) = ( 2 ) 275

2 + b 2 = 55

_ -2 _ -2

b 2 = 35 ft

The missing dimension is 35 ft

17 Find the area of the base of the triangular prism

B = 1 __ 2 bh

= 1 __ 2 ( 10 ) 6 = 30 cm

2


V = Bh

= ( 30 ) ( 25 ) = 75 cm 3

Find the mass of the doorstop

mass asymp ( V in cm 3 ) ( 86 g

_____ cm

3 )

asymp ( 75 cm 3 ) ( 86 g

_____ cm

3 ) = 645 g

The volume of the doorstop is 75 cm 3 The mass is

about 645 g

18 If both the base and height of the triangular base are

tripled the area of the base is multiplied by 9

Tripling the height of the prism as well means the

volume of the prism is multiplied by 27

19 Use the formula for the volume of a trapezoidal

prism to find a set of dimensions that have a volume

of 120 cm 3

V = Bh

V = [ 1 __ 2 ( b 1 + b 2 ) h 1 ] h 2

120 ≟ [ 1 __ 2 ( 2 + 6 ) 4 ] 75

= [ 1 __ 2 ( 8 ) 4 ] 75

= [ 16 ] ( 75 ) = 120

Try another set of dimensions in the formula

V = Bh

V = [ 1 __ 2 ( b 1 + b 2 ) h 1 ] h 2

120 ≟ [ 1 __ 2 ( 1 + 7 ) 25 ] 12

= [ 1 __ 2 ( 8 ) 25 ] 12

= [ 10 ] 12 = 120


Sample answers ( 1 ) height of trapezoid = 4 cm

base lengths = 2 cm and 6 cm height of prism

= 75 cm ( 2 ) height of trapezoid = 25 cm base

lengths = 1 cm and 7 cm height of prism = 12 cm

MODULE 9

Ready to Go On

1 r = 7 m A = π r 2 C = 2πr A asymp 314 sdot ( 7 ) 2

C asymp 2 sdot 314 sdot 7 A asymp 314 sdot 49

C asymp 4396 m A asymp 15386 m 2

2 d = 12 cm d = 6 cm so r = 12 ___ 2 = 6 ft

C = πd A = π r 2 C asymp 314 ( 12 ) A asymp 314 sdot ( 6 ) 2

C asymp 3768 cm A asymp 314 sdot 36

A asymp 11304 ft 2

3 The figure is a composite of a semicircle with

diameter = 16 m so radius is 16 ___ 2 = 8m and a

triangle with base = 16 m and height = 10 m


A asymp 1 __ 2 sdot 314 sdot ( 8 ) 2


A asymp 10048 m 2


A = 1 __ 2 sdot 16 sdot 10

A = 1 __ 2 sdot 160

A = 80 m 2


80 + 10048 = 18048 m 2

4 The figure is a composite of a parallelogram with

base = 20 cm and height = 45 cm and a rectangle

with length = 20 cm and height = 55 cm

Area of parallelogram A = bh

A = 20 sdot 45

A = 90 c m 2

Area of rectangle

A = ℓw = 20 sdot 55 = 110 c m 2


90 + 110 = 200 cm 2

5 Find the area of the triangular base

Area of triangle = 1 __ 2 bh

1 __ 2 ( 4 ) 3 = 6 cm 2


P = 3 + 4 + 5 = 12 cm


S = Ph + 2B

S = 12 ( 10 ) + 2 ( 6 )

thinsp=120 + 12

thinsp= 132 cm 2


V = Bh

= ( 6 ) 10

= 60 cm 3

6 Find the area of the composite base formed by a

rectangle and a triangle


1 __ 2 ( 4 ) 15 = 3 yd 2

Area of rectangle = bh

( 4 ) 2 = 8 yd 2

Area of the composite base 3 + 8 = 11 yd 2

Find the perimeter of the composite base

P = 4 + 2 + 25 + 25 + 2 = 13 yd


S = Ph + 2B

S = 13 ( 25 ) + 2 ( 11 )

thinsp= 325 + 22

thinsp= 545 yd 2

The area of the base of the pentagonal prism

is given

B = 234 yd 3


V = Bh

= ( 11 ) 25

= 275 yd 3

7 Sample answer You can use a composite figure to

model a room then find surface area to decide how

much paint you need to paint the room


Solutions KeyStatistics

unit

5MODULE 10 Random Samples and Populations

Are You Ready

1 x ___16

=45___40

40x=720

40x ____40

=720____40

   x=18

2 x __5=1__

4

4x=5

4x ___4

=5__4

  x=5__4=125

3 25___10

=x ___10

125=10x

125____10

=10x ____10

125=x

4 x __6

=2__9

9x= 12

9x ___9

=12___9

   x=12___9=4__

3

5 4748495152575960range=60-47=13

6 4566689121213range=13-4=9

7 95979799100106108115range=115-95=20

8 121319273539476671range=71-12=59

9 mean=3+5+7+3+6+4+8+6+9+5_________________________________10

=56

10 mean=81+94+113+67+62+75____________________________6

=82

LESSON 101

Your Turn

4 Yeseveryemployeehadanequalchanceofbeingselected

5 Thequestionisbiasedsincecatsaresuggested

6 ThequestionisnotbiasedItdoesnotleadpeopletopickaparticularseason

Guided Practice

1 Method1ASampleanswer

Random Sample of Seventh Grade Male Students

Student Shoe SizeArturo 75

Jimmy 80

Darnell 90

Ping 75

Zach 85

Jamar 80

BSampleanswer

75+80+90+75+85+80___________________________6

=485____6

asymp81

Meanasymp81

Method2ASampleanswer

Student Shoe Size Student Shoe SizeReggie 85 Ling 85

Stan 80 Marcus 90

Alejandro 90 Tio 85

BSampleanswer

85+80+90+85+90+85____________________________6

=515____6 =86

Mean=size86

2Method1producesresultsthataremorerepresentativeoftheentirestudentpopulationbecauseitisarandomsample

3 Method2producesresultsthatarelessrepresentativeoftheentirestudentpopulationbecauseitisabiasedsample

4 YesSampleanswerWhatisyourfavoritecolor

5 Selectarandomsampleofsufficientsizethatrepresentsthepopulationandaskeachparticipantunbiasedquestions


6 SampleanswerPaulrsquossamplewasbiasedMaybehisfriendsstudiedmorethanothers

7 SampleanswerNancyrsquossampledidnotincludeasmanystationsThereportcouldincludestationsnationwide

8 ItisabiasedsampleStudentswhoarenrsquotontheteamwonrsquotbeselected




9 Itisbiasedbecausestudentswhoarenrsquotinthatclasswonrsquotbeselected

10 Itisarandomsamplebecauseallseventhgradershaveanequalchanceofbeingselected

11 Itisarandomsamplebecausetheorganizationselectsnamesatrandomfromallregisteredvoters

12 Itisbiasedbecausebasketballismentioned

13 Jaersquosquestionisnotbiasedsinceitdoesnotsuggestatypeofarttostudents


14 CollinrsquosmethodbetterrepresentstheentirestudentpopulationbecauseheusedarandomsampleKarlrsquosmethodpickedpeoplethatcouldallbefriendsthatgotofootballgamestogetherThesamplemaynotbestrepresenttheentirestudentpopulation

15 a Every10thstudentoutof600meansthatBarbarasurveyed60studentsThiswasarandomsample

b 35___60

= x ____100

xasymp58

Thepercentis58____100

=58

ItappearsreasonablebecauseBarbarausedarandomsampleandsurveyedasignificantpercentofthestudents

16 CarloiscorrectTherearemanyvalidwaystoselectarepresentativesamplefromapopulation

LESSON 102

Your Turn

5 damagedMP3sinsample

______________________sizeofsample

=damagedMP3sinpopulation

________________________sizeofpopulation

6___50

= x_____3500

6sdot70______50sdot70

= x _____3500

420_____3500

= x_____3500

       x=420420damagedMP3s

Guided Practice

1

6 7 8 9 10 11 12 13 14 1550 1 2 3 4

2 Orderthedatafindtheleastandgreatestvaluesthemedianandthelowerandupperquartiles

6 7 7 107 114 4 54

Leastvalue

4

Lower quartile

4

Median

65

Upper quartile

7

Greatestvalue11

Drawaboxplot

10 1550

3 Themostcommonagesofchildrenthatusethelibraryare4and7

4 Therangeofagesofchildrenthatusethelibraryisfrom4to11

5 Themedianageofchildrenthatusethelibraryis65

6 defectivephonesinsample

______________________sizeofsample

=defectivephonesinpopulation

_________________________sizeofpopulation

4___60

= x_____4200

4sdot70______60sdot70

= x_____4200

280_____4200

= x_____4200

  x=280About280smartphonesintheorderarelikelytobedefective

7 infectedelkinsample

__________________sizeofsample

=infectedelkinpopulation

____________________sizeofpopulation

8___50

= x_____4500

8sdot90______50sdot90

= x_____4500

720_____4500

= x_____4500

       x=720About720elkarelikelytobeinfected

8 YoucansetupproportionsusinginformationobtainedinarandomsampleofthepopulationForinstancethenumberofdefectivepartsinabatchcanbeusedtopredicthowmanypartswillbedefectiveinadifferent-sizebatch

divide060

divide060






9 number of people with mispriced item in sample

_______________________________________ size of sample

=

number of people with mispriced item in one day

_______________________________________ size of population

4 ___ 50

= x ____ 600

4 sdot 12 ______ 50 sdot 12

= x ____ 600

48 ____ 600

= x ____ 600

x = 48

About 48 people are likely to have a mispriced item

10 number of boxes with at least one broken crayon in sample

_______________________________________________ size of sample

=

total number of boxes with at least one broken crayon

___________________________________________ size of population

2 ___ 20

= x ____ 130

2 sdot 65 _______ 20 sdot 65

= x ____ 130

13 ____ 130

= x ____ 130

x = 13

About 13 boxes will have at least one broken crayon

11 number of puppies

________________ size of sample

= total number of puppies

___________________ size of population

12 ___ 60

= x _____ 1200

12 sdot 20 ______ 60 sdot 20

= x _____ 1200

240 _____ 1200

= x _____ 1200

x = 240

About 240 puppies are in all of the cityrsquos animal

shelters

12 number of hawks building nests

__________________________ size of sample

= total number of hawks

__________________ size of population

12 ___ 72

= x ______ 10800

12 sdot 150 _______ 72 sdot 150

= x ______ 10800

1800

______ 10800

= x ______ 10800

x = 1800

About 1800 hawks are building nests

13 Yes this seems reasonable because 23 + 27

_______ 2 = 25

is the median of the data

14 Order the data

11 12 12 12 13 13 13 14 14 14 15 17 18 18

19 22

The total number of marathoners is 16 and of those

12 run 13 miles or more

12 ___ 16

= x ____ 100

12 sdot 625 ________ 16 sdot 625

= x ____ 100

75 ____ 100

= x ____ 100

x = 75

No The statement should say that 75 of female

marathoners run 13 or more miles a week

15

6 7 8 9 1050 1 2 3 4

Sample answer Most students at Garland have 2 or

fewer siblings

16 The box plot should show that at least 50 of the

ages are between 20 and 40 years of age

17 Kudrey needs to find the median and the lower and

upper quartiles and plot those points He assumed

all quartiles would be equally long when each

quartile represents an equal number of data values


18 Yes the least and greatest data values The median

and quartiles may or may not be actual data values

depending on how many values are in the data

19 A box plot Since every number is different a dot

plot would only have one dot over each value which

doesnrsquot give much information The box plot would

show the median the range and where data values

are concentrated if in fact they are

20 The typical salary at this company is $24000 the

median Yes it is misleading the average is thrown

off by the outlier value of $79000


9 a 56 + 43 + 62 + 63 + 33 + 34 + 38 + 51 + 59 + 59

___________________________________________ 10

= 498

The average is 498 palms

b 498 sdot 64 = 31872

There are about 3187 palms on the entire farm


10 55 + 57 + 57 + 58 + 59 + 59 + 59 + 59 + 59 + 61 + 62 + 62 + 63 + 64 + 66

_________________________________________________________________ 15

= 60

The mean height is 60 inches Yes it is a good sample generated randomly and contains about 20 of the entire

population so it should provide a good estimate of the mean height of all competitors But taking more samples to

gauge the variability among the samples would make for a more valid estimate

11 Sample answer Answers will vary based on each studentrsquos results but should be about 13 or 14

12 Sample answer The larger the size of the random sample the more likely it is to represent the population

accurately

LESSON 103

Guided Practice

1 (1 600) 20

2 50 51 600

3 No In the sample 4 numbers (38 26 31 and 31)

represent defective batteries which is 20 of the

total In the shipment 50 out of 600 or about 8 of

the batteries are defective

4 Sample answer A too-small or non-random sample

is likely to pick unrepresentative data values


5 Shop A 10 ___ 50

times 500 = 100

Shop B 23 ____ 100

times 500 = 115

Shop C 7 ___ 25

times 500 = 140

Shop A sells 100 whole-wheat bagels

Shop B sells 115 whole-wheat bagels

Shop C sells 140 whole-wheat bagels

6 From most to least likely B A C Shop Brsquos sample

would be the most representative because it

contained the most bagels Shop Crsquos sample would

be the least representative because it contained the

fewest bagels

7 She could use either the Shop A or Shop B sample

Both use a sufficient number of bagels to be

reasonably accurate The sample from Shop C uses

too few bagels to be accurate

8 2 of the 20 T-shirts in the sample are below quality

standards Because 2 ___ 20

times 1000 = 100 the predic-

tion would be that about 100 of the 1000 T-shirts are

below quality standards This is 1 1 __ 3 times the actual

count of 75


MODULE 10

Ready to Go On

1 The population is the customers in the companyrsquos

computer database The sample is biased because

the customers surveyed are more likely to value their

service

2 number of students who speak 3 or more languages

__________________________________________ size of sample

= total number of students ____________________ size of population

18 ____ 270

= x ______ 30330

18 sdot 337 ____

3 ________

270 sdot 337 ____ 3

= x ______ 30330

2022

______ 30330

= x ______ 30330

x = 2022

About 2022 students speak three or more

languages

3 Two of the random numbers 13 and 167 represent

defective MP3 players

simulated defective players

______________________ size of simulation

= defective players

______________ shipment

2 ___ 10

= x _____ 5000

2 middot 500 _______ 10 middot 500

= x _____ 5000

1000

_____ 5000

= x _____ 5000

x = 1000

Based on the sample about 1000 MP3 players are

defective

4 No the sample is too small compared to the size of

the shipment

5 Sample answer You can make predictions about

populations that are too large to survey


MODULE 11 Analyzing and Comparing Data

Are You Ready

0875

1 8 ⟌ _

7000

_ -6 400

600

_ -560

40

_ -40

0

0875 875

08

2 5 ⟌ _

40

_ -4 0

0

08 80

025

3 4 ⟌ _

100

_ -80

20

_ -20

0

025 25

03

4 10 ⟌ _

30

_ -3 0

0

03 30

5 4 6 7 7 9 11 15 17

7 + 9

_____ 2 = 8

Median = 8

Mode = 7

6 36 37 40 43 44 49 50 51 56

Median = 44

Mode none

7 9 + 16 + 13 + 14 + 10 + 16 + 17 + 9

________________________________ 8

= 13

Mean = 13

8 108 + 95 + 104 + 96 + 97 + 106 + 94

________________________________ 7 = 100

Mean = 100

LESSON 111

Your Turn

2 Shape dot plots for field hockey players and

softball players have a similar spread

Center center of the field hockey dot plot is less

than the center for softball or basketball players

Spread dot plots for field hockey players and softball

players have a similar spread

3 The median is the middle value Listing the values

in order

1 4 4 4 5 5 5 6 6 6 6 7 7 8 11

In this case median 6 h

range 10 h

The median for internet usage is greater than the

median for exercise and the range is less than the

range for exercise

Guided Practice

1 Class A clustered around two areas

Class B clustered in the middle The dot plots

appear to have about half of the data clustered in

one area

2 Class A two peaks at 4 and 13 mi

Class B looks centered around 7 mi

3 Class A spread from 4 to 14 mi a wide gap with

no data

Class B spread from 3 to 9 mi

4 Class A

4 4 4 4 4 5 5 5 6 6 12 13 13 13 13 14 14

median 6

Class B

3 4 4 4 5 5 5 5 6 6 7 7 7 7 7 8 8 9

median 6

The median for both dot plots is 6 miles

5 Range for class A 14 - 4 = 10 mi

Range for class B 9 - 3 = 6 mi

6 The medians allow you to compare the centers

The ranges allow you to compare the spreads


7 The dots have a relatively even spread with a peak

at 8 letters

8 The center of the graph is between 6 and 7 letters

9 The dots spread from 3 to 9 letters

10 The mean is the average

3 + 4 + 4 + 5 + 5 + 6 + 7 + 7 + 8 + 8 + 8 + 9

________________________________________ 12

74 ___ 12

asymp 617

Mean asymp 617

3 3 4 5 5 6 7 7 8 8 8 9

Because there are two middle values take their

average

6 + 7

_____ 2 = 13 ___

2 = 65

Median 65

Range 9 - 3 = 6

11 AL clustered in one small interval with an outlier to

the left

VA relatively uniform in height over the same

interval


12 ALcenteredbetween8and9daysofrainVAcenteredaround10daysofrain

13 ALspreadsfrom1to12daysofrainanoutlierat1VAspreadsfrom8to12daysofrain

14 LynchburgVAhasmoreconsistentlevelsofrainandmorerainpermonthcomparedtoMontgomeryAL

15 GroupAclusteredtotheleftofsize9GroupBclusteredtotherightofsize9

16 OrderedvaluesforgroupA6577757575888888585913Thereare15itemsofdataSince15isoddthereisamiddlenumber8Sothereisnoneedtoaverageanyvalues

MedianforGroupAsize8OrderedvaluesforgroupB859999959595951010105105105115MedianforGroupBsize95

17 GroupArangewithoutlier=13-65=65withoutoutlier=9-65=25GroupBrange=115-85=3

18 SampleanswerGroupAcouldbechildrenandGroupBcouldbeadults


19 YesSampleansweronegroupoffivestudentscouldhavethefollowingnumberofpets12345Anothergroupoffivestudentscouldhavethefollowingnumberofpets13335Forbothgroupsofstudentsthemedianwouldbe3andtherangewouldbe4

20RangeanoutliergreatlyincreasestherangewhereasthemedianwillgenerallynotbegreatlyaffectedasitisinthemiddleofallthevaluesAdotplotwillshowboth

LESSON 112

Your Turn

3 SampleanswerTheboxeshavesimilarshapesalthoughGroupBhasashorterboxandshorterwhiskersGroupBrsquosmedianisgreaterthanGroupArsquosGroupBrsquosshorterboxmeansthemiddle50ofitsdataareclosertogetherthanthemiddle50ofGroupArsquos

4 SampleanswerTheshapeissimilartoStoreArsquosThemedianisgreaterthanStoreArsquosandlessthanStoreBrsquosTheinterquartilerangeisaboutthesameasStoreArsquosandlongerthanBrsquos

Guided Practice

1 Minimum72 Maximum88

2 Median79

3 Range88-72=16 IQR85-75=10

4 Themedianheightforhockeyplayersis70inthemedianheightforvolleyballplayersis74Thereforevolleyballplayershavethegreatermedianheight

5 Theminimumheightforhockeyplayersis64intheminimumheightforvolleyballplayersis67inSohockeyplayershavetheshortestplayer

6 IQRforhockeyplayers76-66=10IQRforvolleyballplayers78-68=10BothgroupshaveanIQRof10

7 SampleanswerMinimumandmaximumvaluesmedianrangeandIQRs


8 CarAhasaminimumof165inandamaximumof210inCarBhasaminimumof160inandamaximumof205inCarAhasamedianof180inCarBhasamedianof185in

9 RangeofCarA210-165=45RangeofCarB205-160=45IQRofCarA195-170=25IQRofCarB200-175=25Bothcarshaverangesof45inandinterquartilerangesof25in

10 CarBhasagreatermediandistancethanCarATheinterquartilerangesarethesamesothemiddle50ofthejumpdistancesforthetwocarshavethesamevariability

11 CarAhaslessvariabilityinthelowestquarterofitsdataandgreatervariabilityinthehighestquarterofitsdataThevariabilityisreversedforCarB

12 CityBhasthelowestpriceof$400andalsohasthehighestpriceof$625

13 MedianforCityA$475MedianforCityB$450Difference475-450=$25CityAhasthehighermedianpriceanditis$25higher

14 SampleanswerCityBabout50ofcarsinCityBleaseforlessthan$450ascomparedtoonly25ofcarsinCityA

15 SampleanswerCityAhasagreatermediancarleasingcostthanCityBCityAhasagreaterIQRofcarleasingcoststhanCityBCityBhasamorepredictablecarleasingcostthanCityAforthemiddle50ofdatavalues





16 The box plot with the longer box has more variability

in the middle 50 of the values

17 You can identify the minimum and maximum values

and the range of the data You can identify the

quartiles including the lower and upper quartiles

and the median as well as the interquartile range

Together these values help you recognize the

center of the data both the median and the middle

50 It helps you to recognize how spread out the

data are overall and how spread out the middle

50 of the values are around the median A dot

plot contains all the data values which a box plot

does not

18 Sample answer The range tells you very little but

the interquartile range tells you how closely the

middle half of the data cluster around the median

LESSON 113

Your Turn

1 Team 1

Mean

44 + 47 + 67 + 89 + 55 + 76 +85 + 80 + 87 + 69 + 47 + 58 = 804

804 divide 12 = 67

Mean absolute deviation

ǀ 44 - 67 ǀ = 23 ǀ 47 - 67 ǀ = 20

ǀ 67 - 67 ǀ = 0 ǀ 89 - 67 ǀ = 22

ǀ 55 - 67 ǀ = 12 ǀ 76 - 67 ǀ = 9

ǀ 85 - 67 ǀ = 18 ǀ 80 - 67 ǀ = 13

ǀ 87 - 67 ǀ = 20 ǀ 69 - 67 ǀ = 2

ǀ 47 - 67 ǀ = 20 ǀ 58 - 67 ǀ = 11

Mean of absolute values

23 + 20 + 0 + 22 + 12 + 9 +18 + 13 + 20 + 2 + 20 + 11 = 170


Team 2

Mean

40 + 32 + 52 + 75 + 65 + 70 +72 + 61 + 54 + 43 + 29 + 32 = 625



ǀ 40 - 521 ǀ = 121 ǀ 32 - 521 ǀ = 201

ǀ 52 - 521 ǀ = 01 ǀ 75 - 521 ǀ = 229

ǀ 65 - 521 ǀ = 129 ǀ 70 - 521 ǀ = 179

ǀ 72 - 521 ǀ = 199 ǀ 61 - 521 ǀ = 89

ǀ 54 - 521 ǀ = 19 ǀ 43 - 521 ǀ = 91

ǀ 29 - 521 ǀ = 231 ǀ 32 - 521 ǀ = 201


121 + 201 + 01 + 229 +129 + 179 + 199 + 89 +19 + 91 + 231 + 201 = 169


Difference in means

67 - 521 = 149


The difference of the means is about 11 times the

MAD

2 There is much more overlap between the two

distributions

Guided Practice

1 Class 1 mean

12 + 1 + 6 + 10 + 1 + 2 + 3 +10 + 3 + 8 + 3 + 9 + 8 + 6 + 8 = 90

90 divide 15 = 6

Class 2 mean

11 + 14 + 11 + 13 + 6 + 7 + 8 + 6 +8 + 13 + 8 + 15 + 13 + 17 + 15 = 165

165 divide 15 = 11

Class 1 mean absolute deviation

ǀ 12 - 6 ǀ = 6 ǀ 1 - 6 ǀ = 5 ǀ 6 - 6 ǀ = 0

ǀ 10 - 6 ǀ = 4 ǀ 1 - 6 ǀ = 5 ǀ 2 minus 6 ǀ = 4

ǀ 3 - 6 ǀ = 3 ǀ 10 - 6 ǀ = 4 ǀ 3 - 6 ǀ = 3

ǀ 8 - 6 ǀ = 2 ǀ 3 - 6 ǀ = 3 ǀ 9 - 6 ǀ = 3

ǀ 8 - 6 ǀ = 2 ǀ 6 - 6 ǀ = 0 ǀ 8 - 6 ǀ = 2

6 + 5 + 0 + 4 + 5 + 4 + 3 + 4 +3 + 2 + 3 + 3 + 2 + 0 + 2 = 46



ǀ 11 - 11 ǀ = 0 ǀ 14 - 11 ǀ = 3 ǀ 11 - 11 ǀ = 0

ǀ 13 - 11 ǀ = 2 ǀ 6 - 11 ǀ = 5 ǀ 7 - 11 ǀ = 4

ǀ 8 - 11 ǀ = 3 ǀ 6 - 11 ǀ = 5 ǀ 8 - 11 ǀ = 3

ǀ 13 - 11 ǀ = 2 ǀ 8 - 11 ǀ = 3 ǀ 15 - 11 ǀ = 4

ǀ 13 - 11 ǀ = 2 ǀ 17 - 11 ǀ = 6 ǀ 15 - 11 ǀ = 2

0 + 3 + 0 + 2 + 5 + 4 + 3 + 5 +3 + 2 + 3 + 4 + 2 + 6 + 2 = 44


2 Difference in means

11 minus 6 = 5


3 Sample answer The variation and overlap in the

distributions make it hard to make any convincing

comparison

4 To see how statistical measures vary among the

different samples


5 23 + 38 + 39 + 48 + 55 + 56 + 71 +86 + 57 + 53 + 43 + 31 = 600

600 divide 12 = 50

ǀ 23 - 50 ǀ = 27 ǀ 38 - 50 ǀ = 12

ǀ 39 - 50 ǀ = 11 ǀ 48 - 50 ǀ = 2

ǀ 55 - 50 ǀ = 5 ǀ 56 - 50 ǀ = 6

ǀ 71 - 50 ǀ = 21 ǀ 86 - 50 ǀ = 36

ǀ 57 - 50 ǀ = 7 ǀ 53 - 50 ǀ = 3

ǀ 43 - 50 ǀ = 7 ǀ 31 - 50 ǀ = 19

27 + 12 + 11 + 2 + 5 + 6 + 21 +36 + 7 + 3 + 7 + 19 = 156

156 divide 12 = 13

The mean is 50degF and the MAD is 13degF


6 ǀ 23 - 8 ǀ = 15 ǀ 38 - 23 ǀ = 15

ǀ 39 - 24 ǀ = 15 ǀ 48 - 33 ǀ = 15

ǀ 55 - 40 ǀ = 15 ǀ 56 - 41 ǀ = 15

ǀ 71 - 56 ǀ = 15 ǀ 86 - 71 ǀ = 15

ǀ 57 - 42 ǀ = 15 ǀ 53 - 38 ǀ = 15

ǀ 43 - 28 ǀ = 15 ǀ 31 - 16 ǀ = 15

The difference between each average monthly

temperature for City 1 and the corresponding

temperature for City 2 is 15degF

7 50 - 15 = 35

The mean is 35degF and the MAD is 13degF The

mean for City 2 must be 15degF less than the mean

for City 1 and the MAD must be the same

8 50 - 35 = 15


The difference in the means as a multiple of the

mean absolute deviations is about 12

9

0 4 8 12 16 20 24 28 32 36 40 44

Medians

School B

School A

0 4 8 12 16 20 24 28 32 36 40 44

Means

School B

School A

Both distributions show longer travel times for school

A The distributions of the medians show less

overlap so it is more convincing

10 State A 48 - 38 = 10


State B 50 - 42 = 8

8 divide 4 = 2

Sample answer The difference in ages is more

significant for State A if you look at the difference in

mean ages but the difference in mean ages is more

significant in State B if you consider variability as

well

11 Smiths Range 70 - 64 = 6

Median 665

Thompsons Range 80 - 74 = 6

Median 77

77 - 665 = 105

105 divide 6 = 175

The difference in the medians is 175 times the

ranges


12 Sample answer Jill can reasonably expect the

median of the medians of the samples to be 35

The median of the medians should be close to the

median of the population which should be 35

The outcomes are equally likely

13 Sample answer Ramonrsquos results should produce

more reliable inferences The larger the sample

size the less variability there should be in the

distributions of the medians and means

14 Sample answer Sethrsquos statement is incorrect for any

situation in which the MADs of the population are

not very similar

MODULE 11

Ready to Go On

1 The mean for the start of the school year is given by

5 + 6 + 6 + 7 + 7 + 7 + 7 + 8 + 8 + 8 + 8 + 9 + 9 + 10

________________________________________________ 14

= 105 ____ 14

= 75 mi

The mean for the end of the school year is given by

6 + 6 + 7 + 7 + 8 + 8 + 8 + 8 + 9 + 9 + 9 + 10 + 10 + 10

__________________________________________________ 14

= 115 ___ 14

asymp 82 mi

In summary Start 75 mi End about 82 mi

2 The median is the middle value

List of ordered values for start of school year

5 6 6 7 7 7 7 8 8 8 8 9 9 10


average

7 + 8

_____ 2 = 15 ___

2 = 75

Median 75

List of ordered values for end of school year

6 6 7 7 8 8 8 8 9 9 9 10 10 10

Because there are two middle values we would

generally take their average but since they are both

the same and equal to 8

Median 8

Therefore Start 75 mi End 8 mi

3 Range for start of school year 10 - 5 = 5 mi

Range for end of school year 10 - 6 = 4 mi


4 Median for Airplane A 210 in

Median for Airplane B 204 in

Airplane A has a greater median flight length

5 IQR for Airplane A 225 - 208 = 17 in

IQR for Airplane B 230 - 195 = 35 in

Airplane B has a greater interquartile range


6 The means for the shade plants

7 + 11 + 11 + 12 + 9 + 12 + 8 + 10

______________________________ 8

= 10

The means for the sun plants

21 + 24 + 19 + 19 + 22 + 23 + 24 + 24

__________________________________ 8 = 22

Range of the shade plants 12 - 7 = 5

Range of the sun plants 24 - 19 = 5

Difference in the means 22 - 10 = 12

12 ___ 5

= 24

The difference in the means is 24 times the ranges

7 Sample answer By graphing real-world data you

can identify similarities and differences in related

groups


MODULE 12 Experimental Probability

Are You Ready

1 6 ___ 10

= 6 divide 2 ______ 10 divide 2

= 3 __ 5

2 9 ___ 15

= 9 divide 3 ______ 15 divide 3

= 3 __ 5

3 16 ___ 24

= 16 divide 8 ______ 24 divide 8

= 2 __ 3

4 9 ___ 36

= 9 divide 9 ______ 36 divide 9

= 1 __ 4

5 45 ___ 54

= 45 divide 9 ______ 54 divide 9

= 5 __ 6

6 30 ___ 42

= 30 divide 6 ______ 42 divide 6

= 5 __ 7

7 36 ___ 60

= 36 divide 12 _______ 60 divide 12

= 3 __ 5

8 14 ___ 42

= 14 divide 14 _______ 42 divide 14

= 1 __ 3

075

9 4 ⟌ _

300

_ -2 80

20

_ -20

0

075

0875

10 8 ⟌ _

7000

_ -6400

600

_ -560

40

_ -40

0

0875

015

11 20 ⟌ _

300

_ -2 00

100

_ -100

0

015

038

12 50 ⟌ _

1900

_ -15 00

4 00

_ -4 00

0

038

13 67 = 67 ____ 100

= 067

14 31 = 31 ____ 100

= 031

15 7 = 7 ____ 100

= 007

16 146 = 100 + 46

= 100 ____ 100

+ 46 ____ 100

= 1 + 046

= 146

17 013 = 13

18 055 = 55

19 008 = 8

20 116 = 116

LESSON 121

Your Turn

3 Because every other number from 1 through 16 is

even choosing an even number is as likely as not

and the probability is 1 __ 2

4 There are 20 possible outcomes when picking a

marble from the jar There are 10 purple marbles

Therefore the probability of picking a purple marble

is 10 ___ 20

or 1 __ 2

5 There are 6 possible outcomes when rolling a cube

There are 2 numbers greater than 4 that can be

rolled 5 and 6 Therefore the probability of rolling a

number greater than 4 is 2 __ 6 or 1 __

3

Solutions KeyProbability

UNIT

6


7 P(event) + P(complement) = 1

P(5) + P(not 5) = 1

1 __ 8 + P(not 5) = 1

P(not 5) = 7 __ 8

The probability of picking a marble that is not 5 is 7 __ 8


P(even) + P(odd) = 1

1 __ 2 + P(odd) = 1

P(odd) = 1 __ 2

The probability of rolling an odd number is 1 __ 2

Guided Practice

1 The cards are numbered 1 2 3 4 5 6 7 8 9 10

You pick a number greater than 0 8

You pick an even number 5

You pick a number that is at least 2 7

You pick a number that is at most 0 1

You pick a number divisible by 3 3


You pick a prime number 4

You pick a number less than the

greatest prime number 6

2 There are no green playing cards in a standard

deck so randomly picking a green card is

impossible 0

3 There are as many red cards as black cards in a

standard deck so it is as likely as not 1 __ 2

4 All of the numbers are less than 12 so they are also

less than 15 The probability is certain 1

5 There are only two numbers between 1 and 12 that

are divisible by 5 5 and 10 Therefore the probability

is unlikely close to 0

6 There are 5 possible outcomes when spinning the

spinner There are two even numbers 2 and 4

Therefore the probability of the spinner landing on

an even number is 2 __ 5


card from a standard deck There are 13 cards with

diamonds Therefore the probability of picking a

card with a diamond is 13 ___ 52

= 1 __ 4


P(5) + P(not 5) = 1

1 __ 6 + P(not 5) = 1

P(not 5) = 5 __ 6

The probability of not rolling 5 is 5 __ 6


P(blue) + P(not blue) = 1

1 __ 3 + P(not blue) = 1

P(not blue) = 2 __ 3

The probability of not landing on blue is 2 __ 3


P(4) + P(not 4) = 1

1 __ 5 + P(not 4) = 1

P(not 4) = 4 __ 5

The probability of not landing on 4 is 4 __ 5


P(queen) + P(not queen) = 1

4 ___ 52

+ P(not queen) = 1

P(not blue) = 48 ___ 52

= 12 ___ 13

The probability of not picking a queen is 12 ___ 13

12 Sample answer pulling a red marble out of a bag

that contains only blue marbles pulling a white

marble out of a bag that contains only white marbles


13 There are 52 possible outcomes when picking from

a standard deck of cards There are 8 cards that

have an ace or a king Therefore the probability of

selecting

an ace or a king is 8 ___ 52

or 2 ___ 13


P(apple or peach) + P(not apple or peach) = 1

9 ___ 12

+ P(not apple or peach) = 1

P(not apple or peach) = 3 ___ 12

or 1 __ 4

Therefore the probability of picking a piece of fruit

that is not an apple or a peach is 3 ___ 12

or 1 __ 4

15 No it is unlikely that she will have oatmeal for

breakfast Since there are 4 choices the probability

that she will choose oatmeal is 1 __ 4 or 25

16 Purple There are a lot more plants with purple

flowers than with white flowers The probability of

selecting a white-flowered plant is 2 __ 9 while the

probability of selecting a purple-flowered plant is 7 __ 9

17 Because she has more colored T-shirts than white

T-shirts it is likely that she will pick a colored T-shirt

She has 14 total T-shirts and 10 of the shirts are

colored Therefore the probability she will choose a

colored T-shirt is 10 ___ 14

or 5 __ 7

18 1 None of the students in the class have red hair so

it is certain that a randomly chosen student will not

have red hair


19 a There are 14 total coins and 8 blue coins so the

probability that the coin is blue is 8 ___ 14

or 4 __ 7

b Removing 1 of the 8 blue coins leaves 7 blue

coins Adding 3 more to the 6 red coins makes

9 red coins The total of coins in the bag is now

16 Therefore the probability of choosing a red

coin is 9 ___ 16

c Removing 1 of the 6 red coins leaves 5 red coins

Adding 3 to the 8 blue coins makes 11 blue coins

The total of coins in the bag is now 16 Therefore

the probability of choosing a red coin is 5 ___ 16


20 Sample answer If some marbles in a jar are heavier

than others then the heavier marbles would sink

and be less likely to be selected

21 Yes Because there are only two colors selecting

not black is equal to selecting red So

P(not black) + P(black) =P(not black) + P(not red) = 1

22 2 is the number of ways the event can happen 7 is

the number of outcomes in the sample space

landing on blue

LESSON 122

Your Turn

7 The total number of spins is 6 + 14 + 10 = 30

Red 10 ___ 30

= 1 __ 3

Yellow 14 ___ 30

= 7 ___ 15

Blue 6 ___ 30

= 1 __ 5

8 Sample answer Let 1 and 2 represent blue 3 and 4

represent white and 5 and 6 represent blue Toss

the cube 50 times to determine the experimental

probability for each color Predict the next ball will be

the color with the greatest experimental probability

Guided Practice

1 The total number of spins is 14 + 7 + 11 + 8 = 40

A 14 ___ 40

= 7 ___ 20

= 035 = 35

B 7 ___ 40

= 0175 = 175

C 11 ___ 40

= 0275 = 275

D 8 ___ 40

= 1 __ 5 = 020 = 20

2 Sample answer Write ldquoyesrdquo on 6 cards and ldquonordquo on

4 cards Draw a card at random 50 times Use the

number of ldquoyesrdquo cards drawn as the prediction

3 Use an experiment to find the number of times the

event occurs for a certain number of trials


4 6 ___ 10

or 3 __ 5 It is reasonable to assume that Dreersquos

past performance is an indicator of her future

performance There is no way to accurately

represent 3 __ 5 on a number cube with 6 faces

5 Sample answer Compare the number of wins to the

total number of trials

number of wins _________________ total number of trials

= 8 ___ 48

= 1 __ 6


name Ryan is 1 person Therefore the probability

he is chosen is 1 ___ 20

and the probability he is not

chosen is 19 ___ 20

P(Ryan) + P(not Ryan) = 1

1 ___ 20

+ P(not Ryan) = 1

P(not Ryan) = 19 ___ 20

7 Yes because it is based on actual data of weather

patterns

8 Joan Mica hit the ball 8 ___ 48

times or about 17 of her

times at bat Meanwhile Joan hit the ball 12 ___ 40

times

or 30 of her times at bat Therefore Joan has the

greater experimental probability and is more likely to

get a hit next time

9 Gabbyrsquos experimental probability of hitting an ace

is 4 ___ 10

or 2 __ 5 Gabby could serve 16 aces in her next

40 serves because 2 __ 5 of 40 is 16

10 The experimental probability her dog wonrsquot want to

go outside is 5 ___ 12

or about 417

P(outside) + P(not outside) = 1

7 ___ 12

+ P(not outside) = 1

P(not outside) = 5 ___ 12

or 417


11 She did not add 40 and 60 to find the total number

of trials P(heads) = 40 ____ 100

12 Sample answer coin toss Heads represents male

and tails represents female Toss the coin 50 times

and use the results to make a prediction

13 Sample answer Make an index card to represent

each coin then pick one card at random No since

the coins are different sizes they do not each have

the same probability of getting pulled out of my

pocket


LESSON 123

Your Turn

1 P(coffee + small) = number of coffee + small

_____________________ total number of orders

= 60 ____ 400

= 3 ___ 20

= 15

3 P(goId + 20 in) = number of gold + 20 in

_________________________ total number of necklaces sold

= 12 ___ 75

or 4 ___ 25

Guided Practice

1 P(female + age 22ndash39)

= number of female + age 22ndash39

__________________________ total number of patients

= 50 ____ 400

or 1 __ 8

2 Sample answer There are six possible outcomes

standard with vacuum standard with no vacuum

deluxe with vacuum deluxe with no vacuum

superior with vacuum and superior with no vacuum

Students could write the outcomes on six index

cards and put them in a box Then they can draw a

card 50 times record the results and find the

experimental probability that a customer chooses a

deluxe wash with no vacuum by dividing the

frequency of this compound event by 50 the total

number of trials

3 Find the number of occurrences of the compound

event and divide it by the total number of trials


4 Divide the number of 2 piece + salad orders 33 by

the total number of orders 330

P = number of 2 piece + salad

______________________ total number of orders

= 33 ____ 330

= 1 ___ 10

5 P = number of red notebooks + 150 pages

_______________________________ total number of notebooks sold

= 60 ____ 400

= 3 ___ 20

6 P(red notebook) = number of red notebooks _____________________ total number of notebooks

= 55 + 60 + 23

____________ 400

= 138 ____ 400

= 69 ____ 200

7 12 the total is the product of 3 page-count choices

and 4 color choices

8 She left out the 53 students that read 150 pages

P(7th grade + 100 pages) = 85 ____ 250

= 17 ___ 50

9 Sample answer 8th grade the results table

suggests 8th grade students are the least likely to

have read 150 pages compared to students in 6th or

7th grade


10 Greater heads occurs on about half the occasions

that you roll a 6 so the compound event is half as

likely

11 Sample answer For 2 outcomes he could use even

and odd numbers For 3 outcomes he could use

1 or 2 3 or 4 and 5 or 6 For 6 outcomes he could

use each number once

12 P(male + open toe) = 11 ____ 300

P(male has open toe) = 11 ____ 150

No the first scenario

includes females and the second does not

13 No because coins are fair and the probabilities do

not appear to be equally likely

14 Sample answer On a coin heads = male and

tails = female On a number cube (1 or 2) = 6th

grade (3 or 4) = 7th grade and (5 or 6) = 8th

grade Toss the coin and roll the number cube 50

times each Record the number of outcomes that are

heads and 3 or 4

LESSON 124

Your Turn

1 024 times 550 =132 customers

2 No About 371 of the emails out of 12372 will come

back undelivered because 003 times 12372 asymp 371 The

editorrsquos prediction is too high

3 024 times 350 = 84 customers Yes because 107

customers buying two or more pairs would be more

than only 84 customers

Guided Practice

1 030 times 50 = 15 times

2 015 times 365 asymp 55 days

3 No about 1009 of the candles out of 16824 will be

returned because 006 times 16824 asymp 1009

A prediction of 812 is too low

4 No about 746 toys out of 24850 will be defective

because 003 times 24850 asymp 746 A prediction of 872 is

too high

5 98 ____ 100

= x ___ 40

= 39 ___ 40

or 39 times

No if she were late 6 out of 40 times the rate of

being on time would be only 85 in which case the

light-railrsquos claim of 98 is too high

6 18 ____ 100

= x _____ 5000

= 900 _____ 5000

or 900 students Yes the

collegersquos claim is close to the number actually

accepted

times04

times04

times50

times50


7 Solve a proportion using the experimental probability

to find an expected number of events to happen

Make a prediction based on the expected number of

events


8 4 ____ 100

= x ____ 200

= 8 ____ 200

or 8 students More students

moved than expected because 12 is more than 8

9 Yes 6th grade 2 ____ 100

= x ____ 250

= 5 ____ 250

or 5 students

7th grade 4 ____ 100

= x ____ 200

= 8 ____ 200

or 8 students

8th grade 8 ____ 100

= x ____ 150

= 12 ____ 150

or 12 students

Since 5 + 8 + 12 = 25 the values in the table

support his claim of 30 students

10 6 ____ 100

= x ____ 300

= 18 ____ 300

or 18 seats If an airplane is

overbooked with 310 passengers only 291 are

expected to show up since 310 times 94 asymp 291

11 006 times 600 = 36 clients If 40 clients did not pay it

would be slightly more than average

12 080 times 20 = 16 team members The coachrsquos claim is

not accurate because the average number of

students at practice is 144 ____ 8 = 8

13 He set up the fraction incorrectly it should be

1 ___ 30

= x ____ 180


14 1 __ 2 of 12 = 6 normal rejection rate

500 times 6 = 30 transactions rejected by a

normal gas pump

15 098 times 15000 = 14700 on-time flights Sample

answer No one week of data could be misleading

and not representative of the yearly on-time prob-

ability (because it ignores bad weather etc)

16 Sample answer No They could expect to get 96

responses with the old letter since

4 ____ 100

= x _____ 2400

= 96 _____ 2400

or 96 letters Therefore the

new letter received fewer responses

MODULE 12

Ready to Go On

1 H1 H2 T1 T2

2 6 ___ 10

= 3 __ 5

3 13 ___ 20

4 3 of the 7 total trials resulted in a sum more than 5

Therefore the experimental probability is 3 __ 7

5 I would predict he would reach first base 24 times

because 3 ___ 10

= x ___ 80

= 24 ___ 80

or 24 times

6 You can use the experimental probability based on

observation or simulation to set up a proportion and

use the proportion to predict a value

times15

times15

times24

times24

times2

times2

times3

times3

times2

times2

times25

times25

times8

times8


MODULE 13 Theoretical Probability and

Simulations

Are You Ready

075

1 4 ⟌ _

300

_ -2 80

20

_ -20

0

075 = 75

04

2 5 ⟌ _

20

_ -2 0

0

04 = 40

09

3 10 ⟌ _

90

_ -9 0

0

09 = 90

035

4 20 ⟌ _

700

_ -6 00

1 00

_ -1 00

0

035 = 35

0875

5 8 ⟌ _

7000

_ thinsp-6 400

600

_ -560

40

_ -40

0

0875 = 875

005

6 20 ⟌ _

100

_ -1 00

0

005 = 5

076

7 25 ⟌ _

1900

_ -17 50

1 50

_ -1 50

0

076 = 76

046

8 50 ⟌ _

2300

_ -20 50

3 00

_ -3 00

0

046 = 46

9 1 - 1 __ 5 = 5 __

5 - 1 __

5

= 4 __ 5

10 1 - 2 __ 9 = 9 __

9 - 2 __

9

= 7 __ 9

11 1 - 8 ___ 13

= 13 ___ 13

- 8 ___ 13

= 5 ___ 13

12 1 - 3 ___ 20

= 20 ___ 20

- 3 ___ 20

= 17 ___ 20

13 8 ___ 15

times 5 __ 8 =

18 ___ 315

times 5 1 ___

8 1

= 1 __ 3

14 2 __ 9 times 3 __

4 =

12 __ 39

times 3 1 ___

4 2

= 1 __ 6

15 9 ___ 16

times 12 ___ 13

= 9 ___ 416

times 12 3 _____

13

= 27 ___ 52

16 7 ___ 10

times 5 ___ 28

= 17 ___

210 times 5

1 ____

28 4

= 1 __ 8

LESSON 131

Your Turn

2 The probability of an event is the ratio of the number

of ways the event can occur to the total number of

equally likely outcomes Therefore

P(rolling a 3 or 4) =

number of sides with 3 or 4 ________________________ total number of sides on cube

= 2 __ 6 = 1 __

3

3 The total number of outcomes in the sample space

is the denominator of the formula for theoretical

probability


Guided Practice

1

Basket A Basket B

Total number of outcomes5 + 3 + 8

= 16

7 + 4 + 9

= 20

Number of red balls 3 4

P(win) =

Number of red balls

_____________________ Total number of outcomes

3 ___

16 4 ___

20 = 1 __

5

2 To compare the two probabilities of 1 __ 5 and 3 ___

16 use

the least common denominator of 80

1 __ 5 = 16 ___

80

3 ___ 16

= 15 ___ 80

Therefore 16 ___ 80

gt 15 ___ 80

so 1 __ 5 gt 3 ___

16

Choosing Basket B gives you a better chance of

winning

3 There are a total of 6 odd sections The total number

of sections (odd and even) is 11

P(odd) = number of odd sections ____________________ total number of sections

= 6 ___ 11

4 There are a total of 5 even sections The total

number of sections (odd and even) is 11

P(even) = number of even sections ____________________ total number of sections

= 5 ___ 11

5 The total number faces on a number cube is 6 and

rolling either a 3 or 4 is equal to 2 possibilities

P(rolling a 3 or 4) = number of sides with 3 or 4 ________________________ total number of sides on cube

= 2 __ 6 = 1 __

3

6 Sample answer No but it might be reasonably

close

7 Divide the number of ways the event can occur

by 20


8 P(yellow) = number of yellow sections

_____________________ total number of sections

= 2 __ 6

= 1 __ 3 033 or 33

9 P(blue or green) = number of blue or green sections

___________________________ total number of sections

= 8 ___ 12

= 2 __ 3 067 or 67

10 P(cherry) = number of cherry cough drops

_________________________ total number of cough drops

= 4 ___ 14

= 2 __ 7 029 or 29

11 P(black card) = number of black cards __________________ total number of cards

= 26 ___ 52

= 1 __ 2 050 or 50

12 P(lime) = number of limes ________________________ total number of pieces of fruit

= 12 - 5 ______ 12

= 7 ___ 12

058 or 58

13 There are a total of 20 DVDs There are 12 DVDs

that are not comedies (5 science fiction plus

7 adventure)

P(not a comedy)

= number of DVDs which are not comedies _________________________________ total number of DVDs

= 5 + 7 _________

5 + 7 + 8 = 12 ___

20

= 3 __ 5 060 or 60

14 There are a total of 6 faces on a number cube There

are 2 faces (3 and 4) that are greater than 2 and

less than 5 which means 2 possibilities

P(greater than 2 and less than 5)

= number of sides with 3 and 4 ________________________ total number of sides on cube

= 2 __ 6

= 1 __ 3 033 or 33

15 9 represents the ways the event can occur

13 represents the number of equally likely outcomes

16 There are a total 16 coins and there are 6 coins that

are greater than 5 cents Therefore

P(coin worth more than 5 cents)

= number of coins worth more than 5 cents _________________________________ total number of coins

= 6 ___ 16

or 3 __ 8

The event is choosing a dime or a quarter and 6 of

the 16 coins are dimes or quarters


17 Sample answer Riley divided the number of petunia

seeds by the number of begonia seeds rather than

the total number of seeds The correct probability is

5 ______ 5 + 15

= 5 ___ 20

= 1 __ 4

times16

times16

times5

times5


18 a The total number of students in the club is 35

There are 20 seventh graders Therefore

P(seventh grader) =

number of seventh graders

______________________ total number of students

= 20 ___ 35

= 4 __ 7

There are 15 eighth graders in the club Therefore

P(eighth grader) =

number of eighth graders

_____________________ total number of students

= 15 ___ 35

= 3 __ 7

Because 4 __ 7 gt 3 __

7 choosing a seventh grader is

more likely

b No each student has the same probability of

being selected 1 ___ 35

19 Sample answer The number of trials is twice the

number of marbles in the jar If the probabilities for

each color were the same the number of times that

color was drawn would be twice the number of

marbles with that color in the jar

20 Red The theoretical probability of choosing red is

P(red) = number of red marbles ___________________ total number of marbles

= 8 ___ 20

The experimental probability of choosing red is

14 ___ 40

or 7 ___ 20

Therefore the difference in the theoretical probability

and experimental probability of choosing a red

marble is 8 ___ 20

- 7 ___ 20

= 1 ___ 20

For blue the theoretical probability is

P(blue) = number of blue marbles ____________________ total number of marbles

= 10 ___ 20

The experimental probability is 16 ___ 40

= 8 ___ 20


and experimental probability of choosing a blue

marble is 10 ___ 20

- 8 ___ 20

= 2 ___ 20

= 1 ___ 10

For yellow the theoretical probability is

P(yellow) = number of yellow marbles

_____________________ total number of marbles

= 2 ___ 20


= 5 ___ 20


and experimental probability of choosing a yellow

marble is 5 ___ 20

- 2 ___ 20

= 3 ___ 20

Choosing a red marble has the smallest difference

between theoretical and experimental probability

LESSON 132

Your Turn

3 P(ham sandwich) =

number of combinations containing ham

_________________________________ total number of sandwich combinations

= 4 ___ 12

= 1 __ 3

4 P(sandwich containing Swiss cheese) =

number of combinations containing Swiss

__________________________________ total number of sandwich combinations

= 6 ___ 12

= 1 __ 2

5 To find the sample space make lists of possible

codes First make a list of codes that start with 0

and have 0 as the second digit

0 0 0 0

0 0 0 1

0 0 1 0

0 0 1 1

List of codes that start with 0 and have 1 as the

second digit

0 1 0 0

0 1 0 1

0 1 1 0

0 1 1 1


second digit

1 0 0 0

1 0 0 1

1 0 1 0

1 0 1 1


second digit

1 1 0 0

1 1 0 1

1 1 1 0

1 1 1 1

In total the number of possible outcomes is 16

There are six codes with exactly two 0s

0 0 1 1

0 1 0 1

0 1 1 0

1 0 0 1

1 0 1 0

1 1 0 0

This means the number of outcomes for a code with

exactly two 0s is 6 Therefore

P(Code exactly two 0s)

= number of favorable outcomes ____________________________ total number of possible outcomes

= 6 ___ 16

= 3 __ 8


Guided Practice

1

1 2 3 4 5 6

11 sdot 1

= 1

1 sdot 2

= 2

1 sdot 3

= 3

1 sdot 4

= 4

1 sdot 5

= 5

1 sdot 6

= 6

22 sdot 1

= 2

2 sdot 2

= 4

2 sdot 3

= 6

2 sdot 4

= 8

2 sdot 5

= 10

2 sdot 6

= 12

33 sdot 1

= 3

3 sdot 2

= 6

3 sdot 3

= 9

3 sdot 4

= 12

3 sdot 5

= 15

3 sdot 6

= 18

44 sdot 1

= 4

4 sdot 2

= 8

4 sdot 3

= 12

4 sdot 4

= 16

4 sdot 5

= 20

4 sdot 6

= 24

55 sdot 1

= 5

5 sdot 2

= 10

5 sdot 3

= 15

5 sdot 4

= 20

5 sdot 5

= 25

5 sdot 6

= 30

66 sdot 1

= 6

6 sdot 2

= 12

6 sdot 3

= 18

6 sdot 4

= 24

6 sdot 5

= 30

6 sdot 6

= 36

2 There are 15 entries in the table that are multiples

of 4 The total number of entries in the table is 36

P(multiple of 4) = number of multiples of 4

_________________________ total number of entries in table

= 15 ___ 36

3 There are 23 entries in the table that are less than

13 The total number of entries is 36

P(less than 13) = number of entries less than 13 _________________________ total number of entries in table

= 23 ___ 36

4 H

HHH HHT

H

H

Coin 1

List

Coin 2

Coin 3 T

T

HTH HTT

H T

T

H

H T

THH THT

T

H T

TTH TTT

Coin 1

List

Coin 2

Coin 3

5 Count the total number of outcomes in the list 8

6 The only way to get three tails is TTT

7 P = number of outcomes with 3 tails __________________________ total number of outcomes

= 1 __ 8

8 There are 3 way(s) to obtain exactly two heads

HHT HTH THH

P = number of outcomes with exactly 2 heads

__________________________________ total number of possible outcomes

= 3 __ 8

9 You need to know the number of equally likely

outcomes in the sample space


10

Checkered

Red

Checkered

Red

Blue

Black

Checkered

Red

Checkered

Red

Blue

Black

Checkered

Red

Checkered

Red

Blue

Black

Shirt Pants Shoes

Yellow

Red

Green

11 There are 6 combinations that include red shoes

The total number of combinations is 12 Therefore

P(red shoes) = number of combinations with red shoes ________________________________ total number of combinations

= 6 ___ 12

= 1 __ 2

12 There are four combinations that do not include red

Shirt Pants Shoes

Green Blue Checkered

Green Black Checkered

Yellow Blue Checkered

Yellow Black Checkered

P(no red) = number of outfits with no red _______________________ total number of outfits

= 4 ___ 12

= 1 __ 3

13 Let the other three band members be A B and C

The list of possible combinations is

Rhee Pamela

Rhee A

Rhee B

Rhee C

Pamela A

Pamela B

Pamela C

A B

A C

B C

There is a total of 10 combinations Of these only 1

has Rhee and Pamela so

P(Rhee and Pamela)

= Rhee and Pamela ________________________ total number of combinations

= 1 ___ 10


14 The sample space can be found from adding all

possible combinations of the two numbers

1 2 3 4 5 6

11 + 1

= 2

1 + 2

= 3

1 + 3

= 4

1 + 4

= 5

1 + 5

= 6

1 + 6

= 7

22 + 1

= 3

2 + 2

= 4

2 + 3

= 5

2 + 4

= 6

2 + 5

= 7

2 + 6

= 8

33 + 1

= 4

3 + 2

= 5

3 + 3

= 6

3 + 4

= 7

3 + 5

= 8

3 + 6

= 9

44 + 1

= 5

4 + 2

= 6

4 + 3

= 7

4 + 4

= 8

4 + 5

= 9

4 + 6

= 10

55 + 1

= 6

5 + 2

= 7

5 + 3

= 8

5 + 4

= 9

5 + 5

= 10

5 + 6

= 11

66 + 1

= 7

6 + 2

= 8

6 + 3

= 9

6 + 4

= 10

6 + 5

= 11

6 + 6

= 12

There is a total of 36 possible sums Of these there

are 10 less than 6

P(sum is less than 6)

= number of sums less than 6 ____________________________ total number of possible outcomes

= 10 ___ 36

= 5 ___ 18

15 The sample space can be found from a tree

diagram

Khakis

Shorts

Shirt Pants Shoes

Collared Jeans

Sneakers

Flip-flops

Sandals

Sneakers

Flip-flops

Sandals

Sneakers

Flip-flops

Sandals

Khakis

Shorts

T-shirt Jeans

Sneakers

Flip-flops

Sandals

Sneakers

Flip-flops

Sandals

Sneakers

Flip-flops

Sandals

Total number of possible outcomes is 18 the

number of combinations which include jeans but

not sneakers is 4 Therefore

P(jeans but not sneakers)

= number of outfits with jeans no sneakers

_________________________________ total number of possible outcomes

= 4 ___ 18

= 2 __ 9

16 For each chair lift there are 6 possible trails So you

can multiply the number of choices of chair lifts (3)

by the number of trails (6)

17 Because there are 3 choices for the first item and

2 for the second there are 3 middot 2 = 6 possible

outcomes

18 There is a total of 30 possible shoe sizes Of these

the number of red shoes size 9 or larger is 7

Therefore

P(red and size 9 or larger) =

number of red shoes size 9 or larger

______________________________ total number of possible outcomes

= 7 ___ 30


19 Sondra orders one item from each column There

are 4 main dishes 4 vegetables and two sides so

the sample space is 4 sdot 4 sdot 2 = 32 The possible

outcomes of Sondrarsquos order are shown in the tree

diagram

Carrots

Sweet potato

Pasta

Peas

Asparagus

Tossed saladTomato soup




Carrots

Sweet potato

Peas

Asparagus





Carrots

Sweet potato

Peas

Asparagus





Carrots

Sweet potato

Peas

Asparagus





Salmon

Beef

Pork


There are 8 total number of outcomes that include

salmon Therefore

Sondra P(salmon) = 8 ___ 32

= 1 __ 4

Gretchen orders a main dish and a vegetable There

are 4 main dishes and 4 vegetables so the sample

space is 4 sdot 4 = 16 The possible outcomes of

Gretchenrsquos order are shown in the tree diagram

Carrots

Sweet potato

PastaPeas

Asparagus

Carrots

Sweet potato

Peas

Asparagus

Carrots

Sweet potato

Peas

Asparagus

Carrots

Sweet potato

Peas

Asparagus

Salmon

Beef

Pork


salmon Therefore

Gretchen (salmon) = 4 ___ 16

= 1 __ 4

Because the probabilities for Sondra and Gretchen

are equal neither has a greater probability of getting

a meal that includes salmon

20 a For possible two-digit codes consider first codes

that begin with 1 12 13 14 15 There are a total

of 4 possible codes This pattern continues for

each of the 5 digits and therefore we have a total

of 4 + 4 + 4 + 4 + 4 = 20 possible two-digit

codes (four codes each that begin with each of

the numbers 1ndash5)

For possible three-digit codes there are 12

possible codes that begin with 1 and so there are

12 possible codes for each of the numbers 1ndash5

making a total of 5 sdot 12 = 60 possible three-digit

codes

We can predict the number of possible five-digit

codes because we know there are 60 possible

three-digit codes and for each of these there are

only two digits that can be added to the end of

each code to make them five-digit codes These

are the digits that were not used in the three-digit

code and they have two possible orders for a

total of 60 sdot 2 = 120 possible five-digit codes

As a concrete example again consider the three-

digit codes that begin with 1 Tacking on the digits

which are not included in these three-digit codes

in both orders we have 12345 12354 12435

12453 12534 12543 13245 13254 13425

13452 13524 13542 14235 14253 14325

14352 14523 14532 15234 15243 15324

15342 15423 15432 If we do the same for the

three-digit codes beginning with 2ndash5 we will find

the 120 possible five-digit codes

b Now that the numbers can repeat for two-digit

codes take the 20 codes from before and add five

more codes (11 22 33 44 55) which makes a

total of 25 two-digit codes

For three-digit codes take the 60 codes from

before and add the 5 codes that have all digits

the same plus codes which have two digits

which are repeats To find these consider first the

codes with the first two digits the same 112 113

114 115 221 223 224 225 331 332 334 335

441 442 443 445 551 552 553 554 There

are 20 possible codes There are also 20 possible

codes with the last two digits the same Finally

consider the codes where the first and last digits

are the same For the repeated digit 1 we have

121 131 141 151 or 4 possible codes For each

of the digits 1ndash5 we have 4 possible codes for a

total of 4 sdot 5 = 20 Therefore the overall total

60 + 5 + 20 + 20 + 2 = 125 three-digit codes

To solve for how many possible 5 digit codes

there are notice a pattern in the codes For

two-digit codes the total possible codes is the

number of possible digits raised to the power

equal to the number of digits in the code or

52 = 25 For three-digit codes the number of

possible digits is the same and the number

of digits in the code is 3 so we have 53 = 125

Following this pattern there are 55 = 3125

possible five-digit codes

c Sample answer The better choice is to have the

digits repeat there are more unique codes with

repeated digits than without so it would be more

difficult for someone to guess a code for a locker

LESSON 133

Your Turn

1 There are 4 numbers less than 5 on a standard

number cube There are 6 possible outcomes so

P(number less than 5) = 4 __ 6 = 2 __

3

The number of events is 250 Therefore

P(number less than 5) times Number of events =

2 __ 3 times 250 = 16666 or about 167 times


2 Set up a proportion The probability of getting

heads is 1 __ 2

1 __ 2 = x ___

18

1 __ 2 = x ___

18

x = 9

about 9 times

3 There are 17 total marbles and 8 are red Therefore

P(red) = 8 ___ 17

P(not red) = 1 - 8 ___ 17

= 9 ___ 17

It is more likely that he picks a marble that is not red

4 No Sample answer There is a total of 71 bills in the

bag and there are 11 bills worth $6 or more

Therefore

P(bill worth $6 or more) = 11 ___ 71

This is about a 15 probability so it is not likely you

will win enough to pay for your ticket

Guided Practice

1 An equally likely chance means that the probabilities

of being assigned to each crew are the same and

since there are three possibilities each has a

probability of 1 __ 3

Apartment 1 __ 3 Condo 1 __

3 House 1 __

3

The probability of being assigned to house crew is 1 __ 3

Set up and solve a proportion

1 __ 3 = x ___

18

1 __ 3 = x ___

18

x = 6

This means that Bob can expect to be assigned to

the house crew about 6 times out of 18

2 Since half of the ticket holders will receive a prize

this means that 300 divide 2 = 150 people will receive a

prize Because they are equally likely to receive one

of three prizes the probability of winning each of the

prizes is 1 __ 3 so the probability of winning a movie

ticket is 1 __ 3 The number of events is 150 Therefore

P(movie ticket) times Number of events = 1 __ 3 times 150 =

50 or 50 people are predicted to win a movie ticket

3 The total number of students in Mr Jawaranirsquos class

is 28 The probabilities of picking a student at

random with a certain eye color are

P(hazel) = 9 ___ 28

P(brown) = 10 ___ 28

P(blue) = 7 ___ 28

P(green) = 2 ___ 28

The event with the greatest probability is choosing a

person with brown eyes

4 You can find and compare probabilities Or you can

use probability to set up and solve a proportion or

an equation that relates the probability to the

unknown quantity


5 The total number of marbles in the bag is 9 The

number of white or gray marbles is 3 Therefore

P(white or gray) = 3 __ 9 = 1 __

3

The number of events is 45 The equation to make a

prediction is then

P(white or gray) times Number of events = 1 __ 3 times 45 = 15

You can expect to get 15 white or gray marbles

6 A spinner which has an equal likelihood to land on

green or yellow means that the number of green and

yellow sections must be equal More likely to land on

red means that there must be more red sections

than yellow or green A Sample answer is

Y GRR

R R

RR

7 Because half the deck is red the probability of

drawing a red card is 1 __ 2 Because there are three

face cards for each of four suits there are 3 sdot 4 = 12

face cards and the probability of drawing a face

card is 12 ___ 52

To compare 1 __ 2 and 12 ___

52 use the least

common denominator of 52 so that 1 __ 2 = 26 ___

52 Given

that 12 ___ 52

lt 26 ___ 52

the probability of drawing a red card

is higher than of drawing a face card and it is more

likely that Dawn draws 2 red cards

8 The total number of aces in a deck is 4 Therefore

P(ace) = 4 ___ 52

= 1 ___ 13


prediction is then

P(ace) middot Number of events = 1 ___ 13

times 39 = 3

He is predicted to draw an ace 3 times

9 The total number of red cards is 26 Therefore

P(red card) = 26 ___ 52

= 1 __ 2

The number of events is 1000 The equation to

make a prediction is then

P(red card) sdot Number of events = 1 __ 2 sdot 1000 = 500

The player is predicted to turn over a red card as the

first card 500 times



times6

times6

times9

times9


1 2 3 4 5 6

1 2 3 4 5 6 7

2 3 4 5 6 7 8

3 4 5 6 7 8 9

4 5 6 7 8 9 10

5 6 7 8 9 10 11

6 7 8 9 10 11 12


are 5 ways to roll a sum of 8 and 2 ways to roll a

sum of 11 The probabilities are

P(sum of 8) = 5 ___ 36

P(sum of 11) = 2 ___ 36

Because the probability of rolling a sum of 8 is

greater than that of rolling a sum of 11 ( 5 ___ 36

gt 2 ___ 36

) John is more likely to win

11 There are 5 possible numbers greater than 15 so

P(greater than 15) = 5 ___ 20

= 1 __ 4

The number of events is 180 The equation to make

a prediction is then

P(greater than 15) times Number of events =

1 __ 4 times 180 = 45

The chosen number will be greater than 15 for 45

days in the school year

12 The sample space for a standard cube is 36 and

there are 3 combinations that will have a sum of 4

so P(sum of 3) = 3 ___ 36

= 1 ___ 12


prediction is then

P(sum of 3) times Number of events = 1 ___ 12

middot 36 = 3

Eben is predicted to roll a sum of 4 a total of 3 times

13 Sample answer No Every time you flip a coin the

probability of heads is 1 __ 2 but in reality you could flip

a coin many times and have it land heads up every

time

14 Sample answer A bag of marbles contains red and

blue marbles that are different sizes Since it is easy

to feel the difference between the two colors all of

the outcomes are not equally likely You cannot make

a prediction using theoretical probability


15 Sample answer What is the theoretical probability

that the coin lands on heads and you pick a marble

that is not green

The probability that the coin lands on heads is 1 __ 2

and the probability that the picked marble is not

green is 3 + 9 _________

3 + 8 + 9 = 12 ___

20 The product of these two

probabilities is 1 __ 2 times 12 ___

20 = 12 ___

40

16 Sample answer It is much more likely that he rolls a

5 or the coin lands on heads

The probability that Horace rolls a 5 and the coin

lands on heads is given by

P(5 and heads) = 1 __ 2 times 1 __

6 = 1 ___

12

In the case where Horace rolls a 5 or the coin lands

on heads the probability is given by

P(5 or heads) = 1 __ 6 + 1 __

2 - 1 __

6 times 1 __

2 = 7 ___

12

17 Yes but only theoretically because in reality nothing

can occur 05 times Sample answer The probability

that a flipped coin lands heads up is 1 __ 2 so in 75 flips

you can expect heads about 75 ___ 2 or 375 times

LESSON 134

Your Turn

1 Sample answer (data and percent will vary)

Trial Numbers generated 3 Males first

1 0 0 1 No

2 0 1 No

3 1 No

4 0 1 No

5 1 No

6 0 0 0 1 Yes

7 0 0 1 No

8 0 1 No

9 1 No

10 0 0 0 0 1 Yes

For these data the experimental probability that the

elephant gives birth to 3 male calves before having a

female calf is 2 ___ 10

or 20

2 Sample Answer (data and percent will vary)

Trial Numbers generated Correct answers

1 1 0 1 1 0 3

2 0 1 0 0 1 2

3 0 0 0 0 1 1

4 0 0 1 1 0 2

5 1 1 1 1 1 5

6 1 0 0 0 0 1

7 1 0 1 1 0 3

8 1 0 1 0 0 2

9 0 1 1 1 1 4

10 0 0 0 0 0 0

The experimental probability that he gets at least 2

questions right is 7 ___ 10

= 70


Guided Practice

1 Since there is a 30 or 3 ___ 10

chance of drought let

the numbers 1 to 3 represent years with a drought

and the numbers 4 to 10 represent years without

a drought Since we are interested in the next 4

years perform multiple trials generating 4 random

numbers each time

2

Trial Numbers generated Drought years

1 10 3 5 1 2

2 10 4 6 5 0

3 3 2 10 3 3

4 2 10 4 4 1

5 7 3 6 3 2

6 8 4 8 5 0

7 6 2 2 8 2

8 6 5 2 4 1

9 2 2 3 2 4

10 6 3 1 5 2

3 In 8 out of the 10 trials there was a drought in at

least one of the years The experimental probability

of a drought in at least 1 of the next 4 years is

8 ___ 10

= 80

4 Sample answer Generate whole numbers from

1 to 4 Let 1 to 3 represent the event occurring

and 4 represent the event not occurring


5 There is only 1 trial Trial 6 where it took exactly

4 contestants to get a winner

6 Since 1 out of 10 trials resulted in exactly

4 contestants the probability is 1 ___ 10

= 10

7 The trials for which at least 4 hurricanes struck are

Trials 2 and 7 or 2 out of 10 trials Therefore the

probability is 2 ___ 10

= 20

8 It is fewer than expected based on the simulation

9 It is unlikely but it is not impossible Each of the 3

numbers could be any number from 1 to 10

However there are 10 possible first numbers 10

possible second numbers and 10 possible third

numbers or a total of 1000 possible numbers when

generating three numbers from 1 to 10 The

probability of generating three 10s is 1 _____ 1000

10 Sample answer Use the numbers 1ndash5 where 1 2

and 3 represent packs which contain a player from

Erikarsquos favorite team Generate numbers randomly

and stop when you get a 1 2 or 3

Trial Numbers generated Number of Packs

1 3 1

2 4 2 2

3 2 1

4 1 1

5 2 1

6 4 5 3 2

7 4 2 2

8 4 5 2 1

9 4 4 3 3

10 5 1 2

The average number of packs she needs to buy is

1 + 2 + 1 + 1 + 1 + 2 + 2 + 1 + 3 + 2

_________________________________ 10

= 16 ___ 10

= 1 3 __ 5

packs Since she cannot buy a fraction of a pack

she must buy 2 packs


11 Sample answer The probability that she makes a

shot is 375 = 3 __ 8 Use the whole numbers from 1 to

8 with 1ndash3 representing shots she makes and 4ndash8

representing shots she misses For each new trial

generate 10 random numbers Count the number

of times 1 2 or 3 appears in each trial Divide the

number of trials in which she made at least 3 shots

by the total number of trials

12 Sample answer Their simulation was not

appropriate perhaps because they chose an

incorrect model You would expect there to have

been exactly 4 heads on more of the trials and

more variation in the number of heads in general

MODULE 13

Ready to Go On

1 P(red) = number of red marbles ___________________ total number of marbles

= 12 ___________________ 12 + 12 + 15 + 9 + 12

= 12 ___ 60

= 1 __ 5 020 or 20

2 P(diamond or spade)

= number of diamonds and spades

___________________________ total number of cards

= 13 + 13

_______ 52

= 26 ___ 52

= 1 __ 2 050 or 50

3 The most likely color of marble chosen is the most

common color in this case green


4 In order to find the experimental probability count

the number of trials in which 1 occurs at least once

In this case there are 4 trials that generated a 1

Therefore the experimental probability is 4 ___ 10

or

40

5 Sample answer You can find the theoretical

probability of an event and then use it to make a

prediction by setting up a proportion


Cover Image Credits Baja copyRadius ImagesCorbis

Copyright copy by Houghton Mifflin Harcourt Publishing Company

All rights reserved No part of this work may be reproduced or transmitted in any form or by any means electronic or mechanical including photocopying or recording or by any information storage and retrieval system without the prior written permission of the copyright owner unless such copying is expressly permitted by federal copyright law Requests for permission to make copies of any part of the work should be addressed to Houghton Mifflin Harcourt Publishing Company Attn Contracts Copyrights and Licensing 9400 Southpark Center Loop Orlando Florida 32819-8647

Printed in the USA

ISBN 978-0-544-20723-3

1 2 3 4 5 6 7 8 9 10 XXXX 22 21 20 19 18 17 16 15 14 13

4500000000 B C D E F G

If you have received these materials as examination copies free of charge Houghton Mifflin Harcourt Publishing Company retains title to the materials and they may not be resold Resale of examination copies is strictly prohibited

Possession of this publication in print format does not entitle users to convert this publication or any portion of it into electronic format


7_MCABESK207233_FMCPindd 2 11713 600 PM

Table of Contents


Module 1Lesson 11 1

Lesson 12 2

Lesson 13 3

Lesson 14 4

Module 2Lesson 21 6

Lesson 22 7

Lesson 23 8


Lesson 32 14

Lesson 33 15

Lesson 34 17

Lesson 35 18

Lesson 36 20


Relationships


Lesson 42 25

Lesson 43 25


Lesson 52 29

Lesson 53 30


and Inequalities


Lesson 62 34

Lesson 63 35

Lesson 64 37


Lesson 72 46

Lesson 73 47

UNIT 4 Geometry


Lesson 82 54

Lesson 83 54

Lesson 84 55


Lesson 92 59

Lesson 93 60

Lesson 94 63

Lesson 95 65

UNIT 5 Statistics


Lesson 102 70

Lesson 103 72


Lesson 112 75

Lesson 113 76


Table of Contents

UNIT 6 Probability


Lesson 122 81

Lesson 123 82

Lesson 124 82


Lesson 132 86

Lesson 133 89

Lesson 134 91



Are You Ready


2 a $700 profit 700



1 1

5 183

_ + 78

261

261

5 16 17

6 677

_ -288

389

389

1 1

7 1188

_ +902

2090

2090

1 15 14

8 2647

_ -1885

762

762

9

-8-10 -4-6 -2 2 4 6 8 100 10

-8-10 -4-6 -2 2 4 6 8 100 11

-8-10 -4-6 -2 2 4 6 8 100 12

-8-10 -4-6 -2 2 4 6 8 100

LESSON 11

Your Turn

7 -8 + ( -1 ) = -9

8 -3 + ( -7 ) = -10

9 -48 + ( -12 ) = -60

10 -32 + ( -38 ) = -70

11 109 + 191 = 300

12 -40 + ( -105 ) = -145

13 -150 + ( -1500 ) = -1650

14 -200 + ( -800 ) = -1000

Guided Practice



c -5 + ( -1 ) = -6



c -2 + ( -7 ) = -9

3 -5 + ( -2 ) = -7

-8-7-6-5 -2-1 0-4-3 4 -1 + ( -3 ) = -4

-5-4-3-2 1 2 3-1 0 5 -3 + ( -7 ) = -10

-10 -9-8-7 -4-3-2-6-5 6 -4 + ( -1 ) = -5

-5-4-3-2 1 2 3-1 0 7 -2 + ( -2 ) = -4

-5-4-3-2 1 2 3-1 0 8 -6 + ( -8 ) = -14

-16 -12 -4 0-8 9 -5 + ( -4 ) = -9

10 -1 + ( -10 ) = -11

11 -9 + ( -1 ) = -10

12 -90 + ( -20 ) = -110

13 -52 + ( -48 ) = -100

14 5 + ( 198 ) = 203

15 -4 + ( -5 ) + ( -6 ) = -15

16 -50 + ( -175 ) + ( -345 ) = -570




UNIT

1



18 a

-4

-6

-8

-2

0

2

-5 + (-3)-3 + (-5)

b No -5 + ( -3 ) is -8 and -3 + ( -5 ) is also -8


score is -11


21 -14 + ( -5 ) + ( -12 ) + ( -23 ) = -54 The total


22 a -10 + ( -8 ) = -18

b -6 + ( -2 ) = -8


23 -100 + ( -75 ) + ( -85 ) = -260


24 a -25 + ( -45 ) + ( -75 ) = -145 Jan withdrew

$145

b -35 + ( -55 ) + ( -65 ) = -155 Julie withdrew

$155








six pairs is 8

LESSON 12

Your Turn

7 -51 + 23

ǀ -51 ǀ - ǀ 23 ǀ = 28

-51 + 23 = -28

8 10 + ( -18 )

ǀ -18 ǀ - ǀ 10 ǀ = 8

10 + ( -18 ) = -8

9 13 + ( -13 )

ǀ 13 ǀ - ǀ -13 ǀ = 0

10 25 + ( -26 )

ǀ -26 ǀ - ǀ 25 ǀ = 1

25 + ( -26 ) = -1

Guided Practice

1 9 + ( -3 ) = 6

2 3 4 5 8 9 106 7 2 -2 + 7 = 5

-3-2-1 0 3 4 51 2 3 -15 + 4 = -11

-18 -16 -12 -10-14 4 1 + ( -4 ) = -3

-5-4-3-2 1 2 3-1 0 5 -4 + 5 = 1

6 -6 + 6 = 0

7 2 + ( -5 ) = -3

8 -3 + 7 = 4

9 -8 + 14 = 6

10 7 + ( -5 ) = 2

11 5 + ( -21 ) = -16

12 14 + ( -14 ) = 0

13 0 + ( -5 ) = -5

14 32 + ( -8 ) = 24





16 -15 + 71 = 56

17 -53 + 45 = -8

18 -79 + 79 = 0

19 -25 + 50 = 25

20 18 + ( -32 ) = -14

21 5 + ( -100 ) = -95

22 -12 + 8 + 7 = 3

23 -8 + ( -2 ) + 3 = -7


24 15 + ( -15 ) + 200 = 200

25 -500 + ( -600 ) + 1200 = 100
















is 8 feet deep








LESSON 13

Your Turn

4 -7 - 2 = -7 + ( -2 )

-7 + ( -2 ) = -9

5 -1 - ( -3 ) = -1 + 3

-1 + 3 = 2

6 3 - 5 = 3 + ( -5 )

3 + ( -5 ) = -2

7 -8 - ( -4 ) = -8 + 4

-8 + 4 = -4

Guided Practice







3 -4 - 5 = -4 + ( -5 ) = -9

0-1-2-3-4-5-6-7-8-9 4 1 - 4 = 1 + -4 = -3

0 1 2 3 4-1-2-3-4 5 8 - 11 = 8 + ( -11 ) = -3

6 -3 - ( -5 ) = -3 + 5 = 2

7 15 - 21 = 15 + ( -21 ) = -6

8 -17 - 1 = -17 + ( -1 ) = -18

9 0 - ( -5 ) = 0 + 5 = 5

10 1 - ( -18 ) = 1 + 18 = 19

11 15 - 1 = 14

12 -3 - ( -45 ) = -3 + 45 = 42

13 19 - ( -19 ) = 19 + 19 = 38

14 -87 - ( -87 ) = -87 + 87 = 0


example 6 - 8 = 6 + ( -8 ) = -2




25 - ( -4 ) = 25 + 4 = 29





-127 - ( -225 ) = -127 + 225 = 98



temperature 90degF

90 - ( -2 ) = 92






-425 - ( -275 ) = -425 + 275 = -150



in temperature

Gas A -8 - ( -21 ) = -8 + 21 = 13

13degC increase

Gas B 12 - ( -12 ) = 12 + 12 = 24

24degC increase

Gas C -15 - ( -19 ) = -15 + 19 = 4

4degC increase













-11 + 4 = -7




LESSON 14

Your Turn




Guided Practice


2 -23+5-7=-18-7  =-25-25degF

3 50-40+87-30=10+87-30  =97-30  =6767points

4 -6+15+15=-6+30  =24

5 9- 4- 17= 9- 21  =-12

6 50-42+10=8+10  =18

7 6+13+7-5=19+2  =21

8 65+43-11=108-11  =97

9 -35-14+45+31=-49+76  =27

10 -12+6-4=-6-4  =-10-34-3+39=-37+39  = 2  -10lt2( -12+6-4)lt( -34-3+39)

11 21-3+8=18+8  =26-14+ 31- 6= 17- 6  =11 26gt11( 21-3+8)gt( -14+31-6)



13 a 5-1+6-1=9






b 45gt-55Barry

17 a 300to400


18 100-18+22-53=51$51

19 45-17-22+18=24$24






MODULE 1

Ready to Go On

1 -8+( -6)=-14

2 -4+( -7)=-11

3 -9+( -12)=-21





4 5 + ( -2 )

ǀ 5 ǀ - ǀ -2 ǀ = 3

5 + ( -2 ) = 3

5 -8 + 4

ǀ -8 ǀ - ǀ 4 ǀ = 4

-8 + 4 = -4

6 15 + ( -8 )

ǀ 15 ǀ - ǀ -8 ǀ = 7

15 + ( -8 ) = 7

7 2 - 9 = 2 + ( -9 )

2 + ( -9 ) = -7

8 -3 - ( -4 ) = -3 + 4-3 + 4 = 1

9 11 - ( -12 ) = 11 + 12

11 + 12 = 23

10 -15 + 9 - 4 = -6 - 4

= -10


11 24 + 8 - 12 - 9 = 24 + 8 - ( 12 + 9 ) = 32 - 21

= 11




after she pays them

-10 + ( -5 ) = -15 $15 decrease



Are You Ready

1 9 times 3 = 27

2 7 times 10 = 70

3 9 times 8 = 72

4 15 times 10 = 150

5 6 times 9 = 54

6 10 times 23 = 230

7 9 times 9 = 81

8 10 times 20 = 200

9 54 divide 9 = 6

10 42 divide 6 = 7

11 24 divide 3 = 8

12 64 divide 8 = 8

13 90 divide 10 = 9

14 56 divide 7 = 8

15 81 divide 9 = 9

16 110 divide 11 = 10

17 12 + 8 divide 212 + 4

16

18 15 - ( 4 + 3 ) times 2

15 - 7 times 2

15 - 14

1

19 18 - ( 8 - 5 ) 2

18 - ( 3 ) 2

18 - 9

9

20 6 + 7 times 3 - 5

6 + 21 - 5

27 - 5

22

21 9 + ( 2 2 + 3 ) 2 times 2

9 + ( 4 + 3 ) 2 times 2

9 + ( 7 ) 2 times 2

9 + 49 times 2

9 + 98

107

22 6 + 5 - 4 times 3 divide 2

6 + 5 - 12 divide 2

6 + 5 - 6

11 - 6

5

LESSON 21

Your Turn


will be negative


-3 ( 5 ) = -15


will be positive

ǀ -10 ǀ times ǀ -2 ǀ = 10 times 2 = 20

( -10 ) ( -2 ) = 20


0 ( -22 ) = 0


will be positive

8 ( 4 ) = 32

Guided Practice

1 -1 ( 9 ) = -9

2 14 ( -2 ) = -28

3 ( -9 ) ( -6 ) = 54

4 ( -2 ) ( 50 ) = -100

5 ( -4 ) ( 15 ) = -60

6 -18 ( 0 ) = 0

7 ( -7 ) ( -7 ) = 49

8 -15 ( 9 ) = -135

9 ( 8 ) ( -12 ) = -96

10 -3 ( -100 ) = 300

11 0 ( -153 ) = 0

12 -6 ( 32 ) = -192

13 7 ( -75 ) = -525 -$525



15 6 ( -2 ) = -12 -12degF








19 5 ( -4 ) = -20 $20 decrease





22 9 ( -6 ) = -54 -54 ( 2 ) = -108 Casey has $108

less in his savings

23 7 ( -8 ) = -56 7 ( -5 ) = -35





160 points


25 a 3 ( 3 ) ( -3 ) = 9 ( -3 ) = -27

b 3 ( -3 ) ( -3 ) = -9 ( -3 ) = 27

c -3 ( -3 ) ( -3 ) = 9 ( -3 ) = -27

d 3 ( 3 ) ( 3 ) ( -3 ) = 9 ( 3 ) ( -3 ) = 27 ( -3 ) = -81

e 3 ( 3 ) ( -3 ) ( -3 ) = 9 ( -3 ) ( -3 ) = -27 ( -3 ) = 81

f 3 ( -3 ) ( -3 ) ( -3 ) = -9 ( -3 ) ( -3 ) = 27 ( -3 ) = -81




negative



3 ( 3 ) ( -3 ) ( -3 ) = 9 ( -3 ) ( -3 ) = 81 the sign of the

product is positive


26 -1 ( 3 ) ( 1 ) 1 ( -3 ) ( 1 ) -1 ( -3 ) ( -1 )









negative

LESSON 22

Your Turn


0 divide ( -6 ) = 0


will be negative

38 divide ( -19 ) = -2


will be positive

-13 divide ( -1 ) = 13



Guided Practice

1 -14 ____ 2 = -7

2 21 divide ( -3 ) = -7

3 26 ____ -13

= -2

4 0 divide ( -4 ) = 0

5 -45 ____ -5 = 9

6 -30 divide ( 10 ) = -3

7 -11 ____ -1

= 11

8 -31 divide ( -31 ) = 1

9 0 ___ -7 = 0

10 -121 _____ -11

= 11

11 84 divide ( -7 ) = -12

12 500 ____ -25

= -20


undefined

14 -63 ____ -21

= 3

15 -40 divide ( 4 ) = -10 $10

16 -22 divide ( 11 ) = -2 2 points

17 -75 divide ( -15 ) = 5 5 targets

18 -99 divide ( -9 ) = 11 11 times





20 -24 divide ( 12 ) = -2 $2







is -200 ft _______ 10 min



= -15 ftmin







-20 divide 5 = -4 and -20 times 5 = -100

-100 lt -4



negative





incorrectly

29 a divide ( -3 ) = 8

a = -24

8 divide b = -4






integers

LESSON 23

Your Turn


3 ( -30 ) + 200 = -90 + 200

= 110

2 -6 ( 13 ) - 21 = -78 - 21

= -99

4 ( -12 ) divide 6 + 2 = -2 + 2

= 0

5 -87 divide ( -3 ) -9 = 29 - 9

= 20

6 40 divide ( -5 ) + 30 = -8 + 30

= 22

7 -39 divide 3 -15 = -13 - 15

= -28



moved further back

9 ( -10 ) divide 2 - 2 = -5 - 2 = -7

( -28 ) divide 4 + 1 = -7 + 1 = -6

10 42 divide ( -3 ) + 9 = -14 + 9 = -5

( -36 ) divide 9 - 2 = -4 - 2 = -6

Guided Practice

1 -6 ( -5 ) + 12 = 30 + 12

= 42

2 3 ( -6 ) - 3 = -18 - 3

= -21

3 -2 ( 8 ) + 7 = -16 + 7

= -9

4 4 ( -13 ) + 20 = -52 + 20

= -32

5 -4 ( 0 ) - 4 = 0 - 4

= -4

6 -3 ( -5 ) - 16 = 15 - 16

= -1

7 7 ( -5 ) + 20 = -35 + 20

= -15

15 dollars less

8 7 ( -10 ) + ( -100 ) = -70 + ( -100 )

= -170

170 fewer points

9 6 ( -4 ) + 10 = -24 + 10

= -14

Ned lost 14 points

10 4 ( -12 ) + 10 = -48 + 10

= -38

$38 less

11 -3 ( -2 ) + 3 = 6 + 3

= 9

3 ( -4 ) + 9 = -12 + 9

= -3

9 gt -3

-3 ( -2 ) + 3 gt 3 ( -4 ) + 9

12 -8 ( -2 ) -20 = 16 -20

= -4

3 ( -2 ) + 2 = - 6 + 2

= -4

-4 = -4

-8 ( -2 ) -20 = 3 ( -2 ) + 2

13 -7 ( 5 ) - 9 = -35 - 9

= -44

-3 ( 20 ) + 10 = -60 + 10

= -50

-44 gt -50

-7 ( 5 ) -9 gt -3 ( 20 ) + 10

14 -16 ( 0 ) -3 = 0 -3

= -3

-8 ( -2 ) -3 = 16 -3

= 13

-3 lt 13

-16 ( 0 ) -3 lt -8 ( -2 ) -3





16 -12 ( -3 ) + 7 = 36 + 7

= 43

17 -42 divide ( -6 ) + 5 -8 = 7 + 5 -8

= 12 -8

= 4

18 10 ( -60 ) -18 = -600 -18

= -618

19 ( -11 ) ( -7 ) + 5 - 82 = 77 + 5 - 82

= 82 - 82

= 0

20 35 divide ( -7 ) + 6 = -5 + 6

= 1

21 -13 ( -2 ) - 16 - 8 = 26 - 16 - 8

= 10 - 8

= 2

22 a 5 ( 2 ) -12 + 3 = 10 -12 + 3

= -2 + 3

= 1

b -3 ( 2 ) -1 + 6 + 7 = -6 -1 + 6 + 7

= -7 + 6 + 7

= -1 + 7

= 6


the game

23 5 ( -4 ) -8 = -20 - 8 = -28

24 -36 divide ( -4 ) + 9 = 9 + 9 = 18


25 a 4 ( -35 ) -9 = -140 -9

= -149

$149 less

b Yes $200 - $149 = $51 $51 gt $50 so Arleen

has enough money

26 a 2 ( -10 ) + 3 = -20 + 3= -17

b 7 + 2 + ( -7 ) = 2




7 of clubs





had change








MODULE 2

Ready to Go On


will be negative

( -2 ) ( 3 ) = -6


will be positive

( -5 ) ( -7 ) = 35



( 8 ) ( -11 ) = -88

4 ( -3 ) ( 2 ) ( -2 ) = ( -6 ) ( -2 ) = 12

5 5 ( -3 ) = -15 -15degC

6 -63 ____ 7 = -9

7 -15 ____ -3

= 5

8 0 ____ -15

= 0

9 96 ____ -12

= -8

10 -24 divide 6 = -4 -4 Ib

11 ( -4 ) ( 5 ) + 8 = -20 + 8

= -12

12 ( -3 ) ( -6 ) -7 = 18 -7

= 11

13 -27 ____ 9 - 11 = -3 - 11

= -14

14 -24 ____ -3

- ( -2 ) = 8 + 2

= 10




( -3 ) ( 5 ) + 10 = -15 + 10 = -5 He had $05 less

than before



Are You Ready

1 9 ___ 14

times 7 __ 6 =

3

2

9 ___ 14

times 7 __ 6 1

2

= 3 __ 4

2 3 __ 5 times 4 __

7 = 12 ___

35

3 11 ___ 8

times 10 ___ 33

= 1

4

11 ___ 8 times 10 ___

33 5

3

= 5 ___ 12

4 4 __ 9 times 3 =

3

4 __ 9 times 3 __

1 1

= 4 __ 3 or 1 1 __

3

5 1 __ 2 divide 1 __

4 = 1 __

2 times 4 __

1

=

1 1 __ 2 times 4 __

1 2

= 2 __ 1 = 2

6 3 __ 8 divide 13 ___

16 = 3 __

8 times 16 ___

13

= 1 3 __ 8 times 16 ___

13 2

= 6 ___ 13

7 2 __ 5 divide 14 ___

15 = 2 __

5 times 15 ___

14

= 1

1 2 __ 5 times 15 ___

14 3

7

= 3 __ 7

8 4 __ 9 divide 16 ___

27 = 4 __

9 times 27 ___

16

= 1

1 4 __ 9 times 27 ___

16 3

4

= 3 __ 4

9 3 __ 5 divide 5 __

6 = 3 __

5 times 6 __

5

= 18 ___ 25

10 1 __ 4 divide 23 ___

24 = 1 __

4 times 24 ___

23

= 1 1 __ 4 times 24 ___

23 6

= 6 ___ 23

11 6 divide 3 __ 5 = 6 __

1 times 5 __

3

= 2

6 __ 1 times 5 __

3 1

= 10 ___ 1 = 10

12 4 __ 5 divide 10 = 4 __

5 times 1 ___

10

= 2

4 __ 5 times 1 ___

10 5

= 2 ___ 25

13 21 - 6 divide 3

21 - 2

19

14 18 + ( 7 - 4 ) times 3

18 + 3 times 3

18 + 9

27

15 5 + ( 8 - 3 ) 2

5 + ( 5 ) 2

5 + 25

30

16 9 + 18 divide 3 + 10

9 + 6 + 10

15 + 10

25

17 60 - ( 3 - 1 ) 4 times 3

60 - ( 2 ) 4 times 3

60 - 16 times 3

60 - 48

12

18 10 - 16 divide 4 times 2 + 6

10 - 4 times 2 + 6

10 - 8 + 6

2 + 6

8

LESSON 31

Your Turn

0 _

571428

4 7 ⟌ _


_ -35

50

_ -49

10

_ -7

30

_ -28

20

_ -14

60

_ -56




-0 _

571428 or -0571428571428hellip


0 _ 3

5 3 ⟌ _


_ -3




0333hellip

045

6 20 ⟌ _

900

_ -8 0

1 00

_ -1 00

0

-045

7 -2 3 __ 4 = -thinsp 4 times 2 + 3

_________ 4 = -11 ____

4

275

4 ⟌ _

1100

_ -8

30

_ -28

20

_ -20

0

-275 terminating

8 7 1 __ 3 =

3 times 7 + 1 _________

3 = 22 ___

3

7 _ 3

3 ⟌ _


_ -21





Guided Practice

06

1 5 ⟌ _

30

_ -3 0

0

06 terminating

089

2 100 ⟌ _

8900

_ -80 0

9 00

_ -9 00

0

-089 terminating


4 ___ 12

= 4 times 1 _____ 4 times 3

= 1 __ 3

0 _ 3

3 ⟌ _


_ -3





0 _

25

4 99 ⟌ _


_ -19 8

520

_ -495




25 or


0 _ 7

5 9 ⟌ _


_ -63





036

6 25 ⟌ _

900

_ -7 5

1 50

_ -1 50

0

-036 terminating

004

7 25 ⟌ _

100

_ -1 00

0

004 terminating

01420 _

45

8 176 ⟌ _

250000000

_ -17 6

7 40

_ -7 04

360

_ -352

80

_ -0


_ -704

960

_ -880




-01420 _


0012

9 1000 ⟌ _

12000

_ -10 00

2 000

_ -2 000

0

0012 terminating


10 -11 1 __ 6 = -thinsp 6 times 11 + 1

_________ 6 = -67 ____

6

111 _ 6

6 ⟌ _

67000

_ -6

07

_ -6

1 0

_ -6


_ -36




- 67 ___ 6

-111 _ 6 or -111666hellip

11 2 9 ___ 10

= 10 times 2 + 9

__________ 10

= 29 ___ 10

29

10 ⟌ _

290

_ -20

9 0

_ -9 0

0

29 ___ 10

29

12 -8 23 ____ 100

= - 100 times 8 + 23

____________ 100

= -823 _____ 100

823

100 ⟌ _

82300

_ -800

23 0

_ -20 0

3 00

_ -3 00

0

-823 _____ 100

-823

13 7 3 ___ 15

= 15 times 7 + 3

__________ 15

= 108 ____ 15

72

15 ⟌ _

1080

_ -105

3 0

_ -3 0

0

108 ____ 15

72

14 54 3 ___ 11

= 11 times 54 + 3

__________ 11

= 597 ____ 11

54 _

27

11 ⟌ _

597000

_ -55

47

_ -44


_ -22

80

_ -77




597 ____ 11

54 _

27 or 542727hellip

15 -3 1 ___ 18

= -thinsp 18 times 3 + 1 __________

18 = -55 ____

18

30 _ 5

18 ⟌ _

55000

_ -54

1 0

_ -0


_ -90




-55 ____ 18

-30 _ 5 or -30555hellip

16 3 2 __ 3 =

3 times 3 + 2 _________

3 = 11 ___

3

3 _ 6

3 ⟌ _

1100

_ -9


_ -1 8





17 -2 7 __ 8 = -

8 times 2 + 7 _________

8 = -23 ____

8

2875

8 ⟌ _

23000

_ -16

7 0

_ -6 4

60

_ -56

40

_ -40

0

-2875 lb




3 ___ 47








= 5 ___ 11

0 _

45

11 ⟌ _


_ -4 4

60

_ -55




5 ___ 11

0 _


20 hockey players


= 6 ___ 10

06

10 ⟌ _

60

_ -6 0

0

6 ___ 10

06 terminating

21 polo players


= 4 ___ 11

036

11 ⟌ _


_ -3 3

70

_ -66




4 ___ 11

0 _


22 lacrosse players


= 10 ___ 15

= 5 times 2 _____ 5 times 3

= 2 __ 3

0 _ 6

3 ⟌ _


_ -1 8




10 ___ 15


23 football players


= 11 ___ 11

= 1

11 ___ 11

1 terminating







25 a -4 7 __ 8 = -thinsp 8 times 4 + 7

_________ 8 = - 39 ___

8

b 4875

8 ⟌ _

39000

_ -32

7 0

_ -6 4

60

_ -56

40

_ -40

0

-4875








is equal

to 85 ___ 16


is

equal to 127 ____ 24

or 52916hellip ft




















090625











0121212hellip


LESSON 32

Your Turn

2

50 1 2 3 4

3 + 1 1 __ 2 = 4 1 __

2

3

0-7 -6 -5 -4 -3 -2 -1

-25 + ( -45 ) = -7

6

0 1 2-5-6-7-8 -4 -3-2-1

-8 + 5 = -3

7

10-1

1 __ 2 + ( - 3 __

4 ) = - 1 __

4

8

3 4 5 6 7 80 1 2-3-2-1

-1 + 7 = 6

9

3 4 50 1 2-5-4 -3-2-1

2 1 __ 2 + ( -2 1 __

2 ) = 0

10

3 4 50 1 2-5-4 -3-2-1

-45 + 45 = 0

11

1-1 0

3 __ 4 + ( - 3 __

4 ) = 0


12 -15 + 35 + 2

-15 + 55

55 - 15

4

13 3 1 __ 4 + ( -2 ) + ( -2 1 __

4 )

3 1 __ 4 + ( -4 1 __

4 )

3 1 __ 4 - 4 1 __

4

-1

14 -275 + ( 325 ) + 5

-6 + 5

-1

15 15 + 8 + ( -3 )

23 + 3

20

Guided Practice

1

3 4 50 1 2-5-4 -3-2-1

-3 + ( -15 ) = -45

2

0 54321-5-4-3-2-1

15 + 35 = 5

3

0 105-1 -05

1 __ 4 + 1 __

2 = 3 __

4

4

0 54321-5-4-3-2-1

-1 1 __ 2 + ( -1 1 __

2 ) = -3

5

0 54321-5-4-3-2-1

3 + ( -5 ) = -2

6

0 54321-5-4-3-2-1

-15 + 4 = 25

7 -2150 + 2150 = 0 $0

8 -874 + 874 = 0 $0

9 275 + ( -2 ) + ( -525 )

275 + ( -725 )

- ( 725 - 275 )

-45

10 -3 + 1 1 __ 2 + 2 1 __

2 = -3 + 4 = 1

11 124 + 92 + 1

-124 + 102

- ( 124 - 102 )

-22

12 -12 + 8 +13

-12 + 21

21 - 12

9

13 45 + ( -12 ) + ( -45 )

45 + ( -45 ) + ( -12 )

0 + ( -12 )

-12

14 1 __ 4 + ( - 3 __

4 ) = - ( 3 __

4 - 1 __

4 ) = - 2 __

4 = - 1 __

2


15 -4 1 __ 2 + 2 = - ( 4 1 __

2 - 2 ) = -2 1 __

2

16 -8 + ( -1 1 __ 8 ) = -9 1 __

8


The sum is 2



19 -$225 + $1500 = $1500 - $225 = $1275

20 -3525 m + ( -85 ) = -4375 m

21 4 3 __ 4 mi + ( -3 1 __

4 mi ) = 1 2 __

4 mi = 1 1 __

2 mi


23 30 + 15 - 25 = 45 - 25 = 20 pts

24 January

Income - Expenses

$1205 - $129060

- ( $129060 - $1205 ) -$8560

February

Income - Expenses

$1183 - $134544

-($134544 - $1183)

-$16244


February

25 June

Income - Expenses

$2413 - $210623

$30677

July

Income - Expenses

$2260 - $195850

$30150

August

Income - Expenses

$2183 - $184512

$33788


$33788 in August






the end of August

Income = $1205 + $1183 + $1664 + $2413

$2260 + $2183 = $10908

Expenses = $129060 + $134544 + $1664 +$210623 + $195850 + $184512

= $1020989

Profit = $10908 - $1020989 + $250

= $94811


28 a 7 ( 10 ) + 3 ( -15 ) = 70 - 45 = 25 pts

b 2 ( 10 ) + 8 ( -15 ) = 20 - 120 = -100 pts








the positive number







LESSON 33

Your Turn

1

-9 -8 -7 -6 -5 -4

-65 - 2 = -85

2

42 30-1 1

1 1 __ 2 - 2 = - 1 __

2

3

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0

-225 - 55 = -775

6

1 2-1 0

025 - ( -150 ) = 175

7

1-1 0

- 1 __ 2 - ( - 3 __

4 ) = 1 __

4

Guided Practice

1

1312111098765 14 15

5 - ( -8 ) = 13

2

-9 -8 -7 -6 -5 -4 -3

3 1 __ 2 - 4 1 __

2 = -8


3

-15 -13 -11 -9 -5-7

-7 - 4 = -11

4

-6 -5 -4 -3 -2 -1 0 1

-05 - 35 = -4

5 -14 - 22 = -36

6 -125 - ( -48 )

-125 + 48

- ( 125 - 48 )

-77

7 1 __ 3 - ( - 2 __

3 ) = 1 __

3 + 2 __

3 = 1

8 65 - ( -14 ) = 65 + 14 = 79

9 - 2 __ 9

- ( -3 )

- 2 __ 9

+ 3

3 - 2 __ 9

2 9 __ 9 - 2 __

9

2 7 __ 9

10 24 3 __ 8

- ( -54 1 __ 8 )

24 3 __ 8

+ 54 1 __ 8

78 4 __ 8

78 1 __ 2

11 -1 m + ( 105 m ) = -15 m


12 -12 1 __ 2 + ( -5 ) = -17 1 __

2

17 1 __ 2

or 175 yards


533 ft - ( -10 ft ) = 533 ft + 10 ft = 543 ft

14 -4500 + (-3015) = -7515 $7515






16 -126degC - 75degC = -201degC

17 -2565 ft - 165 ft + 1245 ft = -297 ft


18 -9500 ft - ( -26000 ft ) = 16500 ft

19 29035 ft - ( -36198 ft ) = 65233 ft

70000 ft - ( -26000 ft ) = 96000 ft


96000 ft - ( 65233 ft ) = 30767 ft


b 78degF - 32degF


21 a -$1258 + ( -$3072 ) = -$4330

b -$4330 + ( -$25 ) = -$6830

c $6830 since -$6830 + $6830 = 0



23 a 5 ft - 72 ft + 22 ft

b 5 ft - 72 ft + 22 ft

5 ft + 22 ft - 72 ft

72 ft - 72 ft



24 a Yes

$425 + $089 + $1099

= $1613 lt $20

b $20 - $1613 = $387 left over





- 7 ___ 16

- 1 __ 4 - 5 ___

16 = ( - 7 ___

16 ) + ( - 1 __

4 ) + ( - 5 ___

16 )

( - 7 ___ 16

) + ( - 5 ___ 16

) + ( - 1 __ 4 ) by CPA

( -7 + ( -5 ) __________

16 ) + ( - 1 __

4 )

( -12 ____ 16

) + ( - 1 __ 4 )

( - 4 times 3 _____ 4 times 4

) + ( - 1 __ 4 )

( - 3 __ 4 ) + ( - 1 __

4 )

( -3 + ( -1 ) __________

4 )

( -4 ___ 4 ) = -1





and c __ d

Both fractions









LESSON 34

Your Turn

1

-8 -7 -6 -5 -2 -1 0-4 -3

2 ( -35 ) = -7

2

-2 -1 0 1 2 3 4-4 -3

-3 ( -125 ) = 375

4 ( - 3 __ 4 ) ( - 4 __

7 ) ( - 2 __

3 ) = -



= - 2 __ 7

5 ( - 2 __ 3 ) ( - 3 __

4 ) ( 4 __


__________ 13 times 41 times 5


= 2 __ 5

6 ( 2 __ 3 ) ( - 9 ___

10 ) ( 5 __

6 ) = -


____________ 13 times 210 times 63


= - 1 __ 2

Guided Practice

1

-5 -2 -1 0-4 -3

5 ( - 2 __ 3 ) = 5 __

1 times ( - 2 __

3 )

= - 5 times 2 _____ 1 times 3

= - 10 ___ 3

= -3 1 __ 3

2

-1 -05 0-2 -15

3 ( - 1 __ 4 ) = 3 __

1 times - 1 __

4

= - 3 times 1 _____ 1 times 4

= - 3 __ 4

3

0 1 2-2 -1

-3 ( - 4 __ 7 ) = 3 __

1 times 4 __

7

= 3 times 4 _____ 1 times 7

= 12 ___ 7

= 1 5 __ 7

4

-2 -1 0 1 2 3 4-4 -3

- 3 __ 4 ( -4 ) = 3 __

4 times 4 __

1

= 3 times 41

______ 14 times 1

= 3 times 1 _____ 1 times 1

= 3 __ 1

= 3

5 4 ( -3 ) = -12

6 -18 ( 5 ) = -9

7 -2 ( -34 ) = 68

8 054 ( 8 ) = 432

9 -5 ( -12 ) = 6

10 -24 ( 3 ) = -72

11 1 __ 2 times 2 __

3 times 3 __

4 = ( 1 times 21

______ 12 times 3

) ( 3 __ 4 )

= ( 1 __ 3 ) ( 3 __

4 )

= 1

1 __ 3 times 3 __

4 1

= 1 __ 4

12 - 4 __ 7 ( -thinsp 3 __

5 ) ( - 7 __

3 ) = ( - 4 times 3 _____

7 times 5 ) ( - 7 __

3 )

= 12 ___ 35

( - 7 __ 3 )

= - 4

5 12 times 7 ______ 35 times 3

1

1

= - 4 times 1 _____ 5 times 1

= - 4 __ 5

13 ( - 1 __ 8 ) times 5 times 2 __

3 = ( - 1 __

8 ) times 5 __

1 times 2 __

3


__________ 48 times 1 times 3


= - 5 ___ 12


14 ( - 2 __ 3

) ( 1 __ 2 ) ( - 6 __


__________ 13 times 21 times 7


= 2 __ 7


16 18 ( -100 ) = -1800 or a $1800 change









amount

b 200 + 6 ( -1998 )

= 200 - 11988

= 8012 $8012





which is 6

20 8 ( -3 1 __ 4 ) = -8 ( 13 ___

4 )

= - 1

8 __ 1 times 13 ___

4 1

= - 2 times 13 ______ 1 times 1

= - 26 ___ 1





(below the surface)

22 5 + ( -3 ) ( 15 )

= 5 + ( -45 )

= 05 cups left





a positive



25 Total score is

2 times ( 6 ) + 16 times ( 05 )

+ 7 times ( -05 ) + 2 times ( -15 )

= 12 + 8 - 35 - 3

= 20 - 65

= 135 pts




= 12 + 5 ( -68 )

= 12 + ( -34 )

= -22degC

27 a b c d

+ + + +

+ + - +

+ - + +

- + + +

- - - +

- - + -

- + - -

+ - - -









LESSON 35

Your Turn

3 28 ___ -4

= - 28 ___ 4 = -07

4 -664 ______ -04

= 664 ____ 04

= 166

5 - 55 ___ 05

= - 55 ___ 5 = -11

6 -4256 _______ 112

= -38


per minute

7 - 5 __

8 ___

- 6 __ 7 = - 5 __

8 divide - 6 __

7

= - 5 __ 8 times - 7 __

6

= 35 ___ 48

8 - 5 ___

12 ____

2 __ 3 = - 5 ___

12 divide 2 __

3

= - 5 ___ 12

times 3 __ 2

= - 15 ___ 24

= - 5 __ 8


9 -4__5

___1__2 =-4__5divide1__

2

=-4__5times2__1

=-8__5

=-13__5

Guided Practice

1 072_____-09=-72___

9 =-08

2 -1__5

___7__5 =-1__

15times5

1__

7=-1times1_____

1times7=-1__7

3 56___-7=-56___7=-8

4 251____4 divide(-3__

8)=251____

4 times-8__

3

=-251times82________

14times3


=-502____3

5 75____-1__5

=-75___1times5__

1=-75times5______

1times1=-375

6 -91____-13=91___

13=7

7 -3__7

___9__4 =-

13__7times4__93


=-4___21

8 - 12____003

=-1200_____

3 =-400


changeindays

=-35L______4day

=-0875 L____day

or-0875Lperday


changeindays

=-$4575________5day



numberofminutes

=-044mi________08min

=-44mi______8min

=-055mileperminute



13 5___-2__

8=-5__

1times8__

24

1=-5times4_____

1times1=-20

14 51__3divide(-11__

2)


2

=-16___3divide3__

2

=-16___3times2__

3


=-32___9

15 -120_____-6 =120____

6 =20

16 -4__5

___-2__

3=

24__5times3__

21=2times3_____

5times1=6__

5

17 103divide(-103)=-103____1 times 1____

103

=-103times1________1times103

=-103____103

=-103____103

=-01

18 -04_____80

=-04___80

=-0005

19 1divide9__5=1__

1times5__

9=5__

9

20 -1___4 ___

23___24

=-1__

14times246

___23


=-6___23

21 -1035_______-23 =1035_____

23 =45


= 21h______7days

=3 h____day


times3days=9hours




=-4times15+3___________4 times1__

9

yd___run

=-763___4 times1__

91yd

___run

=-153__

4yd______

9runs

=-153__4times1__

9

yd___run

=-7__4or-13__

4yardsperrun





_____________________________________ 4

= 414degC ______ 4

= -1035degC per day

25 a total profit


= $1750

______ 7 days

= $250 per day

b $150

_____ day


c total change


= - $490

______ 7 days

= -$70 per day


= 996 m ______ 12 s

= 83 ms





- 3 __

4 ___

4 __ 3

= - 3 __

4 times 3 __

4 = - 9 ___

16



= -629 m





-85degF divide 15 d

= - 1785 ____ 315

degF __ d

= - 17 ___ 3 degF __

d or -5 2 __

3 degF __


d


every day





definition

LESSON 36

Your Turn


3 times 2 1 __ 2 = 7 1 __

2


30 - 7 1 __ 2 = 22 1 __

2


22 1 __ 2 divide 4 = 5 5 __

8











12 3 __ 5 = 126

= 0126


750 times 0126 = 945

750 + 945 = 8445


8445 times 0126 asymp 10641

8445 + 10641 = 95091


95091 times 0126 asymp 11981

95091 + 11981 = 107072


Guided Practice











78 times 3 = 234


234 divide 4 = 585




12 - 3 1 __ 2 = 8 1 __

2

Find half the width

8 1 __ 2 divide 2 = 4 1 __

4


of the page


11 times 1 __ 3 = 3 2 __

3

10 times 3 __ 4 = 7 1 __

2

3 2 __ 3 + 7 1 __

2 = 11 1 __

6


box

11 1 __ 6 lt 12





41 3 __ 4 divide 2 = 20 7 __

8


50 - 20 7 __ 8 = 29 1 __

8




( 78 + 10 ) = 88


88 = 88 ____ 100

= 44 ___ 50


Donovan

44 - 39 = 5


Donovan







19 ___ 37


15 times ( - 1 __ 2 ) = -075







-79 9 ___ 10

divide ( -188 ) = 425


19 1 __ 8 - 1275 - 425 = 2 1 __

8


-28 9 ___ 10

- ( -79 9 ___ 10

) = 51


51 divide 2 1 __ 8 = 24


ascent was 24 ftmin

15 Sample answer



the result by 037



(276 + 159)037 = (276)(037) + (159)(037)




make errors








MODULE 3

Ready to Go On

1 4 1 __ 5 =

5 times 4 + 1 _________

5 = 21 ___

5

42

5 ⟌ _

210

_ -20

1 0

_ -1 0

0

42


2 12 14 ___ 15

= 15 times 12 + 14

___________ 15

= 194 ____ 15

129 _ 3

15 ⟌ _

194000

_ -15

44

_ -30

14 0

_ -13 5

50 first 50

_ -45

50 second 50



129 _ 3 or 12933

3 5 5 ___ 32

= 32 times 5 + 5

__________ 32

= 165 ____ 32

515625

32 ⟌ _

16500000

_ -160

5 0

_ -3 2

1 80

_ -1 60

200

_ -192

80

_ -64

160

_ -160

0

515625

4 45 + 71 = 116

5 5 1 __ 6 + ( -3 5 __

6 ) = 4

6+1 ____

6 -3 5 __

6

= 1 2 __ 6

= 1 1 __ 3

6 - 1 __ 8 -6 7 __

8 = - 1 __

8 + ( -6 7 __

8 )

= -6 8 __ 8

= -7

7 142 - ( -49 ) = 142 + 49

= 191

8 -4 ( 7 ___ 10

) = - 4 __ 1 times 7 ___

10

= - 24 times 7 _______ 1 times 105

= - 2 times 7 _____ 1 times 5

= - 14 ___ 5 or -2 4 __

5

9 -32 ( -56 ) ( 4 ) = 32 times 56 times 4

= 7168

10 - 19 ___ 2 divide 38 ___

7 = -

119 times 7 _______ 2 times 382

= - 1 times 7 _____ 2 times 2

= - 7 __ 4

11 -3201 _______ -33

= 3201 _____ 33

97

33 ⟌ _

3201

_ -297

23 1

_ -23 1

0

97


second day

$8360 + $1535 = $9895


-4 3 __ 4 = -475 or -00475




price

$9895 times -00475 asymp -$47

$9895 - $47 = $9425






prices



Are You Ready

1 3 __ 4 divide 4 __

5 = 3 __

4 times 5 __

4

= 15 ___ 16

2 5 __ 9 divide 10 ___

11 = 5 __

9 times 11 ___

10

= 1

5 __ 9 times 11 ___

10 2

= 11 ___ 18

3 3 __ 8 divide 1 __

2 = 3 __

8 times 2 __

1

= 4

3 __ 8 times 2 __

1 1

= 3 __ 4

4 16 ___ 21

divide 8 __ 9 = 16 ___

21 times 9 __

8

=thinsp 2

7 16 ___ 21

times 9 __ 8 3

1

= 6 __ 7

5 B ( -4 1 )

6 C ( 3 0 )

7 D ( 5 4 )

8 E ( -2 -2 )

9 F ( 0 0 )

10 G ( 0 -4 )

LESSON 41

Your Turn

3 1 __ 6 acre divide ( 1 __

4 hour ) = 1 __

6 times 4 __

1

= 3


2

= 1 times 2 _____ 3 times 1


4 3 cups divide ( 3 __ 4 cups ) = 3 __

1 divide 3 __

4

= 3 __ 1 times 4 __

3

= 1


1

= 1 times 4 _____ 1 times 1

= 4 cups


5 = 3 __

4 times 5 __

1 = 15 ___

4 = 3 3 __

4


6 = 2 ___

1 3 times 6

2 __

1 = 4 __

1 = 4






flavor

Guided Practice

1

Distance (mi) 8 1 __ 2 17 25 1 __

2 34 42 1 __

2

Time (h) 1 __ 2 1 1 1 __

2 2 2 1 __

2

2 3 1 __ 2 miles divide ( 1 1 __

4 hours ) = 7 __

2 divide 5 __

4 mi ___ h

= 7 times 4 _____ 2 times 5

= 1 7 times 4 _____ 2 times 5

2

= 7 times 2 _____ 1 times 5

= 14 ___ 5 mi ___

h


3 5 __ 8 page divide ( 2 __

3 minute ) = 5 __

8 times 3 __

2

= 15 ___ 16

page per minute

4 1 __ 6 foot divide ( 1 __

3 hour ) = 1 __

6 times 3 __

1

= 2 1 times 3 _____ 6 times 1

1

= 1 times 1 _____ 2 times 1


5 5 __ 8 sq ft divide ( 1 __

4 hour ) = 5 __

8 times 4 __

1

= 2 5 times 4 _____ 8 times 1

1

= 5 times 1 _____ 2 times 1

= 5 __ 2 or 2 1 __



UNIT

2



1 divide 1 __

3

= 240 ____ 1 times 3 __

1

= 720 ____ 1



1 divide 1 __

2

= 325 ____ 1 times 2 __

1

= 650 ____ 1




1 __ 4 cup divide ( 2 __

3 serving ) = 1 __

4 times 3 __

2

= 3 __ 8

cup _______

serving


1 __ 3 cup divide ( 3 __

4 serving ) = 1 __

3 times 4 __

3

= 4 __ 9

cup _______

serving




72 and 4 __

9 = 32 ___

72




the rate


1 __ 2 hour

= 1 __




$10 divide ( 35 hours ) = 10 ___ 35

$ __



$125 divide ( 1 __ 2 hours ) = 125 ____

05 $ __





multiply by 60


= 005 ____ 1

$ ____


1 h

= $3 per hour



one


8 cup






originally

c 1 __ 2 divide 1 __

8 = 1 ___

1 2 times 8

4 __

1 = 4 __

1 = 4


sunflower seeds

11 10 songs


= 5 songs ____________

1 commercials


6 mi divide ( 1 __ 2 h ) = 6 __

1 times 2 __

1

= 12 miles per hour

Jessersquos rate


4

= 2 __ 1 times 4 __

1 mi ___ h

= 8 miles per hour

b Terrance

50 mi divide ( 12 mi ___ h ) = 50 ___

1 times 1 ___

12

= 50 ___ 12

h

= 4 1 __ 6 h

= 4 10 ___ 60

h


Jesse

50 mi divide ( 8 mi ___ h ) = 50 ___

1 times 1 __

8

= 50 ___ 8 h

= 6 1 __ 4 h

= 6 15 ___ 60

h



4

= 8 __ 1 times 4 __

3

= 32 ___ 3





13 1 ___ 10

h = 6 ___ 60

h = 6 min

300 words _________ 6 min

= 50 words per min

1 ___ 12

h = 5 ___ 60

h = 5 min

300 words _________ 5 min

= 60 words per min










b For the 10-pack



For the 12-pack








2 day ) = 1 room _____

day so at the same





LESSON 42

Your Turn


was not constant




= 12 ___ 1 = 36 ___

3 = 60 ___




s or s = 12a

Guided Practice

1 45 ___ 1 = 45 90 ___

2 = 45 135 ____

3 = 45 180 ____

4 = 45


2 k = y __ x = 10 ___

2 = 5 y = 5x

3 k = y __ x = 2 __

8 = 1 __

4 y = 1 __

4 x


of proportionality


5 k = y __ x = 74 ___

4 = 1850 y = 1850x

6 $1099

_______ 05 days

= $2198 per day


($1850)

8 100 ft _____ 08 s

= 1000 _____ 8 ft __ s = 125 ft __ s

500 ft _____ 31 s

= 5000 _____ 31


1875 ft ______ 15 s

= 1875 ______ 15





9 $3125

______ 5 h


______ 8 h

= $625 per







12 y = $625 ( 3 ) = $1875

13 300 ft _____ 2 min

= 6750

_____ 45


150 ft _____ min

times 60 min ______ 1 h


14 y = 150x



hours




same factor




of corn

LESSON 43

Your Turn

1 No because 11 ___ 1 ne 16 ___





b k = 60 mi _____ 4 h

= 15 mi ___ h


distance in miles

Guided Practice

1

Time (h) 3 5 9 10

Pages 195 325 585 650


per hour

2

Time (h) 2 3 5 8

Earnings 15 2250 3750 60








5 k = 28 ft ____ 8 s

= 7 __ 2 ft __ s = 35 ft __ s y = 7 __



6 k = $2 ______

8 items = 1 __

4

$ _____

items = 025

$ _____

items so y = 1 __

4 x or


y = cost in dollars


origin



0 minutes





x or 2 __ 5 x




5 = 48




2

2

4

6

8

10

4 6 8 10Time (min)

Dis

tanc

e (m

i)

A

B

O








equation

15 a

2

8

16

24

32

40

4 6 8 10DVDs

Cost

($)

O



cost $20






18 k = 8 ft ___ 4 s










because 65 ___ 1 ne 85 ___

2





distance column

MODULE 4

Ready to Go On

1 $140

_____ 18 ft 2


2 $299

_____ 14 lb


3 $56 ______


$3205

______ 15 gal


4 $160

_____ 5 g


$315

_____ 9 g




3


6 k = $9

___ 8euro

= $27 ____

24euro = 9 __

8 $ __

euro or 1125

$ __

euro So y = 9 __

8 x or





_______ pt

or k = 25 servings

_______ pt

Therefore

y = 5 __ 2




2

2

4

6

8

10

4 6 8 10Pints

Serv

ings

Frozen Yogurt

O





constant rate



Are You Ready

1 22 = 22 ____ 100

= 022

2 75 = 75 ____ 100

= 075

3 6 = 6 ____ 100

= 006

4 189 = 100 + 89

= 100 ____ 100

+ 89 ____ 100

= 1 + 089

= 189

5 059 = 59

6 098 = 98

7 002 = 2

8 133 = 133

9 64

_ timesthinsp05

320

32

10 30

_ timesthinsp007

210

21

11 160

_ timesthinsp015

800

_ +1600

2400

24

12 62

_ timesthinsp032

124

_ +thinsp1860

1984

1984

13 4

_ timesthinsp12

8

_ +thinsp40

48

48

14 1000

_ timesthinsp006

6000

60

LESSON 51

Your Turn

2 x = ( $64 - 52 )

__________ $52

x = $12

____ $52

asymp 23

4 x = ( 18 - 12 )

________ 18

x = 6 ___ 18

asymp 33

5 x = ( 16 - 10 )

________ 16

x = 6 ___ 16

= 375

8 010 times $499 = $4990

$499 + $4990 = $54890

9 030 times $499 = $14970

$499 - $14970 = $34930

Guided Practice

1 x = ( $8 - $5 )

_________ $5

x = $3

___ $5

= 60

2 x = ( 30 - 20 )

_________ 20

x = 10 ___ 20

= 50

3 x = ( 150 - 86 )

__________ 86

x = 64 ___ 86

asymp 74

4 x = ( $389 - $349 )

______________ $349

x = $040

_____ $349

asymp 11

5 x = ( 14 - 13 )

________ 13

x = 1 ___ 13

asymp 8

6 x = ( 16 - 5 )

________ 5

x = 11 ___ 5 = 220

7 x = ( 64 - 36 )

_________ 36

x = 28 ___ 36

asymp 78

8 x = ( 80 - 64 )

_________ 80

x = 16 ___ 80

= 20

9 x = ( 95 - 68 )

_________ 95

x = 27 ___ 95

asymp 28


10 x=( 90-45)_________

90

x=45___90

=50

11 x=( 145-132)__________

145

x=13____145

asymp9

12 x=( 64-21)_________

64

x=43___64

asymp67

13 x=( 16-0)________

16

x=16___16

=100

14 x=( 3-1__

2)_______

3

x=21__

2___

3 asymp83

15 010times$900=$090 $900+$090=$990

16 025times48=12 48-12=36cookies

17 020times340=68 $340-68=272pages

18 050times28=14 28+14=42members

19 004times$29000=$1160 $29000-$1160=$27840

20 130times810=1053 810+1053=1863songs

21 030times20=6 20+6=26miles



ItemOriginal

PriceNew Price

Percent Change

Increase or





24 a 55

x=( 8-3)_______

8 =5__

8=625

x=( 12-7)________

12 =5___

12asymp417



x=( 12-3)________

3

x=9__3=300increase



b $100_____5 =$020each$100_____

4 =$025each



=25

26 Percenterror=( 136-133)___________

136 times100

=03____136

times100asymp2







LESSON 52

Your Turn

2 a 1c+01c11c

b s=11times$28=$3080

3 a 200

b 1c+2c3c

5 a

1b - 024b

1b024b

b 1b-024b=076b

6 a 1p-005p095p

b 095p=$1425




Guided Practice

1 a 035s

b 1s + 035s 135s

c 135 times $3200 = $4320

d 035 times $3200 = $1120


Price

2 Hat $18 15 $270 $2070

3 Book $2250 42 $945 $3195

4 Shirt $3375 75 $2531 $5906

5 Shoes $7499 33 $2475 $9974

6 Clock $4860 100 $4860 $9720

7 Painting $18500 125 $23125 $41625

8 $4500 - 022 ( $4500 ) = $3510

9 $8900 - 033 ( $8900 ) = $5963

10 $2399 - 044 ( $2399 ) = $1343

11 $27999 - 075 ( $27999 ) = $7000





13 a 046b

b 1b - 046b 054b

c 054 times $2900 = $1566

d 046 times $2900 = $1334


Sale Price $201

Regular Price $419

Sale Price $245

Regular Price $279

Sale Price $115

Regular Price $309

Sale Price $272

Regular Price $377

Sale Price $224


$050


$9950


$350

16 p = 127 ( $7400 ) = $9398

s = 127 ( $4800 ) = $6096

j = 127 ( $32500 ) = $41275

2 ( 9398 ) + 3 ( $6096 ) + $41275 = $78359









greater




the coat

LESSON 53

Your Turn

1 005 times $2000 = $100 $100 + $2000 = $2100

3 005 times $40000 = $2000

$2000 times 4 years = $8000

$40000 + $8000 = $48000


Total $2200 + $16875 = $236875

Guided Practice

1 005 times $3000 = $150

2 015 times $7000 = $1050

3 0004 times $10000 = $040

4 15 times $2200 = $3300

5 001 times $8000 = $080

6 20 times $500 = $1000

7 a 007 times $4399 = $308

b $4399 + $308 = $4707

8 115 times $7550 = $8683

9 007 times $2000 = $140


10 003 times $550 = $1650

$1650 times 10 years = $165

$550 + $165 = $715

11 a 090 times $20 = $18

b 1085 times $18 = $1953

12 020 times $2999 = $600 tip

00625 times $2999 = $187 tax

$2999 + $600 + $187 = $3786 total



to the price


14 $3275 + $3988 = $7263 total meal cost

014 times $7263 = $1017 tip

$7263 + $1017 = $8280 total with tip


$7865 times 020 = $1573 tip

$7865 + $1573 - $1180 = $8258 total


0075 times $29375 = $2203 tax

$29375 + $2203 = $31578 total with tax


17 $7999 times 012 = $960 discount

$7999 - $960 = $7039 price before tax





19 $4500 + 00725 = $32625 commission

$750 + $32625 = $107625 total income


$475 + $3850 = $51350 total income










nearest inch

22 a $4998 times 05 = $2499 50 discount

$2499 - $1000 = $1499 $10 discount

b $4998 - $1000 = $3998 $10 discount

$3998 times 05 = $1999 50 discount


$8550 + $1599 = $10149 total


$95 + $1439 = $10939 total



d $10149 times 008 = $812 tax

$10149 + $812 = $10961 total

24 a Store 1 $22 divide 2 = $11

Store 2 $1299 times 09 = $1169




b Store 3 $2098 times 045 = $944






to $2050 per month


____________ 137

times 100 = 05 ____ 137

asymp 36

MODULE 5

Ready to Go On

1 x = ( 63 - 36 )

_________ 36

x = 27 ___ 36

= 75 increase

2 x = ( 50 - 35 )

_________ 50

x = 15 ___ 50

= 30 decrease

3 x = ( 72 - 40 )

_________ 40

x = 32 ___ 40

= 80 increase

4 x = ( 92 - 69 )

_________ 92

x = 23 ___ 92

= 25 decrease

5 $60 times 015 = $9

$60 + $9 = $69

6 $32 times 0125 = $4

$32 + $4 = $36

7 $50 times 022 = $11

$50 - $11 = $39

8 $125 times 030 = $3750

$12500 - $3750 = $8750


$325 + $312 = $637 total income

10 $5310

______ $1735

asymp 31



$700 times 020 = $140

$700 + $140 = $840


5 less than Priya

$840 times 005 = $042

$840 - $042 = $798





$45 times 026 = $1170

$45 + $1170 = $5670






Are You Ready

1 5 + x

2 11 - n

3 -9 ___ y

4 2x - 13

5 2x + 3

= 2 ( 3 ) + 3

= 6 + 3

= 9

6 -4x + 7

= -4 ( 1 ) + 7

= -4 + 7

= 11

7 15x - 25

= 15 ( 3 ) - 25

= 45 - 25

= 2

8 04x + 61

= 04 ( -5 ) + 61

= -20 + 61

= 41

9 2 __ 3 x - 12

= 2 __ 3

( 18 ) - 12

= 2 __ 3

times ( 18 ___ 1 ) - 12

= 36 ___ 3 - 12

= 0

10 - 5 __ 8

x + 10

= - 5 __ 8 ( -8 ) + 10

= - 5 __ 8 times- 8 __

1 + 10

= - 5 ___ 1 8

times- 8 1 __

1 + 10

= - 5 __ 1 times- 1 __

1 + 10

= 5 + 10

= 15

11 1 __ 2 divide 1 __

4

= 1 times 4 _____ 2 times 1

= 1 times 4 2 ______

1 2 times 1

= 1 times 2 _____ 1 times 1

= 2

12 3 __ 8 divide 13 ___

16

= 3 __ 8 times 16 ___

13

= 3 times 16 2 _______

1 8 times 13

= 3 times 2 ______ 1 times 13

= 6 ___ 13

13 2 __ 5 divide 14 ___

15

= 2 __ 5 times 15 ___

14

= 1 2 times 15

3 ________

1 5 times 14 7

= 1 times 3 _____ 1 times 7

= 3 __ 7

14 4 __ 9 divide 16 ___

27

= 4 __ 9 times 27 ___

16

= 1 4 times 27

3 ________

1 9 times 16 4

= 1 times 3 _____ 1 times 4

= 3 __ 4

LESSON 61

Your Turn

2 ( 3x + 1 __ 2 ) + ( 7x - 4 1 __

2 )

= 3x + 7x + 1 __ 2 - 4 1 __

2

= 10x - 4

3 ( -025x - 3 ) - ( 15x + 14 ) = -025x - 3 - 15x - 14

= -175x - 44

4 02(3b - 15c) + 6c

= 06b - 3c + 6c

= 06b + 3c

5 2 __ 3 (6e + 9f - 21g) - 7f

= 4e + 6f - 14g - 7f

= 4e - f - 14g

6 5x - 3(x - 2) - x

= 5x - 3x + 6 - x

= x + 6

7 83 + 34y - 05(12y - 7)

= 83 + 34y - 6y + 35

= 118 - 26y


UNIT

3


Guided Practice


14 + 12n + 23 + 16n

14 + 23 + 12n + 16n

37 + 28n


37 + 28n

2 37 + 28n

37 + 28 ( 9 )

= 37 + 252

= 289

3 14 + 5(x + 3) - 7x = 14 + 5x + 15 - 7x

= 29 - 2x

4 3 ( t - 4 ) - 8 ( 2 - 3t ) = 3t - 12 - 16 + 24t

= 27t - 28

5 63c - 2 ( 15c + 41 ) = 63c - 3c - 82

= 33c - 82

6 9 + 1 __ 2 ( 7n - 26 ) - 8n = 9 + 35n - 13 - 8n

= -4 - 4 1 __ 2 n

7 2x + 12

2 ( x + 6 )

8 12x + 24

12 ( x + 2 )

9 7x + 35

7 ( x + 5 )







15 ( 100 + 5d ) + 20 ( 50 + 7d ) = 15 ( 100 ) + 15 ( 5d ) + 20 ( 50 ) + 20 ( 7d )

= 1500 + 75d + 1000 + 140d

= 1500 + 1000 + 75d + 140d

= 2500 + 215d


New width 60 + w


2(96 + l) + 2(60 + w)

=2(96) + 2l + 2(60) + 2w

192 + 2l + 120 + 2w

192 + 120 + 2l + 2w

312 + 2l + 2w

13 Width 3


Factors 3 and x + 2

Product 3 ( x + 2 ) = 3x + 6

14 Width 4



Product 4 ( 2x - 1 ) = 8x - 4




and 6 times 4 ) So 6 ( 9 ) = 6 ( 5 ) + 6 ( 4 )


6x = ( x + 3 ) + ( 2x + 4 ) +

6x = 3x + 7 +

-3x = _ -3x

3x = 7 +

_ -7 = _ -7

3x - 7 =



10x + 6 = 2 ( 3x - 3 ) + 2 ( )

10x + 6 = 6x - 6 + 2

_ -6x = _ -6x

4x + 6 = - 6 + 2

_ + 6 = _ + 6

4x + 12 = 2

( 4x + 12 ) divide 2 = ( 2 ) divide 2

2x + 6 =


18 a P = 2l + 2w


2(2x + 6) + 2(x)

= 4x + 12 + 2x

= 6x + 12


2(3x - 14) + 2( 1 __ 2 x + 32)

= 6x - 28 + x + 64

= 7x + 36

b (7x + 36) - (6x + 12)

= 7x + 36 - 6x - 12

= x + 24


Let x = 36

2x + 6 = 2 ( 36 ) + 6

= 72 + 6

= 78


Let x = 36

1 __ 2 x + 32 = 1 __

2 ( 36 ) + 32

= 18 + 32

= 50


Let x = 36

3x - 14 = 3 ( 36 ) - 14

= 108 - 14

= 94





( x ) ( x ) = x 2

( x ) 1 = x

( 1 ) 1 = 1


x

x

1

11

1 1

x2 x x x

x 1 1 1x 1 1 1

Area =

x 2 + x + x + x + x + x + 1 + 1 + 1 + 1 + 1 + 1

= x 2 + 5x + 6

( x + 3 ) ( x + 2 ) = x 2 + 5x + 6




1160 = 1334 So 58 ( 23 ) = 58 ( 3 ) + 58 ( 20 )


8 ( 1000 - 3 ) = 8000 - 24 = 7976


Property 8 ( 900 + 90 + 7 ) = 7200 + 720 + 56 =

7976

LESSON 62

Your Turn

1 49 + z = -9

_ -49 _ -49

z = -139

2 r - 171 = -48

_ +171 _ +171

r = 123

3 -3c = 36

-3c ____ -3

= 36 ___ -3

c = -12

5 x - 15 = 525

_ +15 _ +15

x = 675


6 x ___ 35

= -12

x ___ 35

( 35 ) = -12 ( 35 )

x = -42


7 25x = 75

25x ____ 25

= 75 ___ 25

x = 3


Guided Practice



x + ( -134 ) = -17 or x - 134 = -17

x - 134 = -17

_ +134 _ +134

x = 117


warmer



-1 1 __ 2 x = -9

( - 2 __ 3 ) ( - 3 __

2 x ) = ( - 2 __

3 ) ( -9 )

x = 18 ___ 3

x = 6


3 -2x = 34

-2x ____ -2

= 34 ___ -2

x = -17

4 y - 35 = -21

_ + 35 _ + 35

y = 14

y = 14

5 2 __ 3 z = -6

( 3 __ 2 ) 2z ___

3 = ( 3 __

2 ) ( -6 )

z = -9





x - 870737 = 203215

_ +870737 _ +870 737

x = 2902887



2825131 - x = 2320106

_ -2825131 _ -2825131

-x = - 505025

x = 505025




2825131 - x = 1119421

_ -2825131 _ -2825131

-x = -1705710

x = 1705710



1250 - 935 = 315

Use an equation


descends

( -22 1 __ 2 ) x = -315

( - 45 ___ 2 ) x = -315

( - 2 ___ 45

) ( - 45 ___ 2 ) x = -315 ( - 2 ___

45 )

x = 14



4106 - 3205 = 901




34x = 901

34x ____ 34

= 901 ____ 34

x = 265 = 26 1 __ 2




- 25 + x = -07

_ + 25 _ + 25

x = 18





181 - x = -07

_ - 181 _ -181

-x = -188

x = 188





125 + x = 181

_ -125 _ -125

x = 56



their next play

-26 1 __ 3

+ x = 10

+26 1 __ 3

______

+26 1 __ 3

______

x = 36 1 __ 3



( -2 1 __ 2 ) x = -156

( -25 ) x = -156

( -25 _____ -25

) x = -156 ______ -25

x = 624



rate and the time


x __ 5 = 455

( 5 ) x __ 5 = 455 ( 5 )

x = 2275


Sample answer


to $22750



below sea level



lower elevation

20 -4x = -48

( -4x ____ -4

) = -48 _____ -4

x = 12

- 1 __ 4 x = -48

( -4 ) ( - 1 __ 4 ) x = -48 ( -4 )

x = 192

192 ____ 12

= 16








$21085

LESSON 63

Your Turn


purchased






Equation 150 - 35x = 45





Guided Practice

1

+ + ++ ++

+++ + +

+++

2

----

+ ++ ++

- - -

























place 28 +1-tiles


bicycle





Equation 85d + 55 = 123






Equation 125r + 675 = 3175








Equation 45n + 60 = 285




means + 45





1 _ 2

bull n + 45 = 172

Equation 1 __ 2 n + 45 = 172





uniforms equipment


Equation 295u + 548 = 2023





weeks


Equation 500 - 20x = 220






Total bill $88


shirts bill















10 + 5c = 25

10 - 10 + 5c = 25 - 10

5c = 15

5c ___ 5 = 15 ___

5

c = 3

3 children



10 + 5 ( 5 ) = $35














bought

LESSON 64

Your Turn


+ ++ +

+ ++ ++ +

+ ++ ++ +

++


+ ++ +

+ ++ ++ +

+ ++ ++ +

++


++

+ ++ +

++


++ ++


+ + ++ + ++ +

+++

+++

__



+ + ++ + ++

++ +

+++

+++

__


+ + ++++ + +++


+ + +++


++++

______

______

____



++++

+

++

+

++

______

______

____


++++

____


++ __



____

________

++



________

________

++

____


________

________

We get -y = -1

____


tile to each side

++

__ ++ __


++++

__


+++

6 3n + 10 = 37


3n + 10 = 37

-10 ____

-10 ____

3n = 27

3n ___ 3 = 27 ___

3

n = 9


7 n __ 4 - 5 = 15


n __ 4 - 5 = 15

+5 ___

+5 ___

n __ 4 = 20

n __ 4 ( 4 ) = 20 ( 4 )

n = 80

The number is 80

8 -20 = 5 __ 9 ( x - 32 )


-20 = 5 __ 9 ( x - 32 )

-20 = 5 __ 9 x - 160 ____

9

+ 160 ____ 9

______

+ 160 ____ 9

______

- 20 ___ 9 = 5 __

9 x

- 20 ___ 9 divide ( 5 __

9 ) = 5 __

9 x divide ( 5 __

9 )

4 20 times 9

1 _______

9 1 times 5

1 = x

- 4 __ 1 = x

-4 = x


9 120 - 4x = 92


120 - 4x = 92

-120 _____

-120 _____

- 4x = -28

-4x ____ -4

= -28 ____ -4

x = 7



Guided Practice





++++

+ +++++++++


++++

++++++++


++ + + + +




Solve the equation

2 ( 18 ) + 2w = 58

36 + 2w = 58

36 - 36 + 2w = 58 - 36

2w = 22

2w ___ 2 = 22 ___

2

w = 11


4 1200 minus 25x = 500


1200 - 25x = 500

_ -1200 _ -1200

-25x = -700

-25x _____ -25

= -700 _____ -25

x = 28






equation


6 9s + 3 = 57

9s + 3 - 3 = 57 - 3

9s = 54

9s ___ 9 = 54 ___

9

s = 6

7 4d + 6 = 42

4d + 6 - 6 = 42 - 6

4d = 36

4d ___ 4 = 36 ___

4

d = 9

8 115 - 3y = -485

115 - 115 - 3y = -485 - 115

thinsp-3y = -60

-3y

____ -3

= -60 ____ -3

y = 20

9 k __ 2 + 9 = 30

k __ 2 + 9 - 9 = 30 - 9

k __ 2 = 21

2 sdot k __ 2 = 2 sdot 21

k = 42

10 g

__ 3 - 7 = 15

g

__ 3 - 7 + 7 = 15 + 7

g

__ 3 = 22

3 sdot g

__ 3 = 3 sdot 22

g = 66

11 z __ 5 + 3 = -35

z __ 5 + 3 - 3 = -35 - 3

z __ 5 = -38

5 sdot z __ 5 = 5 ( -38 )

z = -190

12 -9h - 15 = 93

-9h - 15 + 15 = 93 + 15

-9h = 108

-9h ____ -9 = 108 ____

-9

h = -12

13 - 1 __ 3 (n + 15) = -2

- 1 __ 3 n - 5 = -2

- 1 __ 3 n - 5 + 5 = -2 + 5

- 1 __ 3 n = 3

-3 sdot - 1 __ 3 n = -3 sdot 3

n = -9

14 -17 + b __ 8 = 13

-17 + 17 + b __ 8 = 13 + 17

b __ 8 = 30

8 sdot b __ 8 = 8 sdot 30

b = 240


15 7 ( c - 12 ) = -21

7c - 84 = -21

_ +84 _ +84

7c = 63

7c ___ 7 = 63 ___

7

c = 9

16 -35 + p

__ 7 = -52

-35 + 35 + p

__ 7 = -52 + 35

p

__ 7 = -17

7 sdot p

__ 7 = -17 sdot 7

p = -119

17 46 = -6t - 8

46 + 8 = -6t - 8 + 8

54 = -6t

54 ___ -6

= -6t ____ -6

t = -9





2 (a + $26) = $264

Solve the equation

2 ( a + 26 ) = 264

2 ( a + 26 )

_________ 2 = 264 ____

2

a + 26 = 132

a + 26 - 26 = 132 - 26

a = 106






Solve the equation

2t - 6 = 20

2t - 6 + 6 = 20 + 6

2t = 26

2t __ 2 = 26 ___

2

t = 13


20 -35 = 5 __ 9 ( x - 32 )

-35 = 5 __ 9 x - 160 ____

9

+ 160 ____ 9

______

+ 160 ____ 9

- 155 ____ 9 = 5 __

9 x

thinsp- 155 ____ 9 divide ( 5 __

9 ) = 5 __

9 x divide ( 5 __

9 )

-thinsp 31

155 times 9

1

= x

9 1

times 5

1

- 31 ___ 1 = x

-31 = x




Solve the equation

-a + 40 = 28

-a + 40 - 40 = 28 - 40

-a = -12

-a ___ -1

= -12 ____ -1

a = 12






Solve the equation

2c + 11 = 73

2c + 11 - 11 = 73 - 11

2c = 62

2c ___ 2 = 62 ___

2

c = 31




price paid


1 __ 2

middot p -6 = 88

Solve the equation

1 __ 2 p - 6 = 88

1 __ 2 p - 6 + 6 = 88 + 6

1 __ 2 p = 94

2 sdot 1 __ 2 p = 2 sdot 94

p = 188



24 115 minus 8n = 19


115 - 8n = 19

_ -115 _ -115

-8n = -96

-8n _____ -8

= -96 _____ -8

n = 12


25 -55x + 056 = -164

-55x + 056 - 056 = -164 - 056

-55x = -22

-55x ______ -22

= -22 _____ -22

x = 04

26 -42x + 315 = -651

-42x + 315 - 315 = -651 - 315

-42x = -966

-42x ______ -42

= -966 ______ -42

x = 23

27 k ___ 52

+ 819 = 472

k ___ 52

+ 819 - 819 = 472 - 819

k ___ 52

= -347

52 sdot k ___ 52

= 52 ( -347 )

k = -18044




divide 2 by 3

3x + 2 = 15

3x ___ 3 + 2 __

3 = 15 ___

3

x + 2 __ 3 = 5

- 2 __ 3

___

- 2 __ 3

___

x = 5 - 2 __ 3

x = 5 times3

___ 1

times3 - 2 __

3

x = 15 ___ 3 - 2 __

3

x = 13 ___ 3 or 4 1 __

3


31 a 2(x + 40) = 234


2x + 80 = 234

2x + 80 - 80 = 234 - 80

2x = 154

2x ___ 2 = 154 ____

2

x = 77

Trey saved $77






32 F = 18c + 32

F - 32 = 18c + 32 - 32

F - 32 = 18c

F - 32 ______ 18

= 18c ____ 18

F - 32 ______ 18

= c

33 P = 2 ( ℓ + w ) P = 2ℓ + 2w

P - 2ℓ = 2ℓ - 2ℓ + 2w

P - 2ℓ = 2w

P - 2ℓ ______ 2 = 2w ___

2

P - 2ℓ ______ 2 = w

34 ax + b = c

ax + b - b = c - b

ax = c - b

ax ___ a = c - b ______ a

x = c - b ______ a

MODULE 6

Ready to Go On




15n + 60 + 12n + 95



2 h + 97 = -97

_ -97 _ -97

h = -194

3 - 3 __ 4 + p = 1 __

2

+ 3 __ 4 + 3 __

4

p = 1 __ 2 + 3 __

4

p = 1 times2

___ 2

times2 + 3 __

4

p = 2 __ 4 + 3 __

4

p = 5 __ 4

4 -15 = -02k

-15 _____ -02

= -02k ______ -02

75 = k


5 y ___

-3 = 1 __

6

y ___

-3 ( -3 ) = 1 __

6 ( -3 )

y = 1 __ 6 times -3 ___

1

y = -3 ___ 6

y = -1 ___ 2

6 - 2 __ 3

m = -12

- 2 __

3 m _____

- 2 __ 3 = -12 ____

- 2 __ 3

m = -12 divide - 2 __ 3

m = -12 ____ 1 divide - 2 __

3

m = -12 ____ 1 times - 3 __

2

m = -36 ____ -2

m = 18

7 24 = - t ___ 45

24 ( 45 ) = - t ___ 45

( 45 )

108 = -t

-108 = t







2 middot d + 15 = 33


9 5n + 8 = 43

5n + 8 - 8 = 43 - 8

5n = 35

5n ___ 5 = 35 ___

5

n = 7

10 y __

6 - 7 = 4

y __

6 - 7 + 7 = 4 + 7

y __

6 = 11

6 sdot y __

6 = 6 sdot 11

y = 66

11 8w - 15 = 57

8w - 15 + 15 = 57 + 15

8w = 72

8w ___ 8 = 72 ___

8

w = 9

12 g

__ 3 + 11 = 25

g

__ 3 + 11 - 11 = 25 - 11

g

__ 3 = 14

3 sdot g

__ 3 = 3 sdot 14

g = 42

13 f __ 5 - 22 = -25

f __ 5 - 22 + 22 = -25 + 22

f __ 5 = -03

5 sdot f __ 5 = 5 ( -03 )

f = -15

14 - 1 __ 4 (p + 16) = 2

- 1 __ 4 p - 4 = 2

- 1 __ 4 p - 4 + 4 = 2 + 4

- 1 __ 4 p = 6

-4 sdot - 1 __ 4 p = 6 sdot -4

p = -24




situation



Are You Ready

1 9w = -54

9w ___ 9 = -54 ____

9

w = -6

2 b - 12 = 3

thinsp _ + 12 = _ + 12

b = 15

3 n __ 4

= -11

4 times n __ 4

= 4 ( -11 )

n = -44

4-7


75 4 6

8 3 - (-5)

3 + 5

8

9 -4 - 5

-9

10 6 - 10

-4

11 -5 - (-3)

-5 + 3

-2

12 8 - (-8)

8 + 8

16

13 9 - 5

4

14 -3 - 9

-12

15 0 - (-6)

0 + 6

6

LESSON 71

Your Turn


_ +5 _ +5

y ge minus2

-4-5 -3 -2-1 0 1 2 3 4 5


minus1 ge -8


2 le 16

5 21 gt 12 + x

_ -12 _ minus12

9 gt x

x lt 9

10 2 3 4 5 6 7 8 9 10


21 gt 12 + 8

21 gt 12 + 8

21 gt 20

6 -10y lt 60

-10y

_____ -10

lt 60 ____ -10

y gt -6

-10-9 -8 -7 -6 -5 -4 -3 -2-1 0 1


-10y lt 60

-10(-5) lt 60

50 lt 60

7 7 ge - t __ 6

7(-6) le - t __ 6 (-6)

-42 le t

t ge -42

-46 -45 -44 -43 -42 -41 -40-47


7 ge - t __ 6

7 ge - ( -36 ____

6 )

7 ge 6



35m le 315

35m ____ 35

le 315 ____ 35

m le 9



Guided Practice

1 -5 le -2

_ +7 _ +7

2 le 5

2 -6 lt -3

-6 ___ -3

gt -3 ___ -3

2 gt 1

3 7 gt -4

_ -7 _ -7

0 gtthinsp -11


4 -1 ge -8

-1 ( -2 ) le -8 ( -2 )

2 le 16

5 n - 5 ge -2

_ +5 _ +5

n ge 3

-5 -4 -3 -2-1 0 3 4 51 2


n - 5 ge -2

4 - 5 ge -2

-1 ge -2

6 3 + x lt 7

_ -3 _ -3

x lt 4

-2-1 0 3 4 5 6 7 81 2


3 + x lt 7

3 + 3 lt 7

6 lt 7

7 -7y le 14

-7y

____ -7 ge 14 ___ -7

y ge -2

-5-6-7 -4 -3 -2-1 0 1 2 3


-7y le 14

-7 ( -1 ) le 14

7 le 14

8 b __ 5 gt -1

b __ 5 ( 5 ) gt -1 ( 5 )

b gt -5

-5-6-7-8 -4 -3 -2-1 0 1 2


b __ 5 gt -1

0 __ 5 gt

-1

0 gt -1

9 a -4t ge -80

b -4t ge -80

-4t ____ -4

le -80 ____ -4

t le 20








number


11 x - 35 gt 15

_ + 35 _ +35

x gt 50

100 20 30 40 50 60 70 80 90100


x - 35 gt 15

51 minus 35 gt 15

16 gt 15

12 193 + y ge 201

_ -193 _ minus193

y ge 8

10 2 3 4 5 6 7 8 9 10


193 + y ge 201

193 + 9 ge 201

202 ge 201

13 - q

__ 7 ge -1

- q

__ 7 ( -7 ) le -1 ( -7 )

q le 7

8 9 105 6 70 1 2 3 4


- q

__ 7 ge -1

- -14 ____ 7 ge

-1

2 ge -1

14 -12x lt 60

-12x _____ -12

gt 60 ____ -12

x gt -5

0-10-9 -8 -7 -6 -5 -4 -3 -2-1


-12x lt 60

-12 ( -4 ) lt 60

48 lt 60

15 5 gt z -3

_ +3 _ +3

8 gt z

z lt 8

10 2 3 4 5 6 7 8 9 10


5 gt z - 3

5 gt 7 - 3

5 gt 4


16 05 le y __

8

05 ( 8 ) le y __

8 ( 8 )

4 le y

y ge 4

8 9 105 6 70 1 2 3 4


05 le y __

8

05 le 8 __

8

05 le 1



12 + x le 28

_ -12 _ -12

x le 16




w __ 7 lt 35

w __ 7 ( 7 ) lt 35 ( 7 )

w lt 245





6s le 42

6s ___ 6 le 42 ___

6

s le 7




3025 + x ge 50

_ -3025 _ -3025

x ge 1975




155w ge 1705

155w ______ 155

ge 1705 _____ 155

w ge 11




thinsp-12t lt -120

-12t _____ -12

gt -120 _____ -12

t gt 10






3s le 10

3s ___ 3 le 10 ___

3

s le 3 1 __ 3


pounds



m ___ 05

le 55

m ___ 05

( 05 ) le 55 ( 05 )

m le 275




125x le 3

125x _____ 125

le 3 ____ 125

x le 24



buy 25 pounds







not true





prism

V = lwh



( 13 ) ( 1 __ 2 ) h lt 65

65h lt 65

65h ____ 65

lt 65 ___ 65

h lt 10





LESSON 72Your Turn


raise



Target amount $6000



must raise equal to




can go on

Starting amount $40

Admission price $6




equal to




are looking for




10 is added to 3x



than 30








looking for












Guided Practice

1

- -- -

-

lt

++++++

+ + ++ + +

+

2

---

gt

+ + ++ + +

+ + ++ + +

+ + +


raise








1250 + 92a ge 7000




greater than 32







inequality






3a + 28 gt 200




cheese to has


075n + 129 le 700












120 + 32n le 720




month month


2100 + 005s ge 2400






668 + 7n gt 2000


day



buys to a month


$7 + $10 middot c le $100

7 + 10c le 100






$22 + $17 middot n le $80

22 + 17n le 80














is given by

95 + 86 + 89 + 3s

________________ 6


tests



95 + 86 + 89 + 3s

________________ 6 ge 90 or

95 + 86 + 89 + 3s ge 540 or

270 + 3s ge 540












So -m gt 0

25 n gt 1 __ n if n gt 1


n = 1 __ n if n = 1

LESSON 73

Your Turn


++

++++

+++

++++

++++

+++

gt


++

++++

+++

++++

++++

+++

gt

- -- -- --

- -- -- --


++

++++

gt


++

++++

gt



+ + +gt


+++++

----

+++++

+ +++++

ge


+++++

----

+++++

+ ++

++++

+++

++++

ge


+++++

+++++

+ +++++

++++

ge


+++++

+++++

+ +++++

++++

ge


+ + + +ge


5 - p

__ 6 le 4

5 - 5 - p

__ 6 le 4 - 5

thinsp- p

__ 6 le -1

thinsp-6 ( - p

__ 6 ) ge -6 ( -1 )

p ge 6


arrow

0 1 4 5 72 3 6 8 9 10



3v - 8 gt 22

v = 9 v = 10 v = 11

3 ( 9 ) - 8 gt 22 3 ( 10 ) - 8 gt 22 3 ( 11 ) - 8 gt 22


results

3 ( 9 ) - 8 gt 22 3 ( 10 ) - 8 gt

22 3 ( 11 ) - 8 gt

22

27 - 8 gt 22 30 - 8 gt

22 33 - 8 gt

22

19 gt 22 22 gt

22 25 gt

22


v = 11


5h + 12 le -3

h = -3 h = -4 h = -5

5 ( -3 ) + 12 le -3 5 ( -4 ) + 12 le -3 5 ( -5 ) + 12 le -3


results

5 ( -3 ) + 12 le -3 5 ( -4 ) + 12 le

-3 5 ( -5 ) + 12 le

-3

-15 + 12 le -3 -20 + 12 le

-3 -25 + 12 le

-3

-3 le -3 -8 le

-3 -13 le

-3

true true true

h = -3 h = -4 h = -5


Guided Practice




5d - 13 lt 32

5d - 13 + 13 lt 32 + 13

5d lt 45

5d ___ 5 lt 45 ___

5

d lt 9


20 6 84 10 12 14 16 18 20


-4b + 9 le -7

-4b + 9 - 9 le -7 - 9

-4b le -16

-4b ____ -4

ge -16 ____ -4

b ge 4


20 6 84 10 12 14 16 18 20


2m + 18 gt - 4

m = -12 m = -11 m = -10

2 ( -12 ) + 18 gt -4 2 ( -11 ) + 18 gt -4 2 ( -10 ) + 18 gt -4


results

2 ( -12 ) + 18 gt -4 2 ( -11 ) + 18 gt

- 4 2 ( -10 ) + 18 gt

- 4

- 24 + 18 gt -4 - 22 + 18 gt

- 4 - 20 + 18 gt

- 4

- 6 gt - 4 - 4 gt

- 4 - 2 gt

- 4


m = -10


- 6y + 3 ge 0

y = 1 y = 1 __ 2 y = 0

-6 ( 1 ) + 3 ge 0 -6 ( 1 __ 2 ) + 3 ge 0 -6 ( 0 ) + 3 ge 0


results

-6 ( 1 ) + 3 ge 0 - 6 ( 1 __

2 ) + 3 ge

0 - 6 ( 0 ) + 3 ge

0

-6 + 3 ge 0 -3 + 3 ge

0 0 + 3 ge

0

-3 ge 0 0 ge

0 3 ge

0

not true true true

y = 1 __ 2

y = 0


65 - 4t ge 15

65 - 65 - 4t ge 15 - 65

-4t ge -5

-4t ____ -4

le -5 ___ -4

t le 125


0 05 1 15 2 25



time






8 2s + 5 ge 49

2s + 5 - 5 ge 49 - 5

2s ge 44

2s ___ 2 ge 44 ___

2

s ge 22

10 14 1612 18 20 22 24 26 28 30

9 -3t + 9 ge -21

-3t + 9 - 9 ge -21 -9

-3t ge -30

-3t ____ -3

le -30 ____ -3

t le 10


10 55 gt -7v + 6

55 - 6 gt -7v + 6 - 6

49 gt - 7v

49 ___ -7 lt -7v ____ -7

v gt -7

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0

11 21 1 __ 3 gt 3m - 2 2 __

3

21 1 __ 3 + 2 2 __

3 gt 3m - 2 2 __

3 + 2 2 __

3

24 gt 3m

24 ___ 3 gt 3m ___

3

8 gt m or m lt 8

0 1 4 5 72 3 6 8 9 10

12 a ___ -8

+ 15 gt 23

a ___ -8

+ 15 - 15 gt 23 - 15

a ___ -8

gt 8

-8 ( a ___ -8

) lt -8 ( 8 )

a lt -64

-70 -68 -66 -64 -62 -60


13 f __ 2 - 22 lt 48

f __ 2 - 22 + 22 lt 48 + 22

f __ 2 lt 70

2 ( f __ 2 ) lt 2 ( 70 )

f lt 140

100 110 120 130 140 150

14 -25 + t __ 2 ge 50

-25 + 25 + t __ 2 ge 50 + 25

t __ 2 ge 75

2 ( t __ 2 ) ge 2 ( 75 )

t ge 150

130 140 150 160 170 180

15 10 + g ___

-9 gt 12

10 - 10 + g ___

-9 gt 12 - 10

g ___

-9 gt 2

-9 ( g ___

-9 ) lt -9 ( 2 )

g lt -18

-20 -18 -14 -12 -10-16

16 252 le -15y + 12

252 - 12 le -15y + 12 - 12

24 le - 15y

24 ____ -15

ge -15y

_____ -15

y le -16

-20 -18 -14 -12 -10-16

17 -36 ge -03a + 12

-36 - 12 ge -03a + 12 - 12

-48 ge -03a

-48 _____ -03

le -03a ______ -03

a ge 16

10 11 12 13 14 16 17 18 19 2015

18 80 - 2w ge 50

80 - 80 - 2w ge 50 - 80

- 2w ge -30

-2w ____ -2

le -30 ____ -2

w le 15



11 12 13 14 and 15


7n - 25 ge 65

7n - 25 + 25 ge 65 + 25

7n ge 90

7n ___ 7 ge 90 ___

7

n ge 12 6 __ 7


be a whole number





21 a

10 3 42 5 6 7 8 9 10

b

10 3 42 5 6 7 8 9 10














MODULE 7

Ready to Go On

1 n + 7 lt -3

thinsp _ -7

_ -7

n lt -10

2 5p ge -30

5p

___ 5 ge -30 ____

5

p ge -6

3 14 lt k + 11

_ -11 _ -11

3 lt k

4 d ___ -3

le minus6

( -3 ) ( d ) ge ( -3 ) ( -6 )

d ge 18


5 c - 25 le 25

_ +25 _ +25

c le 5

6 12 ge -3b

12 ___ -3

le -3b _____ -3

-4 le b




562 + n ge 650

_ -562 _ -562

n ge 88


-20 - 20t ge -100

9 2s + 3 gt 15

_ -3 _ -3

2s gt 12

2s ___ 2

gt 12 ___ 2

s gt 6

10 - d ___ 12

- 6 lt 1

_ +6 _ +6

- d ___ 12

lt 7

12 ( - d ___ 12

) lt 12 ( 7 )

-d lt 84

d gt -84

11 -6w - 18 ge 36

_ +18 _ +18

thinsp-6w ge 54

-6w _____ -6

le 54 ___ -6

w le -9

12 z __ 4 + 22 le 38

_ -22 _ -22

z __ 4 le 16

4 ( z __ 4 ) le 4 ( 16 )

z le 64

13 b __ 9 - 34 lt -36

_ +34 _ +34

b __ 9 lt -2

9 ( b __ 9 ) lt 9 ( -2 )

b lt -18

14 -2p + 12 gt 8

-12 ____

-12 ____

-2p gt -4

-2p

____ -2 lt -4 ___

-2

p lt 2






Are You Ready

1 3x + 4 = 10

3x + 4 - 4 =10 - 4

3x = 6

3x ___ 3 = 6 __

3

x = 2

2 5x - 11 = 34

5x - 11 + 11 = 34 + 11

5x = 45

5x ___ 5 = 45 ___

5

x = 9

3 -2x + 5 = -9

-2x + 5 - 5 = -9 - 5

-2x = -14

-2x ____ -2

= -14 ____ -2

x = 7

4 -11 = 8x + 13

-11 - 13 = 8x + 13 - 13

-24 = 8x

-24 ____ 8 = 8x ___

8

-3 = x

5 4x - 7 = -27

4x - 7 + 7 = -27 + 7

4x = -20

4x ___ 4 = -20 ____

4

x = -5

6 1 __ 2 x + 16 = 39

1 __ 2 x + 16 - 16 = 39 - 16

1 __ 2 x = 23

( 2 ) 1 __ 2 x = ( 2 ) 23

x = 46

7 12 = 2x - 16

12 + 16 = 2x - 16 + 16

28 = 2x

28 ___ 2 = 2x ___

2

14 = x

8 5x - 15 = -65

5x - 15 + 15 = -65 + 15

5x = -50

5x ___ 5 = -50 ____

5

x = -10

9 x __ 5 = 18 ___

30


30x = 90

30x ____ 30

= 90 ___ 30

x = 3

10 x ___ 12

= 24 ___ 36


36x = 288

36x ____ 36

= 288 ____ 36

x = 8

11 3 __ 9 = x __

3


9 = 9x

9 __ 9 = 9x ___

9

1 = x

12 14 ___ 15

= x ___ 75


1050 = 15x

1050 _____ 15

= 15x ____ 15

70 = x

13 8 __ x = 14 ___ 7


56 = 14x

56 ___ 14

= 14x ____ 14

4 = x

14 14 ___ x = 2 __ 5


70 = 2x

70 ___ 2 = 2x ___

2

35 = x

15 5 __ 6 = x ___

15


75 = 6x

75 ___ 6 = 6x ___

6

125 = x


UNIT

4


16 81 ___ 33

= x ____ 55


4455 = 33x

4455 _____ 33

= 33x ____ 33

135 = x

LESSON 81

Your Turn


= 22 ft


= 10 ft


Guided Practice

1

Blueprint

length (in)3 6 9 12 15 18

Actual

length (ft)5 10 15 20 25 30



= 15 in







= 25 m


= 15 m


4 a


scales



the drawing


6 a 2 in times 40 cm ______ 1 in

= 80 cm

15 in times 40 cm ______ 1 in

= 60 cm


b 80 cm times 60 cm = 4800 c m 2

c 80 cm times 1 in _______ 254 cm

asymp 315 in

60 cm times 1 in _______ 254 cm

asymp 236 in


315 in by 236 in



= 24 units


= 15 units


15 units




larger



r = 810 m ______ 54 ft

r = 150 m ______ 1 ft



= 648 in



b = 162 bricks



h = 30 ft times 126 cm _______ 1 ft

h = 378 cm



_________ 63 cm

n = 6 toothpicks



asymp 5 swabs






s = 10 cm times 2 ft _____ 1 cm

s = 20 ft










original size


2

LESSON 82

Guided Practice















triangle






6 cm

3 cm120˚








same angle measures








between them






LESSON 83

Guided Practice


2 rectangle

3 triangle





















volume is 480 in 3





LESSON 84

Your Turn



intersecting lines




mangFGD and mangDGC



mangBGC and mangCGD



Because lines _

BE and _




mangCGD = 55deg



3x ___ 3 = 126deg ____

3

x = 42deg





Guided Practice




so mangDGE = 30deg





value by 3














measures are equal

mangKMI = mangHMG

84 = 4x

84 ___ 4 = 4x ___

4

x = 21deg



x + 84 - 84 = 180 - 84

x = 96

mangKMH = 96deg



x + 62 - 62 = 180 - 62

x = 118

mangCBE = 118deg



x + 62 - 62 = 90 - 62

x = 28

mangABF = 28deg




x + 28 - 28 = 152

mangCBA = 152deg




2x ___ 2 = 86deg ___

2





6x ___ 6 = 180deg ____

6









_ -48deg268 _ -48deg268

mangK = 41deg3352






greater than 38deg











( 90 - ( 90 - xdeg ) ) = ( 90 - 90 + xdeg ) = xdeg

MODULE 8

Ready to Go On

1

Living


Actual


Blueprint





created




A point is another




mangFGE = 50deg




3 ( mangY ) ________ 3 = 120deg ____

3

mangY = 40deg

mangY = 40deg


rooms or gardens



Are You Ready

1 416

_ times 13

1248

_ +thinsp4160

5408

5408

2 647

_ times thinsp04

2588

2588

3 705

_ times thinsp94

2820

_ +thinsp63450

66270

6627

4 256

_ timesthinsp049

2304

_ +thinsp10240

12544

12544

5 1 __ 2 ( 14 ) ( 10 )

7 ( 10 )

70 i n 2

6 ( 35 ) ( 35 )

1225 ft 2

7 ( 8 1 __ 2 ) ( 6 )

17 ___ 1 2 sdot 6 3 __

1

51 i n 2

8 1 __ 2 ( 125 ) ( 24 )

1 __ 2 ( 24 ) ( 125 )

( 12 ) ( 125 )

15 m 2

LESSON 91

Your Turn

3 d = 11 cm

C = πd

C asymp 314 ( 11 )

C asymp 3454


6 C = πd

44 asymp 314d

44 ____ 314

asymp d

d asymp 1401 yards


rate

1401 divide 7 = 2001


Guided Practice

1 d = 9 in

C asymp 314 ( 9 )

C asymp 2826 in

2 r = 7 cm

C = 2πr

C asymp 2 ( 22 ___ 7 ) ( 7 )

C asymp 44 cm

3 d = 25 m

C = πd

C asymp 314 ( 25 )

C asymp 785 m

4 r = 48 yd

C = 2πr

C asymp 2 ( 314 ) ( 48 )

C asymp 3014 yd

5 r = 75 in

C = 2πr

C asymp 2 ( 314 ) ( 75 )

C asymp 471 in

6 Find the diameter

C = πd

66 asymp 314d

66 ____ 314

asymp 314d _____ 314

21 asymp d

Find the cost


25 times $045 = $1125



r = 05 yd

d = 1 yd


2πr = 788

2πr ___ 2π

= 788 ____ 2π

r asymp 788 _______ 2 ( 314 )

r asymp 1255 ft

d = 2r asymp 2 ( 1255 ft )

d asymp 2510 ft

9 d = 2r so r = d __ 2 asymp 34 ___

2

r asymp 17 in

C = πd asymp 314 ( 34 )

C = 1068 in





11 d = 59 ft

C = πd

C asymp 314 ( 59 )

C asymp 1853 ft

12 r = 56 cm

C = 2πr

C asymp 2 ( 22 ___ 7 ) ( 56 )

C asymp 352 cm

13 d = 35 in

C = πd

C asymp ( 22 ___ 7 ) ( 35 )

C asymp 110 in



15 r = 94 ft

d = 2r = 2 ( 94 )

d = 188 ft

C = πd

C asymp 314 ( 188 )

C asymp 590 ft

16 d = 475 in

r = d __ 2 = 475 ____

2

r = 2375 in

C = πd

C asymp 314 ( 475 )

C asymp 14915 in

17 d = 18 in

r = d __ 2 = 18 ___

2

r = 9 in

C = πd

C asymp 314 ( 18 )

C asymp 5652 in

18 r = 15 ft

C = 2πr

C asymp 2 ( 314 ) ( 15 ) = 942 ft


so ( 942 ) ( 075 ) = 7065 or about $707

19 C = πd

C asymp ( 22 ___ 7 ) ( 63 )

C asymp 198 ft




20 C = πd asymp 314 ( 2 )

C asymp 628 ft

Converting km to ft

2 km sdot ( 3280 ft _______

1 km ) = 6560 ft

6560 ft

_______ 628 ft

= 104459




1 __ 2 C = 1 __

2 πd asymp 1 __

2 sdot 314 ( 025 ) = 03925





Height 180 ft



_______ 2 ( 314 )

asymp 48 ft

Diameter d = 2r = 2 ( 48 ) = 96 ft



plus the diameter

1 __ 2 C = 1 __

2 πd asymp 1 __

2 sdot 314 ( 30 ) = 471



per linear foot

( 771 ft ) ( $925 _____

ft ) = $71318



C = πd asymp 314 ( 18 ) = 5652 ft


inches to feet

( 54 in ) ( 1 ft _____ 12 in

) = 45 ft



5652 ft _______ 45 ft

= 1256


must buy 13 strands


C inner

= πd asymp 314 ( 150 ) = 471 ft


C outer

= πd asymp 314 ( 154 ) = 48356 ft








smaller gear





314 ( 75 ) - 314 ( 732 ) = 314 ( 018 ) asymp 057

057 m asymp 187 ft

LESSON 92

Your Turn

4 A = π r 2 A = π ( 10 ) 2

A asymp 314 ( 10 ) 2


A asymp 314 f t 2

Guided Practice

1 r = d __ 2 = 14 ___

2 = 7 m

A = π r 2 A = π ( 7 ) 2

A asymp 314 ( 7 ) 2

A asymp 314 sdot 49

A asymp 1539 m 2

2 A = π r 2 A = π ( 12 ) 2

A asymp 314 ( 12 ) 2


A asymp 4522 m m 2

3 r = d __ 2 = 20 ___

2 = 10 yd

A = π r 2 A = π ( 10 ) 2

A asymp 314 ( 10 ) 2


A asymp 314 y d 2

4 A = π r 2 A = π ( 8 ) 2

A asymp 314 ( 8 ) 2

A asymp 314 sdot 64

A asymp 20096 i n 2

5 r = d __ 2 = 12 ___

2 = 6 cm

A = π r 2 A = π ( 6 ) 2

A asymp 314 ( 6 ) 2

A asymp 314 sdot 36

A asymp 11304 c m 2

6 r = d __ 2 = 13 ___

2 = 65 in

A = π r 2 A = π ( 65 ) 2

A asymp 314 ( 65 ) 2


A asymp 13267 i n 2

7 C = 4π = 2πr

4π ___ 2π

= 2πr ___ 2π

r = 2

A = π r 2 A = π ( 2 ) 2


8 C = 12π = 2πr

12π ____ 2π

= 2πr ___ 2π

r = 6

A = π r 2 A = π ( 6 ) 2


9 C = π __ 2 = 2πr

π __ 2 divide 2π = 2πr ___

2π

π __ 2 sdot 1 ___

2π = r

1 __ 4 = r

A = π r 2

A = π ( 1 __ 4 ) 2 = π ( 1 ___

16 )

A = π ___ 16

square units

10 A = π r 2 = 64π

π r 2 ___ π = 64π ____ π

r 2 = 64

r = 8

C = 2πr

= 2π ( 8 )

=16π yd

11 A = π r 2


12 r = d __ 2 = 10 ___

2 = 5 in

A = π r 2 A = π ( 5 ) 2

A asymp 314 ( 5 ) 2

A asymp 314 sdot 25

A asymp 785 i n 2

13 A = π r 2 A = π ( 16 ) 2

A asymp 314 ( 16 ) 2


A asymp 80384 c m 2


diameter 36 in

r = d __ 2 = 36 ___

2 = 18 in

A semicircle

= 1 __ 2 π r 2

A semicircle

= 1 __ 2 π ( 18 ) 2

A semicircle

asymp 1 __ 2 ( 314 ) ( 18 ) 2

A semicircle


A asymp 50868 i n 2




A = π r 2 A = π ( 3 ) 2

A asymp 314 ( 3 ) 2



A r = 75 mi

- A r = 50 mi

π ( 75 ) 2 - π ( 50 ) 2



greater







s 2 minus π r 2 = 1 2 2 minus π ( 6 ) 2

= 144 minus π ( 36 )

asymp 144 minus 11304 = 3096










16π in 2





about $20

_____ π ( 9 ) 2



_____ π ( 6 ) 2

asymp $009






A = π r 2 = π ( 8 ) 2

= π ( 64 )

asymp 20096


201 mi 2




A new

minus A old

= π ( 10 ) 2 - π ( 8 ) 2

= π ( 1 0 2 - 8 2 ) = π ( 100 - 64 )

= π ( 36 ) asymp 11304


more area









A


A whole target

=

π ( 15 ) 2 ______

π ( 75 ) 2

= ( 15 ) 2

_____ ( 75 ) 2

= 225 _____ 5625

= 004


LESSON 93

Your Turn


two right triangles





A = ℓw = 11 sdot 4 = 44 f t 2


A = 1 __ 2 bh = 1 __



A = 1 __ 2 bh = 1 __

2 sdot 3 sdot 3 = 45 f t 2


44 + 3 + 45 = 515 f t 2


semicircle



or 10 ___ 2 = 5 m


A = s 2 = 1 0 2 = 100 m 2


A = 1 __ 2 π r 2

A asymp 1 __ 2 sdot 314 sdot ( 5 ) 2


A asymp 3925 m 2


100 + 3925 = 13925 m 2







4 __ 2 = 2 ft


A = ℓw = 5 sdot 4 = 20 f t 2


A = π r 2 A asymp 314 sdot ( 2 ) 2



two areas

20 + 1256 = 3256 f t 2



( 3256 f t 2 ) ( $28 ____

f t 2 ) = $91168


Guided Practice


a parallelogram



2 ( 4 ) ( 2 ) = 4




2 parallelogram

15 cm 2


4 + 15 + 15 = 34 cm 2


2 Method 1

A 1 = ℓw A

2 = ℓw

= 12 sdot 9 = 20 sdot 9 = 108 = 180


Method 2

A 1 = ℓw A

2 = ℓw

= 9 sdot 8 = 12 sdot 8 = 72 = 216






1 + b

2 )

A = 1 __ 2 ( 5 ) ( 7 + 4 )

A = 1 __ 2 ( 5 ) ( 11 ) = 275 f t 2



275 + 16 = 435 ft 2


find the cost

( 435 f t 2 ) ( $225 _____

f t 2 ) = $9788


simpler figures




A asymp 1 __ 2 sdot 314 sdot ( 13 ) 2


A asymp 26533 i n 2


676 + 26533 = 94133 in 2






A = 1 __ 2 sdot 6 sdot 7

A = 1 __ 2 sdot 42

A = 21 f t 2


40 + 21 = 61 f t 2


square foot

( 61 f t 2 ) ( $250 _____

f t 2 ) = $15250

7

O 42-2-4

2

-4

y

A (-2 4) B (0 4)

C (2 1)D (5 1)

E (5 -2)F (-2 -2)










Area of trapezoid

A = 1 __ 2 h ( b

1 + b

2 )

A = 1 __ 2 ( 3 ) ( 4 + 2 )

A = 1 __ 2 ( 3 ) ( 6 ) = 9 square units











A = 1 __ 2 sdot 8 sdot 8

A = 1 __ 2 sdot 64

A = 32 m 2


A asymp 1 __ 4 sdot 314 sdot ( 8 ) 2


A asymp 5024 f t 2


64 + 32 + 5024 = 14624 m 2









48 + 1256 = 6056 cm 2






A = 1 __ 2 sdot 1 sdot 1

A = 1 __ 2 sdot 1

A = 05 f t 2


3 + 05 = 35 ft 2





( 42 f t 2 ) ( $125 _____

f t 2 ) = $5250


area of triangle

325 ft 2 - 75 ft 2 = 25 ft 2



square is 5 ft






20 ( 15 ) or 300 carrots








triangle



A = 1 __ 2 sdot 12 sdot 8

A = 1 __ 2 sdot 96

A = 48 i n 2


144 + 48 = 192 in 2










420 - 176625 = 243375 in 2 or 243 3 __

8 i n 2










A asymp 1 __ 2 sdot 314 sdot ( 20 ) 2


A asymp 628 i n 2


1600 + 628 = 2228 in 2






40 + 2 sdot 4 = 48 in




total of 40 + 4 = 44 in






A asymp 1 __ 2 sdot 314 sdot ( 24 ) 2


A asymp 90432 i n 2


the sum

2112 + 90432 asymp 3016 in 2

LESSON 94

Your Turn


B = l times w

= 9 times 2

= 18 square inches


P = 2 ( 9 ) + 2 ( 2 )

= 18 + 4 = 22 inches


S = Ph + 2B

S = 22 ( 1 1 __ 2 ) + 2 ( 18 )

= 33 + 36

= 69



B = times w

= 12 times 12

= 144 square inches


P = 4 ( 12 )

= 48 inches


S = Ph + 2B

S = 48 ( 12 ) + 2 ( 144 )

= 576 + 288

= 864 square inches


B = l times w

= 8 times 8

= 64 square inches


P = 4 ( 8 )

= 32 inches


S = Ph + 2B

S = 32 ( 8 ) + 2 ( 64 )

= 256 + 128

= 384 square inches








Guided Practice



Height = 7 ft

Base area = 1 __ 2 ( 3 ) ( 8 ) = 12 ft 2

Surface area

S = ( 18 ft ) ( 7 ft ) + 2 ( 12 ft 2 ) = 150 ft 2


B = l times w

= 25 times 25

= 625 m 2


P = 4 ( 25 )

= 10 m


S = Ph + 2B

S = 10 ( 25 ) + 2 ( 625 )

= 25 + 125

= 375


S = 375 m 2


B = l times w

= 11 times 9

= 99 m 2


prism

P = 2 ( 11 ) + 2 ( 9 )

= 22 + 18

= 40 m


S = Ph + 2B

S = 40 ( 7 ) + 2 ( 99 )

= 280 + 198

= 478


S = 478 m 2


A = ( 25 ) ( 25 ) = 625



= 375 + 478 -2 ( 625 ) = 503 m 2




surface




B = l times w

= 10 times 3

= 30 in 2


P = 2 ( 10 ) + 2 ( 3 )

= 20 + 6

= 26 in


S = Ph + 2B

S = 26 ( 4 ) + 2 ( 30 )

=104 + 60

= 164 in 2



B = l times w

= 20 times 15

= 300 cm 2


P = 2 ( 20 ) + 2 ( 15 )

= 40 + 30

= 70 cm


S = Ph + 2B

S = 70 ( 9 ) + 2 ( 300 )

= 630 + 600

= 1230 cm 2


1230 - 300 = 930 cm 2



Convert cm 2 to mm

2


2 ________

1 cm 2 = 93000 mm

2


93000 divide 25 = 3720




= 2 + 3 = 5 in 2


Perimeter = 3 + 3 + 1 + 2 + 2 + 1

= 12 in


S = Ph + 2B

S = 12 ( 3 ) + 2 ( 5 )

= 36 + 10

= 46 in 2



Perimeter = 25 + 25 + 3 = 8 ft

Base area = 1 __ 2 ( 2 ) ( 3 ) = 3 ft 2


= 8 ( 4 ) + 2 ( 3 )

= 32 + 6 = 38 ft 2


Perimeter = 2 ( 3 ) + 2 ( 4 ) = 14 ft



= 14 ( 2 ) + 2 ( 12 )

= 28 + 24 = 52 ft 2



Surface area = 38 + 52 - 12 - 12 = 66 ft 2







1 + b

2 ) h

1 __ 2 ( 16 + 48 ) 12 = 384 in

2


P = 48 + 20 + 16 + 20 = 104 in


S = Ph + 2B

S = 104 ( 24 ) + 2 ( 384 )

= 2496 + 768

= 3264 in 2



B = l times w

= 7 times l

= 7 ft 2


P = 2 ( 7 ) + 2 ( 1 )

= 14 + 2

= 16 ft


S = Ph + 2B

S = 16 ( 2 ) + 2 ( 7 )

= 32 + 14

= 46 f t 2


B = l times w

= 1 times 1

= 1 ft 2


P = 2 ( 1 ) + 2 ( 1 )

= 2 + 2 = 4 ft


S = Ph + 2B

S = 4 ( 3 ) + 2 ( 1 )

= 12 + 2

= 14 ft 2



Surface area = 46 + 14 - 1 - 1 = 58 ft 2



58 divide 25 = 232


needed


3 times 679 = 2037




B = l times w

= 27 times 24

= 648 cm 2


P = 2 ( 27 ) + 2 ( 24 )

= 54 + 48

= 102 cm


S = Ph + 2B

S = 102 ( 10 ) + 2 ( 648 )

= 1020 + 1296

= 2316 cm 2






2 ( 2l + 2w ) = 2P


New S = 2Ph + 2 ( 4B )


doubles



B = l times w

= 25 times 25

= 625 ft 2


P = 4 ( 25 )

= 10 ft


S = Ph + 2B

S = 10 ( 35 ) + 2 ( 625 )

= 35 + 135

= 485 ft 2



485 - 625 = 4225 ft 2



4225 _____ 485

times 100 asymp 87




15


r = 2 in

9 in


A = πr 2

asymp 31 4 ( 2 ) 2 = 1256 in 2


C = πd

asymp 314 ( 4 ) = 1256 in 2




S = Ch + 2B

asymp 1256 ( 9 ) + 2 ( 1256 ) = 13816 in 2





1500 times 1382 = 207300 in 2



( 207300 in 2 ) 1 ft 2 _______

144 in 2 asymp 1440 ft 2






show

LESSON 95

Your Turn


B = 1 __ 2 bh

= 1 __ 2 ( 24 ) 7

= 84 m 2


V = Bh

= ( 84 ) ( 22 )

= 1848 m 3



B = 1 __ 2 ( b 1 + b 2 ) h

= 1 __ 2 ( 8 + 12 ) 10

= 1 __ 2 ( 20 ) 10 = 100 cm

2


V = Bh

= ( 100 ) ( 22 )

= 2200 cm 3




B = bh

= ( 13 ) 13

= 169 in 2


V = Bh

= ( 169 ) ( 30 )

= 5070 in 3



B = 1 __ 2 bh

= 1 __ 2 ( 9 ) 13

= 585 in 2


V = Bh

= ( 585 ) ( 30 )

= 1755 in 3


5070 + 1755 = 6825 in 3


Guided Practice

1 B = 1 __ 2 bh = 1 __

2 ( 8 ) ( 3 ) = 12 ft 2

V = Bh = ( 12 times 7 ) ft 3 = 84 ft 3

2 B = 1 __ 2 ( b 1 + b 2 ) h = 1 __

2 ( 15 + 5 ) 3 = 30 m

2

V = Bh = ( 30 times 11 ) m 3 = 330 m 3


B = bh

= ( 4 ) 6 = 24 ft 2


V = Bh

= ( 24 ) ( 12 ) = 288 ft 3



B = 1 __ 2 bh

= 1 __ 2 ( 6 ) 4 = 12 ft 2


V = Bh

= ( 12 ) ( 6 ) = 72 ft 3



288 + 72 = 360 ft 3



B = bh

= ( 40 ) ( 50 ) = 2000 ft 2


V = Bh

= ( 2000 ) ( 15 ) = 30000 ft 3


B = 1 __ 2 bh

= 1 __ 2 ( 40 ) ( 10 ) = 200 ft 2


V = Bh

= ( 200 ) ( 50 ) = 10000 ft 3


30000 + 10000 = 40000 ft 3



B = 1 __ 2 ( b 1 + b 2 ) h

= 1 __ 2 ( 10 + 12 ) 5

= 1 __ 2 ( 22 ) 5 = 55 cm

2


V = Bh

= ( 55 ) ( 7 ) = 385 cm 3







V = Bh

= ( 35 ) ( 5 ) = 175 in 3




B = 1 __ 2 bh

= 1 __ 2 ( 7 ) ( 6 ) = 21 in

2


V = Bh

= ( 75 ) ( 7 ) = 525 in 3



B = 1 __ 2 bh

= 1 __ 2 ( 8 ) ( 4 ) = 16 ft 2


V = Bh

= ( 16 ) ( 24 ) = 384 ft 3



B = 1 __ 2 ( b 1 + b 2 ) h

= 1 __ 2 ( 7 + 5 ) 4

= 1 __ 2 ( 12 ) 4 = 24 in

2


V = Bh

= ( 24 ) ( 8 ) = 192 in 3



V = Bh

= ( 20 ) ( 15 ) = 300 in 3


300 cubic inches


given B = 234 in 3


V = Bh

= ( 234 ) ( 3 ) = 702 in 3



B = bh

= ( 3 ) ( 3 ) = 9 in 2


V = Bh

= ( 9 ) ( 3 ) = 27 in 3


702 + 27 = 972 in 3



B = bh

= ( 75 ) 375 = 28125 m 2


V = Bh

= ( 28125 ) ( 75 ) asymp 21094 cm 3


prism


15 - 75 = 75


B = bh

= ( 75 ) 375 = 28125 m 2


V = Bh

= ( 28125 ) ( 375 ) asymp 10547 cm 3


21094 + 10547 = 31641 m 3




V = Bh

= ( 21 ) ( 8 ) = 168 cm 3



260 - 168 = 92 cm 3


V = Bh

= ( 7 ) ( 14 ) = 98 cm 3



260 - 168 = 92 cm 3


a height of 14 cm

V = Bh

92 = B ( 14 )

92 ___ 14

= B ( 14 ) _____ 14

6 8 ___ 14

= B asymp 657





V = Bh

= ( 36 ) ( 5 ) = 180 in 3



prism V = Bh

= ( 32 ) ( 6 ) = 192 in 3





V = Bh

286 = B ( 8 )

286 ____ 8 = B ( 8 )

3575 = B


trapezoidal prism

1 __ 2 ( 2 + b 2 ) 13 = 3575

1 __ 2 ( 2 + b 2 ) ( 13 ___

13 ) = 3575 _____

13

( 2 ) 1 __ 2 ( 2 + b 2 ) = ( 2 ) 275

2 + b 2 = 55

_ -2 _ -2

b 2 = 35 ft



B = 1 __ 2 bh

= 1 __ 2 ( 10 ) 6 = 30 cm

2


V = Bh

= ( 30 ) ( 25 ) = 75 cm 3



_____ cm

3 )

asymp ( 75 cm 3 ) ( 86 g

_____ cm

3 ) = 645 g


about 645 g







of 120 cm 3

V = Bh

V = [ 1 __ 2 ( b 1 + b 2 ) h 1 ] h 2

120 ≟ [ 1 __ 2 ( 2 + 6 ) 4 ] 75

= [ 1 __ 2 ( 8 ) 4 ] 75

= [ 16 ] ( 75 ) = 120


V = Bh

V = [ 1 __ 2 ( b 1 + b 2 ) h 1 ] h 2

120 ≟ [ 1 __ 2 ( 1 + 7 ) 25 ] 12

= [ 1 __ 2 ( 8 ) 25 ] 12

= [ 10 ] 12 = 120






MODULE 9

Ready to Go On




2 d = 12 cm d = 6 cm so r = 12 ___ 2 = 6 ft



A asymp 11304 ft 2





A asymp 1 __ 2 sdot 314 sdot ( 8 ) 2


A asymp 10048 m 2


A = 1 __ 2 sdot 16 sdot 10

A = 1 __ 2 sdot 160

A = 80 m 2


80 + 10048 = 18048 m 2





A = 20 sdot 45

A = 90 c m 2

Area of rectangle

A = ℓw = 20 sdot 55 = 110 c m 2


90 + 110 = 200 cm 2



1 __ 2 ( 4 ) 3 = 6 cm 2


P = 3 + 4 + 5 = 12 cm


S = Ph + 2B

S = 12 ( 10 ) + 2 ( 6 )

thinsp=120 + 12

thinsp= 132 cm 2


V = Bh

= ( 6 ) 10

= 60 cm 3




1 __ 2 ( 4 ) 15 = 3 yd 2


( 4 ) 2 = 8 yd 2



P = 4 + 2 + 25 + 25 + 2 = 13 yd


S = Ph + 2B

S = 13 ( 25 ) + 2 ( 11 )

thinsp= 325 + 22

thinsp= 545 yd 2


is given

B = 234 yd 3


V = Bh

= ( 11 ) 25

= 275 yd 3






unit


Are You Ready

1 x ___16

=45___40

40x=720

40x ____40

=720____40

   x=18

2 x __5=1__

4

4x=5

4x ___4

=5__4

  x=5__4=125

3 25___10

=x ___10

125=10x

125____10

=10x ____10

125=x

4 x __6

=2__9

9x= 12

9x ___9

=12___9

   x=12___9=4__

3

5 4748495152575960range=60-47=13

6 4566689121213range=13-4=9

7 95979799100106108115range=115-95=20

8 121319273539476671range=71-12=59

9 mean=3+5+7+3+6+4+8+6+9+5_________________________________10

=56

10 mean=81+94+113+67+62+75____________________________6

=82

LESSON 101

Your Turn




Guided Practice




Jimmy 80

Darnell 90

Ping 75

Zach 85

Jamar 80

BSampleanswer

75+80+90+75+85+80___________________________6

=485____6

asymp81

Meanasymp81



Stan 80 Marcus 90

Alejandro 90 Tio 85

BSampleanswer

85+80+90+85+90+85____________________________6

=515____6 =86

Mean=size86




















b 35___60

= x ____100

xasymp58


=58



LESSON 102

Your Turn


______________________sizeofsample



6___50

= x_____3500

6sdot70______50sdot70

= x _____3500

420_____3500

= x_____3500


Guided Practice

1

6 7 8 9 10 11 12 13 14 1550 1 2 3 4


6 7 7 107 114 4 54

Leastvalue

4

Lower quartile

4

Median

65

Upper quartile

7

Greatestvalue11

Drawaboxplot

10 1550





______________________sizeofsample



4___60

= x_____4200

4sdot70______60sdot70

= x_____4200

280_____4200

= x_____4200






8___50

= x_____4500

8sdot90______50sdot90

= x_____4500

720_____4500

= x_____4500



divide060

divide060







_______________________________________ size of sample

=



4 ___ 50

= x ____ 600

4 sdot 12 ______ 50 sdot 12

= x ____ 600

48 ____ 600

= x ____ 600

x = 48



_______________________________________________ size of sample

=



2 ___ 20

= x ____ 130

2 sdot 65 _______ 20 sdot 65

= x ____ 130

13 ____ 130

= x ____ 130

x = 13



________________ size of sample



12 ___ 60

= x _____ 1200

12 sdot 20 ______ 60 sdot 20

= x _____ 1200

240 _____ 1200

= x _____ 1200

x = 240


shelters


__________________________ size of sample



12 ___ 72

= x ______ 10800

12 sdot 150 _______ 72 sdot 150

= x ______ 10800

1800

______ 10800

= x ______ 10800

x = 1800



_______ 2 = 25


14 Order the data

11 12 12 12 13 13 13 14 14 14 15 17 18 18

19 22



12 ___ 16

= x ____ 100

12 sdot 625 ________ 16 sdot 625

= x ____ 100

75 ____ 100

= x ____ 100

x = 75



15

6 7 8 9 1050 1 2 3 4


fewer siblings




















9 a 56 + 43 + 62 + 63 + 33 + 34 + 38 + 51 + 59 + 59

___________________________________________ 10

= 498


b 498 sdot 64 = 31872



10 55 + 57 + 57 + 58 + 59 + 59 + 59 + 59 + 59 + 61 + 62 + 62 + 63 + 64 + 66

_________________________________________________________________ 15

= 60






accurately

LESSON 103

Guided Practice

1 (1 600) 20

2 50 51 600








5 Shop A 10 ___ 50

times 500 = 100

Shop B 23 ____ 100

times 500 = 115

Shop C 7 ___ 25

times 500 = 140








fewest bagels










count of 75


MODULE 10

Ready to Go On




service


__________________________________________ size of sample


18 ____ 270

= x ______ 30330

18 sdot 337 ____

3 ________

270 sdot 337 ____ 3

= x ______ 30330

2022

______ 30330

= x ______ 30330

x = 2022


languages





= defective players

______________ shipment

2 ___ 10

= x _____ 5000

2 middot 500 _______ 10 middot 500

= x _____ 5000

1000

_____ 5000

= x _____ 5000

x = 1000


defective


the shipment





Are You Ready

0875

1 8 ⟌ _

7000

_ -6 400

600

_ -560

40

_ -40

0

0875 875

08

2 5 ⟌ _

40

_ -4 0

0

08 80

025

3 4 ⟌ _

100

_ -80

20

_ -20

0

025 25

03

4 10 ⟌ _

30

_ -3 0

0

03 30

5 4 6 7 7 9 11 15 17

7 + 9

_____ 2 = 8

Median = 8

Mode = 7

6 36 37 40 43 44 49 50 51 56

Median = 44

Mode none

7 9 + 16 + 13 + 14 + 10 + 16 + 17 + 9

________________________________ 8

= 13

Mean = 13

8 108 + 95 + 104 + 96 + 97 + 106 + 94

________________________________ 7 = 100

Mean = 100

LESSON 111

Your Turn








in order

1 4 4 4 5 5 5 6 6 6 6 7 7 8 11


range 10 h



range for exercise

Guided Practice




one area




no data


4 Class A

4 4 4 4 4 5 5 5 6 6 12 13 13 13 13 14 14

median 6

Class B

3 4 4 4 5 5 5 5 6 6 7 7 7 7 7 8 8 9

median 6








at 8 letters




3 + 4 + 4 + 5 + 5 + 6 + 7 + 7 + 8 + 8 + 8 + 9

________________________________________ 12

74 ___ 12

asymp 617

Mean asymp 617

3 3 4 5 5 6 7 7 8 8 8 9


average

6 + 7

_____ 2 = 13 ___

2 = 65

Median 65

Range 9 - 3 = 6


the left


interval













LESSON 112

Your Turn



Guided Practice


2 Median79

3 Range88-72=16 IQR85-75=10






























does not




LESSON 113

Your Turn

1 Team 1

Mean

44 + 47 + 67 + 89 + 55 + 76 +85 + 80 + 87 + 69 + 47 + 58 = 804

804 divide 12 = 67


ǀ 44 - 67 ǀ = 23 ǀ 47 - 67 ǀ = 20

ǀ 67 - 67 ǀ = 0 ǀ 89 - 67 ǀ = 22

ǀ 55 - 67 ǀ = 12 ǀ 76 - 67 ǀ = 9

ǀ 85 - 67 ǀ = 18 ǀ 80 - 67 ǀ = 13

ǀ 87 - 67 ǀ = 20 ǀ 69 - 67 ǀ = 2

ǀ 47 - 67 ǀ = 20 ǀ 58 - 67 ǀ = 11


23 + 20 + 0 + 22 + 12 + 9 +18 + 13 + 20 + 2 + 20 + 11 = 170


Team 2

Mean

40 + 32 + 52 + 75 + 65 + 70 +72 + 61 + 54 + 43 + 29 + 32 = 625



ǀ 40 - 521 ǀ = 121 ǀ 32 - 521 ǀ = 201

ǀ 52 - 521 ǀ = 01 ǀ 75 - 521 ǀ = 229

ǀ 65 - 521 ǀ = 129 ǀ 70 - 521 ǀ = 179

ǀ 72 - 521 ǀ = 199 ǀ 61 - 521 ǀ = 89

ǀ 54 - 521 ǀ = 19 ǀ 43 - 521 ǀ = 91

ǀ 29 - 521 ǀ = 231 ǀ 32 - 521 ǀ = 201


121 + 201 + 01 + 229 +129 + 179 + 199 + 89 +19 + 91 + 231 + 201 = 169


Difference in means

67 - 521 = 149



MAD


distributions

Guided Practice

1 Class 1 mean

12 + 1 + 6 + 10 + 1 + 2 + 3 +10 + 3 + 8 + 3 + 9 + 8 + 6 + 8 = 90

90 divide 15 = 6

Class 2 mean

11 + 14 + 11 + 13 + 6 + 7 + 8 + 6 +8 + 13 + 8 + 15 + 13 + 17 + 15 = 165

165 divide 15 = 11


ǀ 12 - 6 ǀ = 6 ǀ 1 - 6 ǀ = 5 ǀ 6 - 6 ǀ = 0

ǀ 10 - 6 ǀ = 4 ǀ 1 - 6 ǀ = 5 ǀ 2 minus 6 ǀ = 4

ǀ 3 - 6 ǀ = 3 ǀ 10 - 6 ǀ = 4 ǀ 3 - 6 ǀ = 3

ǀ 8 - 6 ǀ = 2 ǀ 3 - 6 ǀ = 3 ǀ 9 - 6 ǀ = 3

ǀ 8 - 6 ǀ = 2 ǀ 6 - 6 ǀ = 0 ǀ 8 - 6 ǀ = 2

6 + 5 + 0 + 4 + 5 + 4 + 3 + 4 +3 + 2 + 3 + 3 + 2 + 0 + 2 = 46



ǀ 11 - 11 ǀ = 0 ǀ 14 - 11 ǀ = 3 ǀ 11 - 11 ǀ = 0

ǀ 13 - 11 ǀ = 2 ǀ 6 - 11 ǀ = 5 ǀ 7 - 11 ǀ = 4

ǀ 8 - 11 ǀ = 3 ǀ 6 - 11 ǀ = 5 ǀ 8 - 11 ǀ = 3

ǀ 13 - 11 ǀ = 2 ǀ 8 - 11 ǀ = 3 ǀ 15 - 11 ǀ = 4

ǀ 13 - 11 ǀ = 2 ǀ 17 - 11 ǀ = 6 ǀ 15 - 11 ǀ = 2

0 + 3 + 0 + 2 + 5 + 4 + 3 + 5 +3 + 2 + 3 + 4 + 2 + 6 + 2 = 44



11 minus 6 = 5




comparison


different samples


5 23 + 38 + 39 + 48 + 55 + 56 + 71 +86 + 57 + 53 + 43 + 31 = 600

600 divide 12 = 50

ǀ 23 - 50 ǀ = 27 ǀ 38 - 50 ǀ = 12

ǀ 39 - 50 ǀ = 11 ǀ 48 - 50 ǀ = 2

ǀ 55 - 50 ǀ = 5 ǀ 56 - 50 ǀ = 6

ǀ 71 - 50 ǀ = 21 ǀ 86 - 50 ǀ = 36

ǀ 57 - 50 ǀ = 7 ǀ 53 - 50 ǀ = 3

ǀ 43 - 50 ǀ = 7 ǀ 31 - 50 ǀ = 19

27 + 12 + 11 + 2 + 5 + 6 + 21 +36 + 7 + 3 + 7 + 19 = 156

156 divide 12 = 13



6 ǀ 23 - 8 ǀ = 15 ǀ 38 - 23 ǀ = 15

ǀ 39 - 24 ǀ = 15 ǀ 48 - 33 ǀ = 15

ǀ 55 - 40 ǀ = 15 ǀ 56 - 41 ǀ = 15

ǀ 71 - 56 ǀ = 15 ǀ 86 - 71 ǀ = 15

ǀ 57 - 42 ǀ = 15 ǀ 53 - 38 ǀ = 15

ǀ 43 - 28 ǀ = 15 ǀ 31 - 16 ǀ = 15




7 50 - 15 = 35




8 50 - 35 = 15




9

0 4 8 12 16 20 24 28 32 36 40 44

Medians

School B

School A

0 4 8 12 16 20 24 28 32 36 40 44

Means

School B

School A




10 State A 48 - 38 = 10


State B 50 - 42 = 8

8 divide 4 = 2





well


Median 665


Median 77

77 - 665 = 105

105 divide 6 = 175


ranges













not very similar

MODULE 11

Ready to Go On


5 + 6 + 6 + 7 + 7 + 7 + 7 + 8 + 8 + 8 + 8 + 9 + 9 + 10

________________________________________________ 14

= 105 ____ 14

= 75 mi


6 + 6 + 7 + 7 + 8 + 8 + 8 + 8 + 9 + 9 + 9 + 10 + 10 + 10

__________________________________________________ 14

= 115 ___ 14

asymp 82 mi




5 6 6 7 7 7 7 8 8 8 8 9 9 10


average

7 + 8

_____ 2 = 15 ___

2 = 75

Median 75


6 6 7 7 8 8 8 8 9 9 9 10 10 10




Median 8













7 + 11 + 11 + 12 + 9 + 12 + 8 + 10

______________________________ 8

= 10


21 + 24 + 19 + 19 + 22 + 23 + 24 + 24

__________________________________ 8 = 22




12 ___ 5

= 24




groups



Are You Ready

1 6 ___ 10

= 6 divide 2 ______ 10 divide 2

= 3 __ 5

2 9 ___ 15

= 9 divide 3 ______ 15 divide 3

= 3 __ 5

3 16 ___ 24

= 16 divide 8 ______ 24 divide 8

= 2 __ 3

4 9 ___ 36

= 9 divide 9 ______ 36 divide 9

= 1 __ 4

5 45 ___ 54

= 45 divide 9 ______ 54 divide 9

= 5 __ 6

6 30 ___ 42

= 30 divide 6 ______ 42 divide 6

= 5 __ 7

7 36 ___ 60

= 36 divide 12 _______ 60 divide 12

= 3 __ 5

8 14 ___ 42

= 14 divide 14 _______ 42 divide 14

= 1 __ 3

075

9 4 ⟌ _

300

_ -2 80

20

_ -20

0

075

0875

10 8 ⟌ _

7000

_ -6400

600

_ -560

40

_ -40

0

0875

015

11 20 ⟌ _

300

_ -2 00

100

_ -100

0

015

038

12 50 ⟌ _

1900

_ -15 00

4 00

_ -4 00

0

038

13 67 = 67 ____ 100

= 067

14 31 = 31 ____ 100

= 031

15 7 = 7 ____ 100

= 007

16 146 = 100 + 46

= 100 ____ 100

+ 46 ____ 100

= 1 + 046

= 146

17 013 = 13

18 055 = 55

19 008 = 8

20 116 = 116

LESSON 121

Your Turn







is 10 ___ 20

or 1 __ 2





3


UNIT

6



P(5) + P(not 5) = 1

1 __ 8 + P(not 5) = 1

P(not 5) = 7 __ 8




1 __ 2 + P(odd) = 1

P(odd) = 1 __ 2


Guided Practice













impossible 0
















= 1 __ 4


P(5) + P(not 5) = 1

1 __ 6 + P(not 5) = 1

P(not 5) = 5 __ 6




1 __ 3 + P(not blue) = 1




P(4) + P(not 4) = 1

1 __ 5 + P(not 4) = 1

P(not 4) = 4 __ 5




4 ___ 52

+ P(not queen) = 1

P(not blue) = 48 ___ 52

= 12 ___ 13









selecting


or 2 ___ 13



9 ___ 12



or 1 __ 4



or 1 __ 4













or 5 __ 7



have red hair




or 4 __ 7





coin is 9 ___ 16














landing on blue

LESSON 122

Your Turn


Red 10 ___ 30

= 1 __ 3

Yellow 14 ___ 30

= 7 ___ 15

Blue 6 ___ 30

= 1 __ 5






Guided Practice


A 14 ___ 40

= 7 ___ 20

= 035 = 35

B 7 ___ 40

= 0175 = 175

C 11 ___ 40

= 0275 = 275

D 8 ___ 40

= 1 __ 5 = 020 = 20







4 6 ___ 10








= 8 ___ 48

= 1 __ 6





chosen is 19 ___ 20


1 ___ 20

+ P(not Ryan) = 1

P(not Ryan) = 19 ___ 20


patterns




times



get a hit next time


is 4 ___ 10





or about 417


7 ___ 12



or 417











pocket


LESSON 123

Your Turn



= 60 ____ 400

= 3 ___ 20

= 15



= 12 ___ 75

or 4 ___ 25

Guided Practice




= 50 ____ 400

or 1 __ 8











number of trials








= 33 ____ 330

= 1 ___ 10



= 60 ____ 400

= 3 ___ 20


= 55 + 60 + 23

____________ 400

= 138 ____ 400

= 69 ____ 200


and 4 color choices


P(7th grade + 100 pages) = 85 ____ 250

= 17 ___ 50




7th grade




likely





12 P(male + open toe) = 11 ____ 300











heads and 3 or 4

LESSON 124

Your Turn








Guided Practice








too high

5 98 ____ 100

= x ___ 40

= 39 ___ 40

or 39 times




6 18 ____ 100

= x _____ 5000

= 900 _____ 5000



accepted

times04

times04

times50

times50





events


8 4 ____ 100

= x ____ 200

= 8 ____ 200



9 Yes 6th grade 2 ____ 100

= x ____ 250

= 5 ____ 250

or 5 students

7th grade 4 ____ 100

= x ____ 200

= 8 ____ 200

or 8 students

8th grade 8 ____ 100

= x ____ 150

= 12 ____ 150

or 12 students



10 6 ____ 100

= x ____ 300

= 18 ____ 300










1 ___ 30

= x ____ 180




normal gas pump







4 ____ 100

= x _____ 2400

= 96 _____ 2400



MODULE 12

Ready to Go On

1 H1 H2 T1 T2

2 6 ___ 10

= 3 __ 5

3 13 ___ 20




because 3 ___ 10

= x ___ 80

= 24 ___ 80

or 24 times




times15

times15

times24

times24

times2

times2

times3

times3

times2

times2

times25

times25

times8

times8



Simulations

Are You Ready

075

1 4 ⟌ _

300

_ -2 80

20

_ -20

0

075 = 75

04

2 5 ⟌ _

20

_ -2 0

0

04 = 40

09

3 10 ⟌ _

90

_ -9 0

0

09 = 90

035

4 20 ⟌ _

700

_ -6 00

1 00

_ -1 00

0

035 = 35

0875

5 8 ⟌ _

7000

_ thinsp-6 400

600

_ -560

40

_ -40

0

0875 = 875

005

6 20 ⟌ _

100

_ -1 00

0

005 = 5

076

7 25 ⟌ _

1900

_ -17 50

1 50

_ -1 50

0

076 = 76

046

8 50 ⟌ _

2300

_ -20 50

3 00

_ -3 00

0

046 = 46

9 1 - 1 __ 5 = 5 __

5 - 1 __

5

= 4 __ 5

10 1 - 2 __ 9 = 9 __

9 - 2 __

9

= 7 __ 9

11 1 - 8 ___ 13

= 13 ___ 13

- 8 ___ 13

= 5 ___ 13

12 1 - 3 ___ 20

= 20 ___ 20

- 3 ___ 20

= 17 ___ 20

13 8 ___ 15

times 5 __ 8 =

18 ___ 315

times 5 1 ___

8 1

= 1 __ 3

14 2 __ 9 times 3 __

4 =

12 __ 39

times 3 1 ___

4 2

= 1 __ 6

15 9 ___ 16

times 12 ___ 13

= 9 ___ 416

times 12 3 _____

13

= 27 ___ 52

16 7 ___ 10

times 5 ___ 28

= 17 ___

210 times 5

1 ____

28 4

= 1 __ 8

LESSON 131

Your Turn






= 2 __ 6 = 1 __

3



probability


Guided Practice

1

Basket A Basket B


= 16

7 + 4 + 9

= 20


P(win) =

Number of red balls


3 ___

16 4 ___

20 = 1 __

5


16 use


1 __ 5 = 16 ___

80

3 ___ 16

= 15 ___ 80

Therefore 16 ___ 80

gt 15 ___ 80

so 1 __ 5 gt 3 ___

16


winning




= 6 ___ 11




= 5 ___ 11




= 2 __ 6 = 1 __

3


close


by 20




= 2 __ 6

= 1 __ 3 033 or 33



= 8 ___ 12

= 2 __ 3 067 or 67



= 4 ___ 14

= 2 __ 7 029 or 29


= 26 ___ 52

= 1 __ 2 050 or 50


= 12 - 5 ______ 12

= 7 ___ 12

058 or 58



7 adventure)

P(not a comedy)


= 5 + 7 _________

5 + 7 + 8 = 12 ___

20

= 3 __ 5 060 or 60






= 2 __ 6

= 1 __ 3 033 or 33







= 6 ___ 16

or 3 __ 8







5 ______ 5 + 15

= 5 ___ 20

= 1 __ 4

times16

times16

times5

times5




P(seventh grader) =



= 20 ___ 35

= 4 __ 7


P(eighth grader) =



= 15 ___ 35

= 3 __ 7



more likely










= 8 ___ 20


14 ___ 40

or 7 ___ 20



marble is 8 ___ 20

- 7 ___ 20

= 1 ___ 20



= 10 ___ 20


= 8 ___ 20



marble is 10 ___ 20

- 8 ___ 20

= 2 ___ 20

= 1 ___ 10




= 2 ___ 20


= 5 ___ 20



marble is 5 ___ 20

- 2 ___ 20

= 3 ___ 20



LESSON 132

Your Turn

3 P(ham sandwich) =



= 4 ___ 12

= 1 __ 3




= 6 ___ 12

= 1 __ 2




0 0 0 0

0 0 0 1

0 0 1 0

0 0 1 1


second digit

0 1 0 0

0 1 0 1

0 1 1 0

0 1 1 1


second digit

1 0 0 0

1 0 0 1

1 0 1 0

1 0 1 1


second digit

1 1 0 0

1 1 0 1

1 1 1 0

1 1 1 1



0 0 1 1

0 1 0 1

0 1 1 0

1 0 0 1

1 0 1 0

1 1 0 0





= 6 ___ 16

= 3 __ 8


Guided Practice

1

1 2 3 4 5 6

11 sdot 1

= 1

1 sdot 2

= 2

1 sdot 3

= 3

1 sdot 4

= 4

1 sdot 5

= 5

1 sdot 6

= 6

22 sdot 1

= 2

2 sdot 2

= 4

2 sdot 3

= 6

2 sdot 4

= 8

2 sdot 5

= 10

2 sdot 6

= 12

33 sdot 1

= 3

3 sdot 2

= 6

3 sdot 3

= 9

3 sdot 4

= 12

3 sdot 5

= 15

3 sdot 6

= 18

44 sdot 1

= 4

4 sdot 2

= 8

4 sdot 3

= 12

4 sdot 4

= 16

4 sdot 5

= 20

4 sdot 6

= 24

55 sdot 1

= 5

5 sdot 2

= 10

5 sdot 3

= 15

5 sdot 4

= 20

5 sdot 5

= 25

5 sdot 6

= 30

66 sdot 1

= 6

6 sdot 2

= 12

6 sdot 3

= 18

6 sdot 4

= 24

6 sdot 5

= 30

6 sdot 6

= 36





= 15 ___ 36




= 23 ___ 36

4 H

HHH HHT

H

H

Coin 1

List

Coin 2

Coin 3 T

T

HTH HTT

H T

T

H

H T

THH THT

T

H T

TTH TTT

Coin 1

List

Coin 2

Coin 3




= 1 __ 8


HHT HTH THH



= 3 __ 8




10

Checkered

Red

Checkered

Red

Blue

Black

Checkered

Red

Checkered

Red

Blue

Black

Checkered

Red

Checkered

Red

Blue

Black

Shirt Pants Shoes

Yellow

Red

Green




= 6 ___ 12

= 1 __ 2


Shirt Pants Shoes






= 4 ___ 12

= 1 __ 3



Rhee Pamela

Rhee A

Rhee B

Rhee C

Pamela A

Pamela B

Pamela C

A B

A C

B C



P(Rhee and Pamela)


= 1 ___ 10




1 2 3 4 5 6

11 + 1

= 2

1 + 2

= 3

1 + 3

= 4

1 + 4

= 5

1 + 5

= 6

1 + 6

= 7

22 + 1

= 3

2 + 2

= 4

2 + 3

= 5

2 + 4

= 6

2 + 5

= 7

2 + 6

= 8

33 + 1

= 4

3 + 2

= 5

3 + 3

= 6

3 + 4

= 7

3 + 5

= 8

3 + 6

= 9

44 + 1

= 5

4 + 2

= 6

4 + 3

= 7

4 + 4

= 8

4 + 5

= 9

4 + 6

= 10

55 + 1

= 6

5 + 2

= 7

5 + 3

= 8

5 + 4

= 9

5 + 5

= 10

5 + 6

= 11

66 + 1

= 7

6 + 2

= 8

6 + 3

= 9

6 + 4

= 10

6 + 5

= 11

6 + 6

= 12


are 10 less than 6



= 10 ___ 36

= 5 ___ 18


diagram

Khakis

Shorts

Shirt Pants Shoes

Collared Jeans

Sneakers

Flip-flops

Sandals

Sneakers

Flip-flops

Sandals

Sneakers

Flip-flops

Sandals

Khakis

Shorts

T-shirt Jeans

Sneakers

Flip-flops

Sandals

Sneakers

Flip-flops

Sandals

Sneakers

Flip-flops

Sandals







= 4 ___ 18

= 2 __ 9






outcomes



Therefore




= 7 ___ 30






diagram

Carrots

Sweet potato

Pasta

Peas

Asparagus





Carrots

Sweet potato

Peas

Asparagus





Carrots

Sweet potato

Peas

Asparagus





Carrots

Sweet potato

Peas

Asparagus





Salmon

Beef

Pork



salmon Therefore


= 1 __ 4





Carrots

Sweet potato

PastaPeas

Asparagus

Carrots

Sweet potato

Peas

Asparagus

Carrots

Sweet potato

Peas

Asparagus

Carrots

Sweet potato

Peas

Asparagus

Salmon

Beef

Pork


salmon Therefore


= 1 __ 4















codes













12453 12534 12543 13245 13254 13425

13452 13524 13542 14235 14253 14325

14352 14523 14532 15234 15243 15324













114 115 221 223 224 225 331 332 334 335

441 442 443 445 551 552 553 554 There























LESSON 133

Your Turn




3






heads is 1 __ 2

1 __ 2 = x ___

18

1 __ 2 = x ___

18

x = 9

about 9 times


P(red) = 8 ___ 17

P(not red) = 1 - 8 ___ 17

= 9 ___ 17




Therefore




Guided Practice






3 House 1 __

3



1 __ 3 = x ___

18

1 __ 3 = x ___

18

x = 6














P(hazel) = 9 ___ 28

P(brown) = 10 ___ 28

P(blue) = 7 ___ 28

P(green) = 2 ___ 28






unknown quantity




P(white or gray) = 3 __ 9 = 1 __

3


prediction is then








Y GRR

R R

RR





card is 12 ___ 52


52 use the least


52 Given

that 12 ___ 52

lt 26 ___ 52





P(ace) = 4 ___ 52

= 1 ___ 13


prediction is then


times 39 = 3



P(red card) = 26 ___ 52

= 1 __ 2








times6

times6

times9

times9


1 2 3 4 5 6

1 2 3 4 5 6 7

2 3 4 5 6 7 8

3 4 5 6 7 8 9

4 5 6 7 8 9 10

5 6 7 8 9 10 11

6 7 8 9 10 11 12




P(sum of 8) = 5 ___ 36

P(sum of 11) = 2 ___ 36



gt 2 ___ 36




= 1 __ 4




1 __ 4 times 180 = 45





so P(sum of 3) = 3 ___ 36

= 1 ___ 12


prediction is then


middot 36 = 3





time









that is not green



green is 3 + 9 _________

3 + 8 + 9 = 12 ___



20 = 12 ___

40






6 = 1 ___

12



P(5 or heads) = 1 __ 6 + 1 __

2 - 1 __

6 times 1 __

2 = 7 ___

12





LESSON 134

Your Turn



1 0 0 1 No

2 0 1 No

3 1 No

4 0 1 No

5 1 No

6 0 0 0 1 Yes

7 0 0 1 No

8 0 1 No

9 1 No

10 0 0 0 0 1 Yes




or 20



1 1 0 1 1 0 3

2 0 1 0 0 1 2

3 0 0 0 0 1 1

4 0 0 1 1 0 2

5 1 1 1 1 1 5

6 1 0 0 0 0 1

7 1 0 1 1 0 3

8 1 0 1 0 0 2

9 0 1 1 1 1 4

10 0 0 0 0 0 0



= 70


Guided Practice







numbers each time

2


1 10 3 5 1 2

2 10 4 6 5 0

3 3 2 10 3 3

4 2 10 4 4 1

5 7 3 6 3 2

6 8 4 8 5 0

7 6 2 2 8 2

8 6 5 2 4 1

9 2 2 3 2 4

10 6 3 1 5 2




8 ___ 10

= 80









= 10




= 20














1 3 1

2 4 2 2

3 2 1

4 1 1

5 2 1

6 4 5 3 2

7 4 2 2

8 4 5 2 1

9 4 4 3 3

10 5 1 2


1 + 2 + 1 + 1 + 1 + 2 + 2 + 1 + 3 + 2

_________________________________ 10

= 16 ___ 10

= 1 3 __ 5

















MODULE 13

Ready to Go On


= 12 ___________________ 12 + 12 + 15 + 9 + 12

= 12 ___ 60

= 1 __ 5 020 or 20




= 13 + 13

_______ 52

= 26 ___ 52

= 1 __ 2 050 or 50








or

40





Table of Contents


Module 1Lesson 11 1

Lesson 12 2

Lesson 13 3

Lesson 14 4

Module 2Lesson 21 6

Lesson 22 7

Lesson 23 8


Lesson 32 14

Lesson 33 15

Lesson 34 17

Lesson 35 18

Lesson 36 20


Relationships


Lesson 42 25

Lesson 43 25


Lesson 52 29

Lesson 53 30


and Inequalities


Lesson 62 34

Lesson 63 35

Lesson 64 37


Lesson 72 46

Lesson 73 47

UNIT 4 Geometry


Lesson 82 54

Lesson 83 54

Lesson 84 55


Lesson 92 59

Lesson 93 60

Lesson 94 63

Lesson 95 65

UNIT 5 Statistics


Lesson 102 70

Lesson 103 72


Lesson 112 75

Lesson 113 76


Table of Contents

UNIT 6 Probability


Lesson 122 81

Lesson 123 82

Lesson 124 82


Lesson 132 86

Lesson 133 89

Lesson 134 91



Are You Ready


2 a $700 profit 700



1 1

5 183

_ + 78

261

261

5 16 17

6 677

_ -288

389

389

1 1

7 1188

_ +902

2090

2090

1 15 14

8 2647

_ -1885

762

762

9

-8-10 -4-6 -2 2 4 6 8 100 10

-8-10 -4-6 -2 2 4 6 8 100 11

-8-10 -4-6 -2 2 4 6 8 100 12

-8-10 -4-6 -2 2 4 6 8 100

LESSON 11

Your Turn

7 -8 + ( -1 ) = -9

8 -3 + ( -7 ) = -10

9 -48 + ( -12 ) = -60

10 -32 + ( -38 ) = -70

11 109 + 191 = 300

12 -40 + ( -105 ) = -145

13 -150 + ( -1500 ) = -1650

14 -200 + ( -800 ) = -1000

Guided Practice



c -5 + ( -1 ) = -6



c -2 + ( -7 ) = -9

3 -5 + ( -2 ) = -7

-8-7-6-5 -2-1 0-4-3 4 -1 + ( -3 ) = -4

-5-4-3-2 1 2 3-1 0 5 -3 + ( -7 ) = -10

-10 -9-8-7 -4-3-2-6-5 6 -4 + ( -1 ) = -5

-5-4-3-2 1 2 3-1 0 7 -2 + ( -2 ) = -4

-5-4-3-2 1 2 3-1 0 8 -6 + ( -8 ) = -14

-16 -12 -4 0-8 9 -5 + ( -4 ) = -9

10 -1 + ( -10 ) = -11

11 -9 + ( -1 ) = -10

12 -90 + ( -20 ) = -110

13 -52 + ( -48 ) = -100

14 5 + ( 198 ) = 203

15 -4 + ( -5 ) + ( -6 ) = -15

16 -50 + ( -175 ) + ( -345 ) = -570




UNIT

1



18 a

-4

-6

-8

-2

0

2

-5 + (-3)-3 + (-5)

b No -5 + ( -3 ) is -8 and -3 + ( -5 ) is also -8


score is -11


21 -14 + ( -5 ) + ( -12 ) + ( -23 ) = -54 The total


22 a -10 + ( -8 ) = -18

b -6 + ( -2 ) = -8


23 -100 + ( -75 ) + ( -85 ) = -260


24 a -25 + ( -45 ) + ( -75 ) = -145 Jan withdrew

$145

b -35 + ( -55 ) + ( -65 ) = -155 Julie withdrew

$155








six pairs is 8

LESSON 12

Your Turn

7 -51 + 23

ǀ -51 ǀ - ǀ 23 ǀ = 28

-51 + 23 = -28

8 10 + ( -18 )

ǀ -18 ǀ - ǀ 10 ǀ = 8

10 + ( -18 ) = -8

9 13 + ( -13 )

ǀ 13 ǀ - ǀ -13 ǀ = 0

10 25 + ( -26 )

ǀ -26 ǀ - ǀ 25 ǀ = 1

25 + ( -26 ) = -1

Guided Practice

1 9 + ( -3 ) = 6

2 3 4 5 8 9 106 7 2 -2 + 7 = 5

-3-2-1 0 3 4 51 2 3 -15 + 4 = -11

-18 -16 -12 -10-14 4 1 + ( -4 ) = -3

-5-4-3-2 1 2 3-1 0 5 -4 + 5 = 1

6 -6 + 6 = 0

7 2 + ( -5 ) = -3

8 -3 + 7 = 4

9 -8 + 14 = 6

10 7 + ( -5 ) = 2

11 5 + ( -21 ) = -16

12 14 + ( -14 ) = 0

13 0 + ( -5 ) = -5

14 32 + ( -8 ) = 24





16 -15 + 71 = 56

17 -53 + 45 = -8

18 -79 + 79 = 0

19 -25 + 50 = 25

20 18 + ( -32 ) = -14

21 5 + ( -100 ) = -95

22 -12 + 8 + 7 = 3

23 -8 + ( -2 ) + 3 = -7


24 15 + ( -15 ) + 200 = 200

25 -500 + ( -600 ) + 1200 = 100
















is 8 feet deep








LESSON 13

Your Turn

4 -7 - 2 = -7 + ( -2 )

-7 + ( -2 ) = -9

5 -1 - ( -3 ) = -1 + 3

-1 + 3 = 2

6 3 - 5 = 3 + ( -5 )

3 + ( -5 ) = -2

7 -8 - ( -4 ) = -8 + 4

-8 + 4 = -4

Guided Practice







3 -4 - 5 = -4 + ( -5 ) = -9

0-1-2-3-4-5-6-7-8-9 4 1 - 4 = 1 + -4 = -3

0 1 2 3 4-1-2-3-4 5 8 - 11 = 8 + ( -11 ) = -3

6 -3 - ( -5 ) = -3 + 5 = 2

7 15 - 21 = 15 + ( -21 ) = -6

8 -17 - 1 = -17 + ( -1 ) = -18

9 0 - ( -5 ) = 0 + 5 = 5

10 1 - ( -18 ) = 1 + 18 = 19

11 15 - 1 = 14

12 -3 - ( -45 ) = -3 + 45 = 42

13 19 - ( -19 ) = 19 + 19 = 38

14 -87 - ( -87 ) = -87 + 87 = 0


example 6 - 8 = 6 + ( -8 ) = -2




25 - ( -4 ) = 25 + 4 = 29





-127 - ( -225 ) = -127 + 225 = 98



temperature 90degF

90 - ( -2 ) = 92






-425 - ( -275 ) = -425 + 275 = -150



in temperature

Gas A -8 - ( -21 ) = -8 + 21 = 13

13degC increase

Gas B 12 - ( -12 ) = 12 + 12 = 24

24degC increase

Gas C -15 - ( -19 ) = -15 + 19 = 4

4degC increase













-11 + 4 = -7




LESSON 14

Your Turn




Guided Practice


2 -23+5-7=-18-7  =-25-25degF

3 50-40+87-30=10+87-30  =97-30  =6767points

4 -6+15+15=-6+30  =24

5 9- 4- 17= 9- 21  =-12

6 50-42+10=8+10  =18

7 6+13+7-5=19+2  =21

8 65+43-11=108-11  =97

9 -35-14+45+31=-49+76  =27

10 -12+6-4=-6-4  =-10-34-3+39=-37+39  = 2  -10lt2( -12+6-4)lt( -34-3+39)

11 21-3+8=18+8  =26-14+ 31- 6= 17- 6  =11 26gt11( 21-3+8)gt( -14+31-6)



13 a 5-1+6-1=9






b 45gt-55Barry

17 a 300to400


18 100-18+22-53=51$51

19 45-17-22+18=24$24






MODULE 1

Ready to Go On

1 -8+( -6)=-14

2 -4+( -7)=-11

3 -9+( -12)=-21





4 5 + ( -2 )

ǀ 5 ǀ - ǀ -2 ǀ = 3

5 + ( -2 ) = 3

5 -8 + 4

ǀ -8 ǀ - ǀ 4 ǀ = 4

-8 + 4 = -4

6 15 + ( -8 )

ǀ 15 ǀ - ǀ -8 ǀ = 7

15 + ( -8 ) = 7

7 2 - 9 = 2 + ( -9 )

2 + ( -9 ) = -7

8 -3 - ( -4 ) = -3 + 4-3 + 4 = 1

9 11 - ( -12 ) = 11 + 12

11 + 12 = 23

10 -15 + 9 - 4 = -6 - 4

= -10


11 24 + 8 - 12 - 9 = 24 + 8 - ( 12 + 9 ) = 32 - 21

= 11




after she pays them

-10 + ( -5 ) = -15 $15 decrease



Are You Ready

1 9 times 3 = 27

2 7 times 10 = 70

3 9 times 8 = 72

4 15 times 10 = 150

5 6 times 9 = 54

6 10 times 23 = 230

7 9 times 9 = 81

8 10 times 20 = 200

9 54 divide 9 = 6

10 42 divide 6 = 7

11 24 divide 3 = 8

12 64 divide 8 = 8

13 90 divide 10 = 9

14 56 divide 7 = 8

15 81 divide 9 = 9

16 110 divide 11 = 10

17 12 + 8 divide 212 + 4

16

18 15 - ( 4 + 3 ) times 2

15 - 7 times 2

15 - 14

1

19 18 - ( 8 - 5 ) 2

18 - ( 3 ) 2

18 - 9

9

20 6 + 7 times 3 - 5

6 + 21 - 5

27 - 5

22

21 9 + ( 2 2 + 3 ) 2 times 2

9 + ( 4 + 3 ) 2 times 2

9 + ( 7 ) 2 times 2

9 + 49 times 2

9 + 98

107

22 6 + 5 - 4 times 3 divide 2

6 + 5 - 12 divide 2

6 + 5 - 6

11 - 6

5

LESSON 21

Your Turn


will be negative


-3 ( 5 ) = -15


will be positive

ǀ -10 ǀ times ǀ -2 ǀ = 10 times 2 = 20

( -10 ) ( -2 ) = 20


0 ( -22 ) = 0


will be positive

8 ( 4 ) = 32

Guided Practice

1 -1 ( 9 ) = -9

2 14 ( -2 ) = -28

3 ( -9 ) ( -6 ) = 54

4 ( -2 ) ( 50 ) = -100

5 ( -4 ) ( 15 ) = -60

6 -18 ( 0 ) = 0

7 ( -7 ) ( -7 ) = 49

8 -15 ( 9 ) = -135

9 ( 8 ) ( -12 ) = -96

10 -3 ( -100 ) = 300

11 0 ( -153 ) = 0

12 -6 ( 32 ) = -192

13 7 ( -75 ) = -525 -$525



15 6 ( -2 ) = -12 -12degF








19 5 ( -4 ) = -20 $20 decrease





22 9 ( -6 ) = -54 -54 ( 2 ) = -108 Casey has $108

less in his savings

23 7 ( -8 ) = -56 7 ( -5 ) = -35





160 points


25 a 3 ( 3 ) ( -3 ) = 9 ( -3 ) = -27

b 3 ( -3 ) ( -3 ) = -9 ( -3 ) = 27

c -3 ( -3 ) ( -3 ) = 9 ( -3 ) = -27

d 3 ( 3 ) ( 3 ) ( -3 ) = 9 ( 3 ) ( -3 ) = 27 ( -3 ) = -81

e 3 ( 3 ) ( -3 ) ( -3 ) = 9 ( -3 ) ( -3 ) = -27 ( -3 ) = 81

f 3 ( -3 ) ( -3 ) ( -3 ) = -9 ( -3 ) ( -3 ) = 27 ( -3 ) = -81




negative



3 ( 3 ) ( -3 ) ( -3 ) = 9 ( -3 ) ( -3 ) = 81 the sign of the

product is positive


26 -1 ( 3 ) ( 1 ) 1 ( -3 ) ( 1 ) -1 ( -3 ) ( -1 )









negative

LESSON 22

Your Turn


0 divide ( -6 ) = 0


will be negative

38 divide ( -19 ) = -2


will be positive

-13 divide ( -1 ) = 13



Guided Practice

1 -14 ____ 2 = -7

2 21 divide ( -3 ) = -7

3 26 ____ -13

= -2

4 0 divide ( -4 ) = 0

5 -45 ____ -5 = 9

6 -30 divide ( 10 ) = -3

7 -11 ____ -1

= 11

8 -31 divide ( -31 ) = 1

9 0 ___ -7 = 0

10 -121 _____ -11

= 11

11 84 divide ( -7 ) = -12

12 500 ____ -25

= -20


undefined

14 -63 ____ -21

= 3

15 -40 divide ( 4 ) = -10 $10

16 -22 divide ( 11 ) = -2 2 points

17 -75 divide ( -15 ) = 5 5 targets

18 -99 divide ( -9 ) = 11 11 times





20 -24 divide ( 12 ) = -2 $2







is -200 ft _______ 10 min



= -15 ftmin







-20 divide 5 = -4 and -20 times 5 = -100

-100 lt -4



negative





incorrectly

29 a divide ( -3 ) = 8

a = -24

8 divide b = -4






integers

LESSON 23

Your Turn


3 ( -30 ) + 200 = -90 + 200

= 110

2 -6 ( 13 ) - 21 = -78 - 21

= -99

4 ( -12 ) divide 6 + 2 = -2 + 2

= 0

5 -87 divide ( -3 ) -9 = 29 - 9

= 20

6 40 divide ( -5 ) + 30 = -8 + 30

= 22

7 -39 divide 3 -15 = -13 - 15

= -28



moved further back

9 ( -10 ) divide 2 - 2 = -5 - 2 = -7

( -28 ) divide 4 + 1 = -7 + 1 = -6

10 42 divide ( -3 ) + 9 = -14 + 9 = -5

( -36 ) divide 9 - 2 = -4 - 2 = -6

Guided Practice

1 -6 ( -5 ) + 12 = 30 + 12

= 42

2 3 ( -6 ) - 3 = -18 - 3

= -21

3 -2 ( 8 ) + 7 = -16 + 7

= -9

4 4 ( -13 ) + 20 = -52 + 20

= -32

5 -4 ( 0 ) - 4 = 0 - 4

= -4

6 -3 ( -5 ) - 16 = 15 - 16

= -1

7 7 ( -5 ) + 20 = -35 + 20

= -15

15 dollars less

8 7 ( -10 ) + ( -100 ) = -70 + ( -100 )

= -170

170 fewer points

9 6 ( -4 ) + 10 = -24 + 10

= -14

Ned lost 14 points

10 4 ( -12 ) + 10 = -48 + 10

= -38

$38 less

11 -3 ( -2 ) + 3 = 6 + 3

= 9

3 ( -4 ) + 9 = -12 + 9

= -3

9 gt -3

-3 ( -2 ) + 3 gt 3 ( -4 ) + 9

12 -8 ( -2 ) -20 = 16 -20

= -4

3 ( -2 ) + 2 = - 6 + 2

= -4

-4 = -4

-8 ( -2 ) -20 = 3 ( -2 ) + 2

13 -7 ( 5 ) - 9 = -35 - 9

= -44

-3 ( 20 ) + 10 = -60 + 10

= -50

-44 gt -50

-7 ( 5 ) -9 gt -3 ( 20 ) + 10

14 -16 ( 0 ) -3 = 0 -3

= -3

-8 ( -2 ) -3 = 16 -3

= 13

-3 lt 13

-16 ( 0 ) -3 lt -8 ( -2 ) -3





16 -12 ( -3 ) + 7 = 36 + 7

= 43

17 -42 divide ( -6 ) + 5 -8 = 7 + 5 -8

= 12 -8

= 4

18 10 ( -60 ) -18 = -600 -18

= -618

19 ( -11 ) ( -7 ) + 5 - 82 = 77 + 5 - 82

= 82 - 82

= 0

20 35 divide ( -7 ) + 6 = -5 + 6

= 1

21 -13 ( -2 ) - 16 - 8 = 26 - 16 - 8

= 10 - 8

= 2

22 a 5 ( 2 ) -12 + 3 = 10 -12 + 3

= -2 + 3

= 1

b -3 ( 2 ) -1 + 6 + 7 = -6 -1 + 6 + 7

= -7 + 6 + 7

= -1 + 7

= 6


the game

23 5 ( -4 ) -8 = -20 - 8 = -28

24 -36 divide ( -4 ) + 9 = 9 + 9 = 18


25 a 4 ( -35 ) -9 = -140 -9

= -149

$149 less

b Yes $200 - $149 = $51 $51 gt $50 so Arleen

has enough money

26 a 2 ( -10 ) + 3 = -20 + 3= -17

b 7 + 2 + ( -7 ) = 2




7 of clubs





had change








MODULE 2

Ready to Go On


will be negative

( -2 ) ( 3 ) = -6


will be positive

( -5 ) ( -7 ) = 35



( 8 ) ( -11 ) = -88

4 ( -3 ) ( 2 ) ( -2 ) = ( -6 ) ( -2 ) = 12

5 5 ( -3 ) = -15 -15degC

6 -63 ____ 7 = -9

7 -15 ____ -3

= 5

8 0 ____ -15

= 0

9 96 ____ -12

= -8

10 -24 divide 6 = -4 -4 Ib

11 ( -4 ) ( 5 ) + 8 = -20 + 8

= -12

12 ( -3 ) ( -6 ) -7 = 18 -7

= 11

13 -27 ____ 9 - 11 = -3 - 11

= -14

14 -24 ____ -3

- ( -2 ) = 8 + 2

= 10




( -3 ) ( 5 ) + 10 = -15 + 10 = -5 He had $05 less

than before



Are You Ready

1 9 ___ 14

times 7 __ 6 =

3

2

9 ___ 14

times 7 __ 6 1

2

= 3 __ 4

2 3 __ 5 times 4 __

7 = 12 ___

35

3 11 ___ 8

times 10 ___ 33

= 1

4

11 ___ 8 times 10 ___

33 5

3

= 5 ___ 12

4 4 __ 9 times 3 =

3

4 __ 9 times 3 __

1 1

= 4 __ 3 or 1 1 __

3

5 1 __ 2 divide 1 __

4 = 1 __

2 times 4 __

1

=

1 1 __ 2 times 4 __

1 2

= 2 __ 1 = 2

6 3 __ 8 divide 13 ___

16 = 3 __

8 times 16 ___

13

= 1 3 __ 8 times 16 ___

13 2

= 6 ___ 13

7 2 __ 5 divide 14 ___

15 = 2 __

5 times 15 ___

14

= 1

1 2 __ 5 times 15 ___

14 3

7

= 3 __ 7

8 4 __ 9 divide 16 ___

27 = 4 __

9 times 27 ___

16

= 1

1 4 __ 9 times 27 ___

16 3

4

= 3 __ 4

9 3 __ 5 divide 5 __

6 = 3 __

5 times 6 __

5

= 18 ___ 25

10 1 __ 4 divide 23 ___

24 = 1 __

4 times 24 ___

23

= 1 1 __ 4 times 24 ___

23 6

= 6 ___ 23

11 6 divide 3 __ 5 = 6 __

1 times 5 __

3

= 2

6 __ 1 times 5 __

3 1

= 10 ___ 1 = 10

12 4 __ 5 divide 10 = 4 __

5 times 1 ___

10

= 2

4 __ 5 times 1 ___

10 5

= 2 ___ 25

13 21 - 6 divide 3

21 - 2

19

14 18 + ( 7 - 4 ) times 3

18 + 3 times 3

18 + 9

27

15 5 + ( 8 - 3 ) 2

5 + ( 5 ) 2

5 + 25

30

16 9 + 18 divide 3 + 10

9 + 6 + 10

15 + 10

25

17 60 - ( 3 - 1 ) 4 times 3

60 - ( 2 ) 4 times 3

60 - 16 times 3

60 - 48

12

18 10 - 16 divide 4 times 2 + 6

10 - 4 times 2 + 6

10 - 8 + 6

2 + 6

8

LESSON 31

Your Turn

0 _

571428

4 7 ⟌ _


_ -35

50

_ -49

10

_ -7

30

_ -28

20

_ -14

60

_ -56




-0 _

571428 or -0571428571428hellip


0 _ 3

5 3 ⟌ _


_ -3




0333hellip

045

6 20 ⟌ _

900

_ -8 0

1 00

_ -1 00

0

-045

7 -2 3 __ 4 = -thinsp 4 times 2 + 3

_________ 4 = -11 ____

4

275

4 ⟌ _

1100

_ -8

30

_ -28

20

_ -20

0

-275 terminating

8 7 1 __ 3 =

3 times 7 + 1 _________

3 = 22 ___

3

7 _ 3

3 ⟌ _


_ -21





Guided Practice

06

1 5 ⟌ _

30

_ -3 0

0

06 terminating

089

2 100 ⟌ _

8900

_ -80 0

9 00

_ -9 00

0

-089 terminating


4 ___ 12

= 4 times 1 _____ 4 times 3

= 1 __ 3

0 _ 3

3 ⟌ _


_ -3





0 _

25

4 99 ⟌ _


_ -19 8

520

_ -495




25 or


0 _ 7

5 9 ⟌ _


_ -63





036

6 25 ⟌ _

900

_ -7 5

1 50

_ -1 50

0

-036 terminating

004

7 25 ⟌ _

100

_ -1 00

0

004 terminating

01420 _

45

8 176 ⟌ _

250000000

_ -17 6

7 40

_ -7 04

360

_ -352

80

_ -0


_ -704

960

_ -880




-01420 _


0012

9 1000 ⟌ _

12000

_ -10 00

2 000

_ -2 000

0

0012 terminating


10 -11 1 __ 6 = -thinsp 6 times 11 + 1

_________ 6 = -67 ____

6

111 _ 6

6 ⟌ _

67000

_ -6

07

_ -6

1 0

_ -6


_ -36




- 67 ___ 6

-111 _ 6 or -111666hellip

11 2 9 ___ 10

= 10 times 2 + 9

__________ 10

= 29 ___ 10

29

10 ⟌ _

290

_ -20

9 0

_ -9 0

0

29 ___ 10

29

12 -8 23 ____ 100

= - 100 times 8 + 23

____________ 100

= -823 _____ 100

823

100 ⟌ _

82300

_ -800

23 0

_ -20 0

3 00

_ -3 00

0

-823 _____ 100

-823

13 7 3 ___ 15

= 15 times 7 + 3

__________ 15

= 108 ____ 15

72

15 ⟌ _

1080

_ -105

3 0

_ -3 0

0

108 ____ 15

72

14 54 3 ___ 11

= 11 times 54 + 3

__________ 11

= 597 ____ 11

54 _

27

11 ⟌ _

597000

_ -55

47

_ -44


_ -22

80

_ -77




597 ____ 11

54 _

27 or 542727hellip

15 -3 1 ___ 18

= -thinsp 18 times 3 + 1 __________

18 = -55 ____

18

30 _ 5

18 ⟌ _

55000

_ -54

1 0

_ -0


_ -90




-55 ____ 18

-30 _ 5 or -30555hellip

16 3 2 __ 3 =

3 times 3 + 2 _________

3 = 11 ___

3

3 _ 6

3 ⟌ _

1100

_ -9


_ -1 8





17 -2 7 __ 8 = -

8 times 2 + 7 _________

8 = -23 ____

8

2875

8 ⟌ _

23000

_ -16

7 0

_ -6 4

60

_ -56

40

_ -40

0

-2875 lb




3 ___ 47








= 5 ___ 11

0 _

45

11 ⟌ _


_ -4 4

60

_ -55




5 ___ 11

0 _


20 hockey players


= 6 ___ 10

06

10 ⟌ _

60

_ -6 0

0

6 ___ 10

06 terminating

21 polo players


= 4 ___ 11

036

11 ⟌ _


_ -3 3

70

_ -66




4 ___ 11

0 _


22 lacrosse players


= 10 ___ 15

= 5 times 2 _____ 5 times 3

= 2 __ 3

0 _ 6

3 ⟌ _


_ -1 8




10 ___ 15


23 football players


= 11 ___ 11

= 1

11 ___ 11

1 terminating







25 a -4 7 __ 8 = -thinsp 8 times 4 + 7

_________ 8 = - 39 ___

8

b 4875

8 ⟌ _

39000

_ -32

7 0

_ -6 4

60

_ -56

40

_ -40

0

-4875








is equal

to 85 ___ 16


is

equal to 127 ____ 24

or 52916hellip ft




















090625











0121212hellip


LESSON 32

Your Turn

2

50 1 2 3 4

3 + 1 1 __ 2 = 4 1 __

2

3

0-7 -6 -5 -4 -3 -2 -1

-25 + ( -45 ) = -7

6

0 1 2-5-6-7-8 -4 -3-2-1

-8 + 5 = -3

7

10-1

1 __ 2 + ( - 3 __

4 ) = - 1 __

4

8

3 4 5 6 7 80 1 2-3-2-1

-1 + 7 = 6

9

3 4 50 1 2-5-4 -3-2-1

2 1 __ 2 + ( -2 1 __

2 ) = 0

10

3 4 50 1 2-5-4 -3-2-1

-45 + 45 = 0

11

1-1 0

3 __ 4 + ( - 3 __

4 ) = 0


12 -15 + 35 + 2

-15 + 55

55 - 15

4

13 3 1 __ 4 + ( -2 ) + ( -2 1 __

4 )

3 1 __ 4 + ( -4 1 __

4 )

3 1 __ 4 - 4 1 __

4

-1

14 -275 + ( 325 ) + 5

-6 + 5

-1

15 15 + 8 + ( -3 )

23 + 3

20

Guided Practice

1

3 4 50 1 2-5-4 -3-2-1

-3 + ( -15 ) = -45

2

0 54321-5-4-3-2-1

15 + 35 = 5

3

0 105-1 -05

1 __ 4 + 1 __

2 = 3 __

4

4

0 54321-5-4-3-2-1

-1 1 __ 2 + ( -1 1 __

2 ) = -3

5

0 54321-5-4-3-2-1

3 + ( -5 ) = -2

6

0 54321-5-4-3-2-1

-15 + 4 = 25

7 -2150 + 2150 = 0 $0

8 -874 + 874 = 0 $0

9 275 + ( -2 ) + ( -525 )

275 + ( -725 )

- ( 725 - 275 )

-45

10 -3 + 1 1 __ 2 + 2 1 __

2 = -3 + 4 = 1

11 124 + 92 + 1

-124 + 102

- ( 124 - 102 )

-22

12 -12 + 8 +13

-12 + 21

21 - 12

9

13 45 + ( -12 ) + ( -45 )

45 + ( -45 ) + ( -12 )

0 + ( -12 )

-12

14 1 __ 4 + ( - 3 __

4 ) = - ( 3 __

4 - 1 __

4 ) = - 2 __

4 = - 1 __

2


15 -4 1 __ 2 + 2 = - ( 4 1 __

2 - 2 ) = -2 1 __

2

16 -8 + ( -1 1 __ 8 ) = -9 1 __

8


The sum is 2



19 -$225 + $1500 = $1500 - $225 = $1275

20 -3525 m + ( -85 ) = -4375 m

21 4 3 __ 4 mi + ( -3 1 __

4 mi ) = 1 2 __

4 mi = 1 1 __

2 mi


23 30 + 15 - 25 = 45 - 25 = 20 pts

24 January

Income - Expenses

$1205 - $129060

- ( $129060 - $1205 ) -$8560

February

Income - Expenses

$1183 - $134544

-($134544 - $1183)

-$16244


February

25 June

Income - Expenses

$2413 - $210623

$30677

July

Income - Expenses

$2260 - $195850

$30150

August

Income - Expenses

$2183 - $184512

$33788


$33788 in August






the end of August

Income = $1205 + $1183 + $1664 + $2413

$2260 + $2183 = $10908

Expenses = $129060 + $134544 + $1664 +$210623 + $195850 + $184512

= $1020989

Profit = $10908 - $1020989 + $250

= $94811


28 a 7 ( 10 ) + 3 ( -15 ) = 70 - 45 = 25 pts

b 2 ( 10 ) + 8 ( -15 ) = 20 - 120 = -100 pts








the positive number







LESSON 33

Your Turn

1

-9 -8 -7 -6 -5 -4

-65 - 2 = -85

2

42 30-1 1

1 1 __ 2 - 2 = - 1 __

2

3

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0

-225 - 55 = -775

6

1 2-1 0

025 - ( -150 ) = 175

7

1-1 0

- 1 __ 2 - ( - 3 __

4 ) = 1 __

4

Guided Practice

1

1312111098765 14 15

5 - ( -8 ) = 13

2

-9 -8 -7 -6 -5 -4 -3

3 1 __ 2 - 4 1 __

2 = -8


3

-15 -13 -11 -9 -5-7

-7 - 4 = -11

4

-6 -5 -4 -3 -2 -1 0 1

-05 - 35 = -4

5 -14 - 22 = -36

6 -125 - ( -48 )

-125 + 48

- ( 125 - 48 )

-77

7 1 __ 3 - ( - 2 __

3 ) = 1 __

3 + 2 __

3 = 1

8 65 - ( -14 ) = 65 + 14 = 79

9 - 2 __ 9

- ( -3 )

- 2 __ 9

+ 3

3 - 2 __ 9

2 9 __ 9 - 2 __

9

2 7 __ 9

10 24 3 __ 8

- ( -54 1 __ 8 )

24 3 __ 8

+ 54 1 __ 8

78 4 __ 8

78 1 __ 2

11 -1 m + ( 105 m ) = -15 m


12 -12 1 __ 2 + ( -5 ) = -17 1 __

2

17 1 __ 2

or 175 yards


533 ft - ( -10 ft ) = 533 ft + 10 ft = 543 ft

14 -4500 + (-3015) = -7515 $7515






16 -126degC - 75degC = -201degC

17 -2565 ft - 165 ft + 1245 ft = -297 ft


18 -9500 ft - ( -26000 ft ) = 16500 ft

19 29035 ft - ( -36198 ft ) = 65233 ft

70000 ft - ( -26000 ft ) = 96000 ft


96000 ft - ( 65233 ft ) = 30767 ft


b 78degF - 32degF


21 a -$1258 + ( -$3072 ) = -$4330

b -$4330 + ( -$25 ) = -$6830

c $6830 since -$6830 + $6830 = 0



23 a 5 ft - 72 ft + 22 ft

b 5 ft - 72 ft + 22 ft

5 ft + 22 ft - 72 ft

72 ft - 72 ft



24 a Yes

$425 + $089 + $1099

= $1613 lt $20

b $20 - $1613 = $387 left over





- 7 ___ 16

- 1 __ 4 - 5 ___

16 = ( - 7 ___

16 ) + ( - 1 __

4 ) + ( - 5 ___

16 )

( - 7 ___ 16

) + ( - 5 ___ 16

) + ( - 1 __ 4 ) by CPA

( -7 + ( -5 ) __________

16 ) + ( - 1 __

4 )

( -12 ____ 16

) + ( - 1 __ 4 )

( - 4 times 3 _____ 4 times 4

) + ( - 1 __ 4 )

( - 3 __ 4 ) + ( - 1 __

4 )

( -3 + ( -1 ) __________

4 )

( -4 ___ 4 ) = -1





and c __ d

Both fractions









LESSON 34

Your Turn

1

-8 -7 -6 -5 -2 -1 0-4 -3

2 ( -35 ) = -7

2

-2 -1 0 1 2 3 4-4 -3

-3 ( -125 ) = 375

4 ( - 3 __ 4 ) ( - 4 __

7 ) ( - 2 __

3 ) = -



= - 2 __ 7

5 ( - 2 __ 3 ) ( - 3 __

4 ) ( 4 __


__________ 13 times 41 times 5


= 2 __ 5

6 ( 2 __ 3 ) ( - 9 ___

10 ) ( 5 __

6 ) = -


____________ 13 times 210 times 63


= - 1 __ 2

Guided Practice

1

-5 -2 -1 0-4 -3

5 ( - 2 __ 3 ) = 5 __

1 times ( - 2 __

3 )

= - 5 times 2 _____ 1 times 3

= - 10 ___ 3

= -3 1 __ 3

2

-1 -05 0-2 -15

3 ( - 1 __ 4 ) = 3 __

1 times - 1 __

4

= - 3 times 1 _____ 1 times 4

= - 3 __ 4

3

0 1 2-2 -1

-3 ( - 4 __ 7 ) = 3 __

1 times 4 __

7

= 3 times 4 _____ 1 times 7

= 12 ___ 7

= 1 5 __ 7

4

-2 -1 0 1 2 3 4-4 -3

- 3 __ 4 ( -4 ) = 3 __

4 times 4 __

1

= 3 times 41

______ 14 times 1

= 3 times 1 _____ 1 times 1

= 3 __ 1

= 3

5 4 ( -3 ) = -12

6 -18 ( 5 ) = -9

7 -2 ( -34 ) = 68

8 054 ( 8 ) = 432

9 -5 ( -12 ) = 6

10 -24 ( 3 ) = -72

11 1 __ 2 times 2 __

3 times 3 __

4 = ( 1 times 21

______ 12 times 3

) ( 3 __ 4 )

= ( 1 __ 3 ) ( 3 __

4 )

= 1

1 __ 3 times 3 __

4 1

= 1 __ 4

12 - 4 __ 7 ( -thinsp 3 __

5 ) ( - 7 __

3 ) = ( - 4 times 3 _____

7 times 5 ) ( - 7 __

3 )

= 12 ___ 35

( - 7 __ 3 )

= - 4

5 12 times 7 ______ 35 times 3

1

1

= - 4 times 1 _____ 5 times 1

= - 4 __ 5

13 ( - 1 __ 8 ) times 5 times 2 __

3 = ( - 1 __

8 ) times 5 __

1 times 2 __

3


__________ 48 times 1 times 3


= - 5 ___ 12


14 ( - 2 __ 3

) ( 1 __ 2 ) ( - 6 __


__________ 13 times 21 times 7


= 2 __ 7


16 18 ( -100 ) = -1800 or a $1800 change









amount

b 200 + 6 ( -1998 )

= 200 - 11988

= 8012 $8012





which is 6

20 8 ( -3 1 __ 4 ) = -8 ( 13 ___

4 )

= - 1

8 __ 1 times 13 ___

4 1

= - 2 times 13 ______ 1 times 1

= - 26 ___ 1





(below the surface)

22 5 + ( -3 ) ( 15 )

= 5 + ( -45 )

= 05 cups left





a positive



25 Total score is

2 times ( 6 ) + 16 times ( 05 )

+ 7 times ( -05 ) + 2 times ( -15 )

= 12 + 8 - 35 - 3

= 20 - 65

= 135 pts




= 12 + 5 ( -68 )

= 12 + ( -34 )

= -22degC

27 a b c d

+ + + +

+ + - +

+ - + +

- + + +

- - - +

- - + -

- + - -

+ - - -









LESSON 35

Your Turn

3 28 ___ -4

= - 28 ___ 4 = -07

4 -664 ______ -04

= 664 ____ 04

= 166

5 - 55 ___ 05

= - 55 ___ 5 = -11

6 -4256 _______ 112

= -38


per minute

7 - 5 __

8 ___

- 6 __ 7 = - 5 __

8 divide - 6 __

7

= - 5 __ 8 times - 7 __

6

= 35 ___ 48

8 - 5 ___

12 ____

2 __ 3 = - 5 ___

12 divide 2 __

3

= - 5 ___ 12

times 3 __ 2

= - 15 ___ 24

= - 5 __ 8


9 -4__5

___1__2 =-4__5divide1__

2

=-4__5times2__1

=-8__5

=-13__5

Guided Practice

1 072_____-09=-72___

9 =-08

2 -1__5

___7__5 =-1__

15times5

1__

7=-1times1_____

1times7=-1__7

3 56___-7=-56___7=-8

4 251____4 divide(-3__

8)=251____

4 times-8__

3

=-251times82________

14times3


=-502____3

5 75____-1__5

=-75___1times5__

1=-75times5______

1times1=-375

6 -91____-13=91___

13=7

7 -3__7

___9__4 =-

13__7times4__93


=-4___21

8 - 12____003

=-1200_____

3 =-400


changeindays

=-35L______4day

=-0875 L____day

or-0875Lperday


changeindays

=-$4575________5day



numberofminutes

=-044mi________08min

=-44mi______8min

=-055mileperminute



13 5___-2__

8=-5__

1times8__

24

1=-5times4_____

1times1=-20

14 51__3divide(-11__

2)


2

=-16___3divide3__

2

=-16___3times2__

3


=-32___9

15 -120_____-6 =120____

6 =20

16 -4__5

___-2__

3=

24__5times3__

21=2times3_____

5times1=6__

5

17 103divide(-103)=-103____1 times 1____

103

=-103times1________1times103

=-103____103

=-103____103

=-01

18 -04_____80

=-04___80

=-0005

19 1divide9__5=1__

1times5__

9=5__

9

20 -1___4 ___

23___24

=-1__

14times246

___23


=-6___23

21 -1035_______-23 =1035_____

23 =45


= 21h______7days

=3 h____day


times3days=9hours




=-4times15+3___________4 times1__

9

yd___run

=-763___4 times1__

91yd

___run

=-153__

4yd______

9runs

=-153__4times1__

9

yd___run

=-7__4or-13__

4yardsperrun





_____________________________________ 4

= 414degC ______ 4

= -1035degC per day

25 a total profit


= $1750

______ 7 days

= $250 per day

b $150

_____ day


c total change


= - $490

______ 7 days

= -$70 per day


= 996 m ______ 12 s

= 83 ms





- 3 __

4 ___

4 __ 3

= - 3 __

4 times 3 __

4 = - 9 ___

16



= -629 m





-85degF divide 15 d

= - 1785 ____ 315

degF __ d

= - 17 ___ 3 degF __

d or -5 2 __

3 degF __


d


every day





definition

LESSON 36

Your Turn


3 times 2 1 __ 2 = 7 1 __

2


30 - 7 1 __ 2 = 22 1 __

2


22 1 __ 2 divide 4 = 5 5 __

8











12 3 __ 5 = 126

= 0126


750 times 0126 = 945

750 + 945 = 8445


8445 times 0126 asymp 10641

8445 + 10641 = 95091


95091 times 0126 asymp 11981

95091 + 11981 = 107072


Guided Practice











78 times 3 = 234


234 divide 4 = 585




12 - 3 1 __ 2 = 8 1 __

2

Find half the width

8 1 __ 2 divide 2 = 4 1 __

4


of the page


11 times 1 __ 3 = 3 2 __

3

10 times 3 __ 4 = 7 1 __

2

3 2 __ 3 + 7 1 __

2 = 11 1 __

6


box

11 1 __ 6 lt 12





41 3 __ 4 divide 2 = 20 7 __

8


50 - 20 7 __ 8 = 29 1 __

8




( 78 + 10 ) = 88


88 = 88 ____ 100

= 44 ___ 50


Donovan

44 - 39 = 5


Donovan







19 ___ 37


15 times ( - 1 __ 2 ) = -075







-79 9 ___ 10

divide ( -188 ) = 425


19 1 __ 8 - 1275 - 425 = 2 1 __

8


-28 9 ___ 10

- ( -79 9 ___ 10

) = 51


51 divide 2 1 __ 8 = 24


ascent was 24 ftmin

15 Sample answer



the result by 037



(276 + 159)037 = (276)(037) + (159)(037)




make errors








MODULE 3

Ready to Go On

1 4 1 __ 5 =

5 times 4 + 1 _________

5 = 21 ___

5

42

5 ⟌ _

210

_ -20

1 0

_ -1 0

0

42


2 12 14 ___ 15

= 15 times 12 + 14

___________ 15

= 194 ____ 15

129 _ 3

15 ⟌ _

194000

_ -15

44

_ -30

14 0

_ -13 5

50 first 50

_ -45

50 second 50



129 _ 3 or 12933

3 5 5 ___ 32

= 32 times 5 + 5

__________ 32

= 165 ____ 32

515625

32 ⟌ _

16500000

_ -160

5 0

_ -3 2

1 80

_ -1 60

200

_ -192

80

_ -64

160

_ -160

0

515625

4 45 + 71 = 116

5 5 1 __ 6 + ( -3 5 __

6 ) = 4

6+1 ____

6 -3 5 __

6

= 1 2 __ 6

= 1 1 __ 3

6 - 1 __ 8 -6 7 __

8 = - 1 __

8 + ( -6 7 __

8 )

= -6 8 __ 8

= -7

7 142 - ( -49 ) = 142 + 49

= 191

8 -4 ( 7 ___ 10

) = - 4 __ 1 times 7 ___

10

= - 24 times 7 _______ 1 times 105

= - 2 times 7 _____ 1 times 5

= - 14 ___ 5 or -2 4 __

5

9 -32 ( -56 ) ( 4 ) = 32 times 56 times 4

= 7168

10 - 19 ___ 2 divide 38 ___

7 = -

119 times 7 _______ 2 times 382

= - 1 times 7 _____ 2 times 2

= - 7 __ 4

11 -3201 _______ -33

= 3201 _____ 33

97

33 ⟌ _

3201

_ -297

23 1

_ -23 1

0

97


second day

$8360 + $1535 = $9895


-4 3 __ 4 = -475 or -00475




price

$9895 times -00475 asymp -$47

$9895 - $47 = $9425






prices



Are You Ready

1 3 __ 4 divide 4 __

5 = 3 __

4 times 5 __

4

= 15 ___ 16

2 5 __ 9 divide 10 ___

11 = 5 __

9 times 11 ___

10

= 1

5 __ 9 times 11 ___

10 2

= 11 ___ 18

3 3 __ 8 divide 1 __

2 = 3 __

8 times 2 __

1

= 4

3 __ 8 times 2 __

1 1

= 3 __ 4

4 16 ___ 21

divide 8 __ 9 = 16 ___

21 times 9 __

8

=thinsp 2

7 16 ___ 21

times 9 __ 8 3

1

= 6 __ 7

5 B ( -4 1 )

6 C ( 3 0 )

7 D ( 5 4 )

8 E ( -2 -2 )

9 F ( 0 0 )

10 G ( 0 -4 )

LESSON 41

Your Turn

3 1 __ 6 acre divide ( 1 __

4 hour ) = 1 __

6 times 4 __

1

= 3


2

= 1 times 2 _____ 3 times 1


4 3 cups divide ( 3 __ 4 cups ) = 3 __

1 divide 3 __

4

= 3 __ 1 times 4 __

3

= 1


1

= 1 times 4 _____ 1 times 1

= 4 cups


5 = 3 __

4 times 5 __

1 = 15 ___

4 = 3 3 __

4


6 = 2 ___

1 3 times 6

2 __

1 = 4 __

1 = 4






flavor

Guided Practice

1

Distance (mi) 8 1 __ 2 17 25 1 __

2 34 42 1 __

2

Time (h) 1 __ 2 1 1 1 __

2 2 2 1 __

2

2 3 1 __ 2 miles divide ( 1 1 __

4 hours ) = 7 __

2 divide 5 __

4 mi ___ h

= 7 times 4 _____ 2 times 5

= 1 7 times 4 _____ 2 times 5

2

= 7 times 2 _____ 1 times 5

= 14 ___ 5 mi ___

h


3 5 __ 8 page divide ( 2 __

3 minute ) = 5 __

8 times 3 __

2

= 15 ___ 16

page per minute

4 1 __ 6 foot divide ( 1 __

3 hour ) = 1 __

6 times 3 __

1

= 2 1 times 3 _____ 6 times 1

1

= 1 times 1 _____ 2 times 1


5 5 __ 8 sq ft divide ( 1 __

4 hour ) = 5 __

8 times 4 __

1

= 2 5 times 4 _____ 8 times 1

1

= 5 times 1 _____ 2 times 1

= 5 __ 2 or 2 1 __



UNIT

2



1 divide 1 __

3

= 240 ____ 1 times 3 __

1

= 720 ____ 1



1 divide 1 __

2

= 325 ____ 1 times 2 __

1

= 650 ____ 1




1 __ 4 cup divide ( 2 __

3 serving ) = 1 __

4 times 3 __

2

= 3 __ 8

cup _______

serving


1 __ 3 cup divide ( 3 __

4 serving ) = 1 __

3 times 4 __

3

= 4 __ 9

cup _______

serving




72 and 4 __

9 = 32 ___

72




the rate


1 __ 2 hour

= 1 __




$10 divide ( 35 hours ) = 10 ___ 35

$ __



$125 divide ( 1 __ 2 hours ) = 125 ____

05 $ __





multiply by 60


= 005 ____ 1

$ ____


1 h

= $3 per hour



one


8 cup






originally

c 1 __ 2 divide 1 __

8 = 1 ___

1 2 times 8

4 __

1 = 4 __

1 = 4


sunflower seeds

11 10 songs


= 5 songs ____________

1 commercials


6 mi divide ( 1 __ 2 h ) = 6 __

1 times 2 __

1

= 12 miles per hour

Jessersquos rate


4

= 2 __ 1 times 4 __

1 mi ___ h

= 8 miles per hour

b Terrance

50 mi divide ( 12 mi ___ h ) = 50 ___

1 times 1 ___

12

= 50 ___ 12

h

= 4 1 __ 6 h

= 4 10 ___ 60

h


Jesse

50 mi divide ( 8 mi ___ h ) = 50 ___

1 times 1 __

8

= 50 ___ 8 h

= 6 1 __ 4 h

= 6 15 ___ 60

h



4

= 8 __ 1 times 4 __

3

= 32 ___ 3





13 1 ___ 10

h = 6 ___ 60

h = 6 min

300 words _________ 6 min

= 50 words per min

1 ___ 12

h = 5 ___ 60

h = 5 min

300 words _________ 5 min

= 60 words per min










b For the 10-pack



For the 12-pack








2 day ) = 1 room _____

day so at the same





LESSON 42

Your Turn


was not constant




= 12 ___ 1 = 36 ___

3 = 60 ___




s or s = 12a

Guided Practice

1 45 ___ 1 = 45 90 ___

2 = 45 135 ____

3 = 45 180 ____

4 = 45


2 k = y __ x = 10 ___

2 = 5 y = 5x

3 k = y __ x = 2 __

8 = 1 __

4 y = 1 __

4 x


of proportionality


5 k = y __ x = 74 ___

4 = 1850 y = 1850x

6 $1099

_______ 05 days

= $2198 per day


($1850)

8 100 ft _____ 08 s

= 1000 _____ 8 ft __ s = 125 ft __ s

500 ft _____ 31 s

= 5000 _____ 31


1875 ft ______ 15 s

= 1875 ______ 15





9 $3125

______ 5 h


______ 8 h

= $625 per







12 y = $625 ( 3 ) = $1875

13 300 ft _____ 2 min

= 6750

_____ 45


150 ft _____ min

times 60 min ______ 1 h


14 y = 150x



hours




same factor




of corn

LESSON 43

Your Turn

1 No because 11 ___ 1 ne 16 ___





b k = 60 mi _____ 4 h

= 15 mi ___ h


distance in miles

Guided Practice

1

Time (h) 3 5 9 10

Pages 195 325 585 650


per hour

2

Time (h) 2 3 5 8

Earnings 15 2250 3750 60








5 k = 28 ft ____ 8 s

= 7 __ 2 ft __ s = 35 ft __ s y = 7 __



6 k = $2 ______

8 items = 1 __

4

$ _____

items = 025

$ _____

items so y = 1 __

4 x or


y = cost in dollars


origin



0 minutes





x or 2 __ 5 x




5 = 48




2

2

4

6

8

10

4 6 8 10Time (min)

Dis

tanc

e (m

i)

A

B

O








equation

15 a

2

8

16

24

32

40

4 6 8 10DVDs

Cost

($)

O



cost $20






18 k = 8 ft ___ 4 s










because 65 ___ 1 ne 85 ___

2





distance column

MODULE 4

Ready to Go On

1 $140

_____ 18 ft 2


2 $299

_____ 14 lb


3 $56 ______


$3205

______ 15 gal


4 $160

_____ 5 g


$315

_____ 9 g




3


6 k = $9

___ 8euro

= $27 ____

24euro = 9 __

8 $ __

euro or 1125

$ __

euro So y = 9 __

8 x or





_______ pt

or k = 25 servings

_______ pt

Therefore

y = 5 __ 2




2

2

4

6

8

10

4 6 8 10Pints

Serv

ings

Frozen Yogurt

O





constant rate



Are You Ready

1 22 = 22 ____ 100

= 022

2 75 = 75 ____ 100

= 075

3 6 = 6 ____ 100

= 006

4 189 = 100 + 89

= 100 ____ 100

+ 89 ____ 100

= 1 + 089

= 189

5 059 = 59

6 098 = 98

7 002 = 2

8 133 = 133

9 64

_ timesthinsp05

320

32

10 30

_ timesthinsp007

210

21

11 160

_ timesthinsp015

800

_ +1600

2400

24

12 62

_ timesthinsp032

124

_ +thinsp1860

1984

1984

13 4

_ timesthinsp12

8

_ +thinsp40

48

48

14 1000

_ timesthinsp006

6000

60

LESSON 51

Your Turn

2 x = ( $64 - 52 )

__________ $52

x = $12

____ $52

asymp 23

4 x = ( 18 - 12 )

________ 18

x = 6 ___ 18

asymp 33

5 x = ( 16 - 10 )

________ 16

x = 6 ___ 16

= 375

8 010 times $499 = $4990

$499 + $4990 = $54890

9 030 times $499 = $14970

$499 - $14970 = $34930

Guided Practice

1 x = ( $8 - $5 )

_________ $5

x = $3

___ $5

= 60

2 x = ( 30 - 20 )

_________ 20

x = 10 ___ 20

= 50

3 x = ( 150 - 86 )

__________ 86

x = 64 ___ 86

asymp 74

4 x = ( $389 - $349 )

______________ $349

x = $040

_____ $349

asymp 11

5 x = ( 14 - 13 )

________ 13

x = 1 ___ 13

asymp 8

6 x = ( 16 - 5 )

________ 5

x = 11 ___ 5 = 220

7 x = ( 64 - 36 )

_________ 36

x = 28 ___ 36

asymp 78

8 x = ( 80 - 64 )

_________ 80

x = 16 ___ 80

= 20

9 x = ( 95 - 68 )

_________ 95

x = 27 ___ 95

asymp 28


10 x=( 90-45)_________

90

x=45___90

=50

11 x=( 145-132)__________

145

x=13____145

asymp9

12 x=( 64-21)_________

64

x=43___64

asymp67

13 x=( 16-0)________

16

x=16___16

=100

14 x=( 3-1__

2)_______

3

x=21__

2___

3 asymp83

15 010times$900=$090 $900+$090=$990

16 025times48=12 48-12=36cookies

17 020times340=68 $340-68=272pages

18 050times28=14 28+14=42members

19 004times$29000=$1160 $29000-$1160=$27840

20 130times810=1053 810+1053=1863songs

21 030times20=6 20+6=26miles



ItemOriginal

PriceNew Price

Percent Change

Increase or





24 a 55

x=( 8-3)_______

8 =5__

8=625

x=( 12-7)________

12 =5___

12asymp417



x=( 12-3)________

3

x=9__3=300increase



b $100_____5 =$020each$100_____

4 =$025each



=25

26 Percenterror=( 136-133)___________

136 times100

=03____136

times100asymp2







LESSON 52

Your Turn

2 a 1c+01c11c

b s=11times$28=$3080

3 a 200

b 1c+2c3c

5 a

1b - 024b

1b024b

b 1b-024b=076b

6 a 1p-005p095p

b 095p=$1425




Guided Practice

1 a 035s

b 1s + 035s 135s

c 135 times $3200 = $4320

d 035 times $3200 = $1120


Price

2 Hat $18 15 $270 $2070

3 Book $2250 42 $945 $3195

4 Shirt $3375 75 $2531 $5906

5 Shoes $7499 33 $2475 $9974

6 Clock $4860 100 $4860 $9720

7 Painting $18500 125 $23125 $41625

8 $4500 - 022 ( $4500 ) = $3510

9 $8900 - 033 ( $8900 ) = $5963

10 $2399 - 044 ( $2399 ) = $1343

11 $27999 - 075 ( $27999 ) = $7000





13 a 046b

b 1b - 046b 054b

c 054 times $2900 = $1566

d 046 times $2900 = $1334


Sale Price $201

Regular Price $419

Sale Price $245

Regular Price $279

Sale Price $115

Regular Price $309

Sale Price $272

Regular Price $377

Sale Price $224


$050


$9950


$350

16 p = 127 ( $7400 ) = $9398

s = 127 ( $4800 ) = $6096

j = 127 ( $32500 ) = $41275

2 ( 9398 ) + 3 ( $6096 ) + $41275 = $78359









greater




the coat

LESSON 53

Your Turn

1 005 times $2000 = $100 $100 + $2000 = $2100

3 005 times $40000 = $2000

$2000 times 4 years = $8000

$40000 + $8000 = $48000


Total $2200 + $16875 = $236875

Guided Practice

1 005 times $3000 = $150

2 015 times $7000 = $1050

3 0004 times $10000 = $040

4 15 times $2200 = $3300

5 001 times $8000 = $080

6 20 times $500 = $1000

7 a 007 times $4399 = $308

b $4399 + $308 = $4707

8 115 times $7550 = $8683

9 007 times $2000 = $140


10 003 times $550 = $1650

$1650 times 10 years = $165

$550 + $165 = $715

11 a 090 times $20 = $18

b 1085 times $18 = $1953

12 020 times $2999 = $600 tip

00625 times $2999 = $187 tax

$2999 + $600 + $187 = $3786 total



to the price


14 $3275 + $3988 = $7263 total meal cost

014 times $7263 = $1017 tip

$7263 + $1017 = $8280 total with tip


$7865 times 020 = $1573 tip

$7865 + $1573 - $1180 = $8258 total


0075 times $29375 = $2203 tax

$29375 + $2203 = $31578 total with tax


17 $7999 times 012 = $960 discount

$7999 - $960 = $7039 price before tax





19 $4500 + 00725 = $32625 commission

$750 + $32625 = $107625 total income


$475 + $3850 = $51350 total income










nearest inch

22 a $4998 times 05 = $2499 50 discount

$2499 - $1000 = $1499 $10 discount

b $4998 - $1000 = $3998 $10 discount

$3998 times 05 = $1999 50 discount


$8550 + $1599 = $10149 total


$95 + $1439 = $10939 total



d $10149 times 008 = $812 tax

$10149 + $812 = $10961 total

24 a Store 1 $22 divide 2 = $11

Store 2 $1299 times 09 = $1169




b Store 3 $2098 times 045 = $944






to $2050 per month


____________ 137

times 100 = 05 ____ 137

asymp 36

MODULE 5

Ready to Go On

1 x = ( 63 - 36 )

_________ 36

x = 27 ___ 36

= 75 increase

2 x = ( 50 - 35 )

_________ 50

x = 15 ___ 50

= 30 decrease

3 x = ( 72 - 40 )

_________ 40

x = 32 ___ 40

= 80 increase

4 x = ( 92 - 69 )

_________ 92

x = 23 ___ 92

= 25 decrease

5 $60 times 015 = $9

$60 + $9 = $69

6 $32 times 0125 = $4

$32 + $4 = $36

7 $50 times 022 = $11

$50 - $11 = $39

8 $125 times 030 = $3750

$12500 - $3750 = $8750


$325 + $312 = $637 total income

10 $5310

______ $1735

asymp 31



$700 times 020 = $140

$700 + $140 = $840


5 less than Priya

$840 times 005 = $042

$840 - $042 = $798





$45 times 026 = $1170

$45 + $1170 = $5670






Are You Ready

1 5 + x

2 11 - n

3 -9 ___ y

4 2x - 13

5 2x + 3

= 2 ( 3 ) + 3

= 6 + 3

= 9

6 -4x + 7

= -4 ( 1 ) + 7

= -4 + 7

= 11

7 15x - 25

= 15 ( 3 ) - 25

= 45 - 25

= 2

8 04x + 61

= 04 ( -5 ) + 61

= -20 + 61

= 41

9 2 __ 3 x - 12

= 2 __ 3

( 18 ) - 12

= 2 __ 3

times ( 18 ___ 1 ) - 12

= 36 ___ 3 - 12

= 0

10 - 5 __ 8

x + 10

= - 5 __ 8 ( -8 ) + 10

= - 5 __ 8 times- 8 __

1 + 10

= - 5 ___ 1 8

times- 8 1 __

1 + 10

= - 5 __ 1 times- 1 __

1 + 10

= 5 + 10

= 15

11 1 __ 2 divide 1 __

4

= 1 times 4 _____ 2 times 1

= 1 times 4 2 ______

1 2 times 1

= 1 times 2 _____ 1 times 1

= 2

12 3 __ 8 divide 13 ___

16

= 3 __ 8 times 16 ___

13

= 3 times 16 2 _______

1 8 times 13

= 3 times 2 ______ 1 times 13

= 6 ___ 13

13 2 __ 5 divide 14 ___

15

= 2 __ 5 times 15 ___

14

= 1 2 times 15

3 ________

1 5 times 14 7

= 1 times 3 _____ 1 times 7

= 3 __ 7

14 4 __ 9 divide 16 ___

27

= 4 __ 9 times 27 ___

16

= 1 4 times 27

3 ________

1 9 times 16 4

= 1 times 3 _____ 1 times 4

= 3 __ 4

LESSON 61

Your Turn

2 ( 3x + 1 __ 2 ) + ( 7x - 4 1 __

2 )

= 3x + 7x + 1 __ 2 - 4 1 __

2

= 10x - 4

3 ( -025x - 3 ) - ( 15x + 14 ) = -025x - 3 - 15x - 14

= -175x - 44

4 02(3b - 15c) + 6c

= 06b - 3c + 6c

= 06b + 3c

5 2 __ 3 (6e + 9f - 21g) - 7f

= 4e + 6f - 14g - 7f

= 4e - f - 14g

6 5x - 3(x - 2) - x

= 5x - 3x + 6 - x

= x + 6

7 83 + 34y - 05(12y - 7)

= 83 + 34y - 6y + 35

= 118 - 26y


UNIT

3


Guided Practice


14 + 12n + 23 + 16n

14 + 23 + 12n + 16n

37 + 28n


37 + 28n

2 37 + 28n

37 + 28 ( 9 )

= 37 + 252

= 289

3 14 + 5(x + 3) - 7x = 14 + 5x + 15 - 7x

= 29 - 2x

4 3 ( t - 4 ) - 8 ( 2 - 3t ) = 3t - 12 - 16 + 24t

= 27t - 28

5 63c - 2 ( 15c + 41 ) = 63c - 3c - 82

= 33c - 82

6 9 + 1 __ 2 ( 7n - 26 ) - 8n = 9 + 35n - 13 - 8n

= -4 - 4 1 __ 2 n

7 2x + 12

2 ( x + 6 )

8 12x + 24

12 ( x + 2 )

9 7x + 35

7 ( x + 5 )







15 ( 100 + 5d ) + 20 ( 50 + 7d ) = 15 ( 100 ) + 15 ( 5d ) + 20 ( 50 ) + 20 ( 7d )

= 1500 + 75d + 1000 + 140d

= 1500 + 1000 + 75d + 140d

= 2500 + 215d


New width 60 + w


2(96 + l) + 2(60 + w)

=2(96) + 2l + 2(60) + 2w

192 + 2l + 120 + 2w

192 + 120 + 2l + 2w

312 + 2l + 2w

13 Width 3


Factors 3 and x + 2

Product 3 ( x + 2 ) = 3x + 6

14 Width 4



Product 4 ( 2x - 1 ) = 8x - 4




and 6 times 4 ) So 6 ( 9 ) = 6 ( 5 ) + 6 ( 4 )


6x = ( x + 3 ) + ( 2x + 4 ) +

6x = 3x + 7 +

-3x = _ -3x

3x = 7 +

_ -7 = _ -7

3x - 7 =



10x + 6 = 2 ( 3x - 3 ) + 2 ( )

10x + 6 = 6x - 6 + 2

_ -6x = _ -6x

4x + 6 = - 6 + 2

_ + 6 = _ + 6

4x + 12 = 2

( 4x + 12 ) divide 2 = ( 2 ) divide 2

2x + 6 =


18 a P = 2l + 2w


2(2x + 6) + 2(x)

= 4x + 12 + 2x

= 6x + 12


2(3x - 14) + 2( 1 __ 2 x + 32)

= 6x - 28 + x + 64

= 7x + 36

b (7x + 36) - (6x + 12)

= 7x + 36 - 6x - 12

= x + 24


Let x = 36

2x + 6 = 2 ( 36 ) + 6

= 72 + 6

= 78


Let x = 36

1 __ 2 x + 32 = 1 __

2 ( 36 ) + 32

= 18 + 32

= 50


Let x = 36

3x - 14 = 3 ( 36 ) - 14

= 108 - 14

= 94





( x ) ( x ) = x 2

( x ) 1 = x

( 1 ) 1 = 1


x

x

1

11

1 1

x2 x x x

x 1 1 1x 1 1 1

Area =

x 2 + x + x + x + x + x + 1 + 1 + 1 + 1 + 1 + 1

= x 2 + 5x + 6

( x + 3 ) ( x + 2 ) = x 2 + 5x + 6




1160 = 1334 So 58 ( 23 ) = 58 ( 3 ) + 58 ( 20 )


8 ( 1000 - 3 ) = 8000 - 24 = 7976


Property 8 ( 900 + 90 + 7 ) = 7200 + 720 + 56 =

7976

LESSON 62

Your Turn

1 49 + z = -9

_ -49 _ -49

z = -139

2 r - 171 = -48

_ +171 _ +171

r = 123

3 -3c = 36

-3c ____ -3

= 36 ___ -3

c = -12

5 x - 15 = 525

_ +15 _ +15

x = 675


6 x ___ 35

= -12

x ___ 35

( 35 ) = -12 ( 35 )

x = -42


7 25x = 75

25x ____ 25

= 75 ___ 25

x = 3


Guided Practice



x + ( -134 ) = -17 or x - 134 = -17

x - 134 = -17

_ +134 _ +134

x = 117


warmer



-1 1 __ 2 x = -9

( - 2 __ 3 ) ( - 3 __

2 x ) = ( - 2 __

3 ) ( -9 )

x = 18 ___ 3

x = 6


3 -2x = 34

-2x ____ -2

= 34 ___ -2

x = -17

4 y - 35 = -21

_ + 35 _ + 35

y = 14

y = 14

5 2 __ 3 z = -6

( 3 __ 2 ) 2z ___

3 = ( 3 __

2 ) ( -6 )

z = -9





x - 870737 = 203215

_ +870737 _ +870 737

x = 2902887



2825131 - x = 2320106

_ -2825131 _ -2825131

-x = - 505025

x = 505025




2825131 - x = 1119421

_ -2825131 _ -2825131

-x = -1705710

x = 1705710



1250 - 935 = 315

Use an equation


descends

( -22 1 __ 2 ) x = -315

( - 45 ___ 2 ) x = -315

( - 2 ___ 45

) ( - 45 ___ 2 ) x = -315 ( - 2 ___

45 )

x = 14



4106 - 3205 = 901




34x = 901

34x ____ 34

= 901 ____ 34

x = 265 = 26 1 __ 2




- 25 + x = -07

_ + 25 _ + 25

x = 18





181 - x = -07

_ - 181 _ -181

-x = -188

x = 188





125 + x = 181

_ -125 _ -125

x = 56



their next play

-26 1 __ 3

+ x = 10

+26 1 __ 3

______

+26 1 __ 3

______

x = 36 1 __ 3



( -2 1 __ 2 ) x = -156

( -25 ) x = -156

( -25 _____ -25

) x = -156 ______ -25

x = 624



rate and the time


x __ 5 = 455

( 5 ) x __ 5 = 455 ( 5 )

x = 2275


Sample answer


to $22750



below sea level



lower elevation

20 -4x = -48

( -4x ____ -4

) = -48 _____ -4

x = 12

- 1 __ 4 x = -48

( -4 ) ( - 1 __ 4 ) x = -48 ( -4 )

x = 192

192 ____ 12

= 16








$21085

LESSON 63

Your Turn


purchased






Equation 150 - 35x = 45





Guided Practice

1

+ + ++ ++

+++ + +

+++

2

----

+ ++ ++

- - -

























place 28 +1-tiles


bicycle





Equation 85d + 55 = 123






Equation 125r + 675 = 3175








Equation 45n + 60 = 285




means + 45





1 _ 2

bull n + 45 = 172

Equation 1 __ 2 n + 45 = 172





uniforms equipment


Equation 295u + 548 = 2023





weeks


Equation 500 - 20x = 220






Total bill $88


shirts bill















10 + 5c = 25

10 - 10 + 5c = 25 - 10

5c = 15

5c ___ 5 = 15 ___

5

c = 3

3 children



10 + 5 ( 5 ) = $35














bought

LESSON 64

Your Turn


+ ++ +

+ ++ ++ +

+ ++ ++ +

++


+ ++ +

+ ++ ++ +

+ ++ ++ +

++


++

+ ++ +

++


++ ++


+ + ++ + ++ +

+++

+++

__



+ + ++ + ++

++ +

+++

+++

__


+ + ++++ + +++


+ + +++


++++

______

______

____



++++

+

++

+

++

______

______

____


++++

____


++ __



____

________

++



________

________

++

____


________

________

We get -y = -1

____


tile to each side

++

__ ++ __


++++

__


+++

6 3n + 10 = 37


3n + 10 = 37

-10 ____

-10 ____

3n = 27

3n ___ 3 = 27 ___

3

n = 9


7 n __ 4 - 5 = 15


n __ 4 - 5 = 15

+5 ___

+5 ___

n __ 4 = 20

n __ 4 ( 4 ) = 20 ( 4 )

n = 80

The number is 80

8 -20 = 5 __ 9 ( x - 32 )


-20 = 5 __ 9 ( x - 32 )

-20 = 5 __ 9 x - 160 ____

9

+ 160 ____ 9

______

+ 160 ____ 9

______

- 20 ___ 9 = 5 __

9 x

- 20 ___ 9 divide ( 5 __

9 ) = 5 __

9 x divide ( 5 __

9 )

4 20 times 9

1 _______

9 1 times 5

1 = x

- 4 __ 1 = x

-4 = x


9 120 - 4x = 92


120 - 4x = 92

-120 _____

-120 _____

- 4x = -28

-4x ____ -4

= -28 ____ -4

x = 7



Guided Practice





++++

+ +++++++++


++++

++++++++


++ + + + +




Solve the equation

2 ( 18 ) + 2w = 58

36 + 2w = 58

36 - 36 + 2w = 58 - 36

2w = 22

2w ___ 2 = 22 ___

2

w = 11


4 1200 minus 25x = 500


1200 - 25x = 500

_ -1200 _ -1200

-25x = -700

-25x _____ -25

= -700 _____ -25

x = 28






equation


6 9s + 3 = 57

9s + 3 - 3 = 57 - 3

9s = 54

9s ___ 9 = 54 ___

9

s = 6

7 4d + 6 = 42

4d + 6 - 6 = 42 - 6

4d = 36

4d ___ 4 = 36 ___

4

d = 9

8 115 - 3y = -485

115 - 115 - 3y = -485 - 115

thinsp-3y = -60

-3y

____ -3

= -60 ____ -3

y = 20

9 k __ 2 + 9 = 30

k __ 2 + 9 - 9 = 30 - 9

k __ 2 = 21

2 sdot k __ 2 = 2 sdot 21

k = 42

10 g

__ 3 - 7 = 15

g

__ 3 - 7 + 7 = 15 + 7

g

__ 3 = 22

3 sdot g

__ 3 = 3 sdot 22

g = 66

11 z __ 5 + 3 = -35

z __ 5 + 3 - 3 = -35 - 3

z __ 5 = -38

5 sdot z __ 5 = 5 ( -38 )

z = -190

12 -9h - 15 = 93

-9h - 15 + 15 = 93 + 15

-9h = 108

-9h ____ -9 = 108 ____

-9

h = -12

13 - 1 __ 3 (n + 15) = -2

- 1 __ 3 n - 5 = -2

- 1 __ 3 n - 5 + 5 = -2 + 5

- 1 __ 3 n = 3

-3 sdot - 1 __ 3 n = -3 sdot 3

n = -9

14 -17 + b __ 8 = 13

-17 + 17 + b __ 8 = 13 + 17

b __ 8 = 30

8 sdot b __ 8 = 8 sdot 30

b = 240


15 7 ( c - 12 ) = -21

7c - 84 = -21

_ +84 _ +84

7c = 63

7c ___ 7 = 63 ___

7

c = 9

16 -35 + p

__ 7 = -52

-35 + 35 + p

__ 7 = -52 + 35

p

__ 7 = -17

7 sdot p

__ 7 = -17 sdot 7

p = -119

17 46 = -6t - 8

46 + 8 = -6t - 8 + 8

54 = -6t

54 ___ -6

= -6t ____ -6

t = -9





2 (a + $26) = $264

Solve the equation

2 ( a + 26 ) = 264

2 ( a + 26 )

_________ 2 = 264 ____

2

a + 26 = 132

a + 26 - 26 = 132 - 26

a = 106






Solve the equation

2t - 6 = 20

2t - 6 + 6 = 20 + 6

2t = 26

2t __ 2 = 26 ___

2

t = 13


20 -35 = 5 __ 9 ( x - 32 )

-35 = 5 __ 9 x - 160 ____

9

+ 160 ____ 9

______

+ 160 ____ 9

- 155 ____ 9 = 5 __

9 x

thinsp- 155 ____ 9 divide ( 5 __

9 ) = 5 __

9 x divide ( 5 __

9 )

-thinsp 31

155 times 9

1

= x

9 1

times 5

1

- 31 ___ 1 = x

-31 = x




Solve the equation

-a + 40 = 28

-a + 40 - 40 = 28 - 40

-a = -12

-a ___ -1

= -12 ____ -1

a = 12






Solve the equation

2c + 11 = 73

2c + 11 - 11 = 73 - 11

2c = 62

2c ___ 2 = 62 ___

2

c = 31




price paid


1 __ 2

middot p -6 = 88

Solve the equation

1 __ 2 p - 6 = 88

1 __ 2 p - 6 + 6 = 88 + 6

1 __ 2 p = 94

2 sdot 1 __ 2 p = 2 sdot 94

p = 188



24 115 minus 8n = 19


115 - 8n = 19

_ -115 _ -115

-8n = -96

-8n _____ -8

= -96 _____ -8

n = 12


25 -55x + 056 = -164

-55x + 056 - 056 = -164 - 056

-55x = -22

-55x ______ -22

= -22 _____ -22

x = 04

26 -42x + 315 = -651

-42x + 315 - 315 = -651 - 315

-42x = -966

-42x ______ -42

= -966 ______ -42

x = 23

27 k ___ 52

+ 819 = 472

k ___ 52

+ 819 - 819 = 472 - 819

k ___ 52

= -347

52 sdot k ___ 52

= 52 ( -347 )

k = -18044




divide 2 by 3

3x + 2 = 15

3x ___ 3 + 2 __

3 = 15 ___

3

x + 2 __ 3 = 5

- 2 __ 3

___

- 2 __ 3

___

x = 5 - 2 __ 3

x = 5 times3

___ 1

times3 - 2 __

3

x = 15 ___ 3 - 2 __

3

x = 13 ___ 3 or 4 1 __

3


31 a 2(x + 40) = 234


2x + 80 = 234

2x + 80 - 80 = 234 - 80

2x = 154

2x ___ 2 = 154 ____

2

x = 77

Trey saved $77






32 F = 18c + 32

F - 32 = 18c + 32 - 32

F - 32 = 18c

F - 32 ______ 18

= 18c ____ 18

F - 32 ______ 18

= c

33 P = 2 ( ℓ + w ) P = 2ℓ + 2w

P - 2ℓ = 2ℓ - 2ℓ + 2w

P - 2ℓ = 2w

P - 2ℓ ______ 2 = 2w ___

2

P - 2ℓ ______ 2 = w

34 ax + b = c

ax + b - b = c - b

ax = c - b

ax ___ a = c - b ______ a

x = c - b ______ a

MODULE 6

Ready to Go On




15n + 60 + 12n + 95



2 h + 97 = -97

_ -97 _ -97

h = -194

3 - 3 __ 4 + p = 1 __

2

+ 3 __ 4 + 3 __

4

p = 1 __ 2 + 3 __

4

p = 1 times2

___ 2

times2 + 3 __

4

p = 2 __ 4 + 3 __

4

p = 5 __ 4

4 -15 = -02k

-15 _____ -02

= -02k ______ -02

75 = k


5 y ___

-3 = 1 __

6

y ___

-3 ( -3 ) = 1 __

6 ( -3 )

y = 1 __ 6 times -3 ___

1

y = -3 ___ 6

y = -1 ___ 2

6 - 2 __ 3

m = -12

- 2 __

3 m _____

- 2 __ 3 = -12 ____

- 2 __ 3

m = -12 divide - 2 __ 3

m = -12 ____ 1 divide - 2 __

3

m = -12 ____ 1 times - 3 __

2

m = -36 ____ -2

m = 18

7 24 = - t ___ 45

24 ( 45 ) = - t ___ 45

( 45 )

108 = -t

-108 = t







2 middot d + 15 = 33


9 5n + 8 = 43

5n + 8 - 8 = 43 - 8

5n = 35

5n ___ 5 = 35 ___

5

n = 7

10 y __

6 - 7 = 4

y __

6 - 7 + 7 = 4 + 7

y __

6 = 11

6 sdot y __

6 = 6 sdot 11

y = 66

11 8w - 15 = 57

8w - 15 + 15 = 57 + 15

8w = 72

8w ___ 8 = 72 ___

8

w = 9

12 g

__ 3 + 11 = 25

g

__ 3 + 11 - 11 = 25 - 11

g

__ 3 = 14

3 sdot g

__ 3 = 3 sdot 14

g = 42

13 f __ 5 - 22 = -25

f __ 5 - 22 + 22 = -25 + 22

f __ 5 = -03

5 sdot f __ 5 = 5 ( -03 )

f = -15

14 - 1 __ 4 (p + 16) = 2

- 1 __ 4 p - 4 = 2

- 1 __ 4 p - 4 + 4 = 2 + 4

- 1 __ 4 p = 6

-4 sdot - 1 __ 4 p = 6 sdot -4

p = -24




situation



Are You Ready

1 9w = -54

9w ___ 9 = -54 ____

9

w = -6

2 b - 12 = 3

thinsp _ + 12 = _ + 12

b = 15

3 n __ 4

= -11

4 times n __ 4

= 4 ( -11 )

n = -44

4-7


75 4 6

8 3 - (-5)

3 + 5

8

9 -4 - 5

-9

10 6 - 10

-4

11 -5 - (-3)

-5 + 3

-2

12 8 - (-8)

8 + 8

16

13 9 - 5

4

14 -3 - 9

-12

15 0 - (-6)

0 + 6

6

LESSON 71

Your Turn


_ +5 _ +5

y ge minus2

-4-5 -3 -2-1 0 1 2 3 4 5


minus1 ge -8


2 le 16

5 21 gt 12 + x

_ -12 _ minus12

9 gt x

x lt 9

10 2 3 4 5 6 7 8 9 10


21 gt 12 + 8

21 gt 12 + 8

21 gt 20

6 -10y lt 60

-10y

_____ -10

lt 60 ____ -10

y gt -6

-10-9 -8 -7 -6 -5 -4 -3 -2-1 0 1


-10y lt 60

-10(-5) lt 60

50 lt 60

7 7 ge - t __ 6

7(-6) le - t __ 6 (-6)

-42 le t

t ge -42

-46 -45 -44 -43 -42 -41 -40-47


7 ge - t __ 6

7 ge - ( -36 ____

6 )

7 ge 6



35m le 315

35m ____ 35

le 315 ____ 35

m le 9



Guided Practice

1 -5 le -2

_ +7 _ +7

2 le 5

2 -6 lt -3

-6 ___ -3

gt -3 ___ -3

2 gt 1

3 7 gt -4

_ -7 _ -7

0 gtthinsp -11


4 -1 ge -8

-1 ( -2 ) le -8 ( -2 )

2 le 16

5 n - 5 ge -2

_ +5 _ +5

n ge 3

-5 -4 -3 -2-1 0 3 4 51 2


n - 5 ge -2

4 - 5 ge -2

-1 ge -2

6 3 + x lt 7

_ -3 _ -3

x lt 4

-2-1 0 3 4 5 6 7 81 2


3 + x lt 7

3 + 3 lt 7

6 lt 7

7 -7y le 14

-7y

____ -7 ge 14 ___ -7

y ge -2

-5-6-7 -4 -3 -2-1 0 1 2 3


-7y le 14

-7 ( -1 ) le 14

7 le 14

8 b __ 5 gt -1

b __ 5 ( 5 ) gt -1 ( 5 )

b gt -5

-5-6-7-8 -4 -3 -2-1 0 1 2


b __ 5 gt -1

0 __ 5 gt

-1

0 gt -1

9 a -4t ge -80

b -4t ge -80

-4t ____ -4

le -80 ____ -4

t le 20








number


11 x - 35 gt 15

_ + 35 _ +35

x gt 50

100 20 30 40 50 60 70 80 90100


x - 35 gt 15

51 minus 35 gt 15

16 gt 15

12 193 + y ge 201

_ -193 _ minus193

y ge 8

10 2 3 4 5 6 7 8 9 10


193 + y ge 201

193 + 9 ge 201

202 ge 201

13 - q

__ 7 ge -1

- q

__ 7 ( -7 ) le -1 ( -7 )

q le 7

8 9 105 6 70 1 2 3 4


- q

__ 7 ge -1

- -14 ____ 7 ge

-1

2 ge -1

14 -12x lt 60

-12x _____ -12

gt 60 ____ -12

x gt -5

0-10-9 -8 -7 -6 -5 -4 -3 -2-1


-12x lt 60

-12 ( -4 ) lt 60

48 lt 60

15 5 gt z -3

_ +3 _ +3

8 gt z

z lt 8

10 2 3 4 5 6 7 8 9 10


5 gt z - 3

5 gt 7 - 3

5 gt 4


16 05 le y __

8

05 ( 8 ) le y __

8 ( 8 )

4 le y

y ge 4

8 9 105 6 70 1 2 3 4


05 le y __

8

05 le 8 __

8

05 le 1



12 + x le 28

_ -12 _ -12

x le 16




w __ 7 lt 35

w __ 7 ( 7 ) lt 35 ( 7 )

w lt 245





6s le 42

6s ___ 6 le 42 ___

6

s le 7




3025 + x ge 50

_ -3025 _ -3025

x ge 1975




155w ge 1705

155w ______ 155

ge 1705 _____ 155

w ge 11




thinsp-12t lt -120

-12t _____ -12

gt -120 _____ -12

t gt 10






3s le 10

3s ___ 3 le 10 ___

3

s le 3 1 __ 3


pounds



m ___ 05

le 55

m ___ 05

( 05 ) le 55 ( 05 )

m le 275




125x le 3

125x _____ 125

le 3 ____ 125

x le 24



buy 25 pounds







not true





prism

V = lwh



( 13 ) ( 1 __ 2 ) h lt 65

65h lt 65

65h ____ 65

lt 65 ___ 65

h lt 10





LESSON 72Your Turn


raise



Target amount $6000



must raise equal to




can go on

Starting amount $40

Admission price $6




equal to




are looking for




10 is added to 3x



than 30








looking for












Guided Practice

1

- -- -

-

lt

++++++

+ + ++ + +

+

2

---

gt

+ + ++ + +

+ + ++ + +

+ + +


raise








1250 + 92a ge 7000




greater than 32







inequality






3a + 28 gt 200




cheese to has


075n + 129 le 700












120 + 32n le 720




month month


2100 + 005s ge 2400






668 + 7n gt 2000


day



buys to a month


$7 + $10 middot c le $100

7 + 10c le 100






$22 + $17 middot n le $80

22 + 17n le 80














is given by

95 + 86 + 89 + 3s

________________ 6


tests



95 + 86 + 89 + 3s

________________ 6 ge 90 or

95 + 86 + 89 + 3s ge 540 or

270 + 3s ge 540












So -m gt 0

25 n gt 1 __ n if n gt 1


n = 1 __ n if n = 1

LESSON 73

Your Turn


++

++++

+++

++++

++++

+++

gt


++

++++

+++

++++

++++

+++

gt

- -- -- --

- -- -- --


++

++++

gt


++

++++

gt



+ + +gt


+++++

----

+++++

+ +++++

ge


+++++

----

+++++

+ ++

++++

+++

++++

ge


+++++

+++++

+ +++++

++++

ge


+++++

+++++

+ +++++

++++

ge


+ + + +ge


5 - p

__ 6 le 4

5 - 5 - p

__ 6 le 4 - 5

thinsp- p

__ 6 le -1

thinsp-6 ( - p

__ 6 ) ge -6 ( -1 )

p ge 6


arrow

0 1 4 5 72 3 6 8 9 10



3v - 8 gt 22

v = 9 v = 10 v = 11

3 ( 9 ) - 8 gt 22 3 ( 10 ) - 8 gt 22 3 ( 11 ) - 8 gt 22


results

3 ( 9 ) - 8 gt 22 3 ( 10 ) - 8 gt

22 3 ( 11 ) - 8 gt

22

27 - 8 gt 22 30 - 8 gt

22 33 - 8 gt

22

19 gt 22 22 gt

22 25 gt

22


v = 11


5h + 12 le -3

h = -3 h = -4 h = -5

5 ( -3 ) + 12 le -3 5 ( -4 ) + 12 le -3 5 ( -5 ) + 12 le -3


results

5 ( -3 ) + 12 le -3 5 ( -4 ) + 12 le

-3 5 ( -5 ) + 12 le

-3

-15 + 12 le -3 -20 + 12 le

-3 -25 + 12 le

-3

-3 le -3 -8 le

-3 -13 le

-3

true true true

h = -3 h = -4 h = -5


Guided Practice




5d - 13 lt 32

5d - 13 + 13 lt 32 + 13

5d lt 45

5d ___ 5 lt 45 ___

5

d lt 9


20 6 84 10 12 14 16 18 20


-4b + 9 le -7

-4b + 9 - 9 le -7 - 9

-4b le -16

-4b ____ -4

ge -16 ____ -4

b ge 4


20 6 84 10 12 14 16 18 20


2m + 18 gt - 4

m = -12 m = -11 m = -10

2 ( -12 ) + 18 gt -4 2 ( -11 ) + 18 gt -4 2 ( -10 ) + 18 gt -4


results

2 ( -12 ) + 18 gt -4 2 ( -11 ) + 18 gt

- 4 2 ( -10 ) + 18 gt

- 4

- 24 + 18 gt -4 - 22 + 18 gt

- 4 - 20 + 18 gt

- 4

- 6 gt - 4 - 4 gt

- 4 - 2 gt

- 4


m = -10


- 6y + 3 ge 0

y = 1 y = 1 __ 2 y = 0

-6 ( 1 ) + 3 ge 0 -6 ( 1 __ 2 ) + 3 ge 0 -6 ( 0 ) + 3 ge 0


results

-6 ( 1 ) + 3 ge 0 - 6 ( 1 __

2 ) + 3 ge

0 - 6 ( 0 ) + 3 ge

0

-6 + 3 ge 0 -3 + 3 ge

0 0 + 3 ge

0

-3 ge 0 0 ge

0 3 ge

0

not true true true

y = 1 __ 2

y = 0


65 - 4t ge 15

65 - 65 - 4t ge 15 - 65

-4t ge -5

-4t ____ -4

le -5 ___ -4

t le 125


0 05 1 15 2 25



time






8 2s + 5 ge 49

2s + 5 - 5 ge 49 - 5

2s ge 44

2s ___ 2 ge 44 ___

2

s ge 22

10 14 1612 18 20 22 24 26 28 30

9 -3t + 9 ge -21

-3t + 9 - 9 ge -21 -9

-3t ge -30

-3t ____ -3

le -30 ____ -3

t le 10


10 55 gt -7v + 6

55 - 6 gt -7v + 6 - 6

49 gt - 7v

49 ___ -7 lt -7v ____ -7

v gt -7

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0

11 21 1 __ 3 gt 3m - 2 2 __

3

21 1 __ 3 + 2 2 __

3 gt 3m - 2 2 __

3 + 2 2 __

3

24 gt 3m

24 ___ 3 gt 3m ___

3

8 gt m or m lt 8

0 1 4 5 72 3 6 8 9 10

12 a ___ -8

+ 15 gt 23

a ___ -8

+ 15 - 15 gt 23 - 15

a ___ -8

gt 8

-8 ( a ___ -8

) lt -8 ( 8 )

a lt -64

-70 -68 -66 -64 -62 -60


13 f __ 2 - 22 lt 48

f __ 2 - 22 + 22 lt 48 + 22

f __ 2 lt 70

2 ( f __ 2 ) lt 2 ( 70 )

f lt 140

100 110 120 130 140 150

14 -25 + t __ 2 ge 50

-25 + 25 + t __ 2 ge 50 + 25

t __ 2 ge 75

2 ( t __ 2 ) ge 2 ( 75 )

t ge 150

130 140 150 160 170 180

15 10 + g ___

-9 gt 12

10 - 10 + g ___

-9 gt 12 - 10

g ___

-9 gt 2

-9 ( g ___

-9 ) lt -9 ( 2 )

g lt -18

-20 -18 -14 -12 -10-16

16 252 le -15y + 12

252 - 12 le -15y + 12 - 12

24 le - 15y

24 ____ -15

ge -15y

_____ -15

y le -16

-20 -18 -14 -12 -10-16

17 -36 ge -03a + 12

-36 - 12 ge -03a + 12 - 12

-48 ge -03a

-48 _____ -03

le -03a ______ -03

a ge 16

10 11 12 13 14 16 17 18 19 2015

18 80 - 2w ge 50

80 - 80 - 2w ge 50 - 80

- 2w ge -30

-2w ____ -2

le -30 ____ -2

w le 15



11 12 13 14 and 15


7n - 25 ge 65

7n - 25 + 25 ge 65 + 25

7n ge 90

7n ___ 7 ge 90 ___

7

n ge 12 6 __ 7


be a whole number





21 a

10 3 42 5 6 7 8 9 10

b

10 3 42 5 6 7 8 9 10














MODULE 7

Ready to Go On

1 n + 7 lt -3

thinsp _ -7

_ -7

n lt -10

2 5p ge -30

5p

___ 5 ge -30 ____

5

p ge -6

3 14 lt k + 11

_ -11 _ -11

3 lt k

4 d ___ -3

le minus6

( -3 ) ( d ) ge ( -3 ) ( -6 )

d ge 18


5 c - 25 le 25

_ +25 _ +25

c le 5

6 12 ge -3b

12 ___ -3

le -3b _____ -3

-4 le b




562 + n ge 650

_ -562 _ -562

n ge 88


-20 - 20t ge -100

9 2s + 3 gt 15

_ -3 _ -3

2s gt 12

2s ___ 2

gt 12 ___ 2

s gt 6

10 - d ___ 12

- 6 lt 1

_ +6 _ +6

- d ___ 12

lt 7

12 ( - d ___ 12

) lt 12 ( 7 )

-d lt 84

d gt -84

11 -6w - 18 ge 36

_ +18 _ +18

thinsp-6w ge 54

-6w _____ -6

le 54 ___ -6

w le -9

12 z __ 4 + 22 le 38

_ -22 _ -22

z __ 4 le 16

4 ( z __ 4 ) le 4 ( 16 )

z le 64

13 b __ 9 - 34 lt -36

_ +34 _ +34

b __ 9 lt -2

9 ( b __ 9 ) lt 9 ( -2 )

b lt -18

14 -2p + 12 gt 8

-12 ____

-12 ____

-2p gt -4

-2p

____ -2 lt -4 ___

-2

p lt 2






Are You Ready

1 3x + 4 = 10

3x + 4 - 4 =10 - 4

3x = 6

3x ___ 3 = 6 __

3

x = 2

2 5x - 11 = 34

5x - 11 + 11 = 34 + 11

5x = 45

5x ___ 5 = 45 ___

5

x = 9

3 -2x + 5 = -9

-2x + 5 - 5 = -9 - 5

-2x = -14

-2x ____ -2

= -14 ____ -2

x = 7

4 -11 = 8x + 13

-11 - 13 = 8x + 13 - 13

-24 = 8x

-24 ____ 8 = 8x ___

8

-3 = x

5 4x - 7 = -27

4x - 7 + 7 = -27 + 7

4x = -20

4x ___ 4 = -20 ____

4

x = -5

6 1 __ 2 x + 16 = 39

1 __ 2 x + 16 - 16 = 39 - 16

1 __ 2 x = 23

( 2 ) 1 __ 2 x = ( 2 ) 23

x = 46

7 12 = 2x - 16

12 + 16 = 2x - 16 + 16

28 = 2x

28 ___ 2 = 2x ___

2

14 = x

8 5x - 15 = -65

5x - 15 + 15 = -65 + 15

5x = -50

5x ___ 5 = -50 ____

5

x = -10

9 x __ 5 = 18 ___

30


30x = 90

30x ____ 30

= 90 ___ 30

x = 3

10 x ___ 12

= 24 ___ 36


36x = 288

36x ____ 36

= 288 ____ 36

x = 8

11 3 __ 9 = x __

3


9 = 9x

9 __ 9 = 9x ___

9

1 = x

12 14 ___ 15

= x ___ 75


1050 = 15x

1050 _____ 15

= 15x ____ 15

70 = x

13 8 __ x = 14 ___ 7


56 = 14x

56 ___ 14

= 14x ____ 14

4 = x

14 14 ___ x = 2 __ 5


70 = 2x

70 ___ 2 = 2x ___

2

35 = x

15 5 __ 6 = x ___

15


75 = 6x

75 ___ 6 = 6x ___

6

125 = x


UNIT

4


16 81 ___ 33

= x ____ 55


4455 = 33x

4455 _____ 33

= 33x ____ 33

135 = x

LESSON 81

Your Turn


= 22 ft


= 10 ft


Guided Practice

1

Blueprint

length (in)3 6 9 12 15 18

Actual

length (ft)5 10 15 20 25 30



= 15 in







= 25 m


= 15 m


4 a


scales



the drawing


6 a 2 in times 40 cm ______ 1 in

= 80 cm

15 in times 40 cm ______ 1 in

= 60 cm


b 80 cm times 60 cm = 4800 c m 2

c 80 cm times 1 in _______ 254 cm

asymp 315 in

60 cm times 1 in _______ 254 cm

asymp 236 in


315 in by 236 in



= 24 units


= 15 units


15 units




larger



r = 810 m ______ 54 ft

r = 150 m ______ 1 ft



= 648 in



b = 162 bricks



h = 30 ft times 126 cm _______ 1 ft

h = 378 cm



_________ 63 cm

n = 6 toothpicks



asymp 5 swabs






s = 10 cm times 2 ft _____ 1 cm

s = 20 ft










original size


2

LESSON 82

Guided Practice















triangle






6 cm

3 cm120˚








same angle measures








between them






LESSON 83

Guided Practice


2 rectangle

3 triangle





















volume is 480 in 3





LESSON 84

Your Turn



intersecting lines




mangFGD and mangDGC



mangBGC and mangCGD



Because lines _

BE and _




mangCGD = 55deg



3x ___ 3 = 126deg ____

3

x = 42deg





Guided Practice




so mangDGE = 30deg





value by 3














measures are equal

mangKMI = mangHMG

84 = 4x

84 ___ 4 = 4x ___

4

x = 21deg



x + 84 - 84 = 180 - 84

x = 96

mangKMH = 96deg



x + 62 - 62 = 180 - 62

x = 118

mangCBE = 118deg



x + 62 - 62 = 90 - 62

x = 28

mangABF = 28deg




x + 28 - 28 = 152

mangCBA = 152deg




2x ___ 2 = 86deg ___

2





6x ___ 6 = 180deg ____

6









_ -48deg268 _ -48deg268

mangK = 41deg3352






greater than 38deg











( 90 - ( 90 - xdeg ) ) = ( 90 - 90 + xdeg ) = xdeg

MODULE 8

Ready to Go On

1

Living


Actual


Blueprint





created




A point is another




mangFGE = 50deg




3 ( mangY ) ________ 3 = 120deg ____

3

mangY = 40deg

mangY = 40deg


rooms or gardens



Are You Ready

1 416

_ times 13

1248

_ +thinsp4160

5408

5408

2 647

_ times thinsp04

2588

2588

3 705

_ times thinsp94

2820

_ +thinsp63450

66270

6627

4 256

_ timesthinsp049

2304

_ +thinsp10240

12544

12544

5 1 __ 2 ( 14 ) ( 10 )

7 ( 10 )

70 i n 2

6 ( 35 ) ( 35 )

1225 ft 2

7 ( 8 1 __ 2 ) ( 6 )

17 ___ 1 2 sdot 6 3 __

1

51 i n 2

8 1 __ 2 ( 125 ) ( 24 )

1 __ 2 ( 24 ) ( 125 )

( 12 ) ( 125 )

15 m 2

LESSON 91

Your Turn

3 d = 11 cm

C = πd

C asymp 314 ( 11 )

C asymp 3454


6 C = πd

44 asymp 314d

44 ____ 314

asymp d

d asymp 1401 yards


rate

1401 divide 7 = 2001


Guided Practice

1 d = 9 in

C asymp 314 ( 9 )

C asymp 2826 in

2 r = 7 cm

C = 2πr

C asymp 2 ( 22 ___ 7 ) ( 7 )

C asymp 44 cm

3 d = 25 m

C = πd

C asymp 314 ( 25 )

C asymp 785 m

4 r = 48 yd

C = 2πr

C asymp 2 ( 314 ) ( 48 )

C asymp 3014 yd

5 r = 75 in

C = 2πr

C asymp 2 ( 314 ) ( 75 )

C asymp 471 in

6 Find the diameter

C = πd

66 asymp 314d

66 ____ 314

asymp 314d _____ 314

21 asymp d

Find the cost


25 times $045 = $1125



r = 05 yd

d = 1 yd


2πr = 788

2πr ___ 2π

= 788 ____ 2π

r asymp 788 _______ 2 ( 314 )

r asymp 1255 ft

d = 2r asymp 2 ( 1255 ft )

d asymp 2510 ft

9 d = 2r so r = d __ 2 asymp 34 ___

2

r asymp 17 in

C = πd asymp 314 ( 34 )

C = 1068 in





11 d = 59 ft

C = πd

C asymp 314 ( 59 )

C asymp 1853 ft

12 r = 56 cm

C = 2πr

C asymp 2 ( 22 ___ 7 ) ( 56 )

C asymp 352 cm

13 d = 35 in

C = πd

C asymp ( 22 ___ 7 ) ( 35 )

C asymp 110 in



15 r = 94 ft

d = 2r = 2 ( 94 )

d = 188 ft

C = πd

C asymp 314 ( 188 )

C asymp 590 ft

16 d = 475 in

r = d __ 2 = 475 ____

2

r = 2375 in

C = πd

C asymp 314 ( 475 )

C asymp 14915 in

17 d = 18 in

r = d __ 2 = 18 ___

2

r = 9 in

C = πd

C asymp 314 ( 18 )

C asymp 5652 in

18 r = 15 ft

C = 2πr

C asymp 2 ( 314 ) ( 15 ) = 942 ft


so ( 942 ) ( 075 ) = 7065 or about $707

19 C = πd

C asymp ( 22 ___ 7 ) ( 63 )

C asymp 198 ft




20 C = πd asymp 314 ( 2 )

C asymp 628 ft

Converting km to ft

2 km sdot ( 3280 ft _______

1 km ) = 6560 ft

6560 ft

_______ 628 ft

= 104459




1 __ 2 C = 1 __

2 πd asymp 1 __

2 sdot 314 ( 025 ) = 03925





Height 180 ft



_______ 2 ( 314 )

asymp 48 ft

Diameter d = 2r = 2 ( 48 ) = 96 ft



plus the diameter

1 __ 2 C = 1 __

2 πd asymp 1 __

2 sdot 314 ( 30 ) = 471



per linear foot

( 771 ft ) ( $925 _____

ft ) = $71318



C = πd asymp 314 ( 18 ) = 5652 ft


inches to feet

( 54 in ) ( 1 ft _____ 12 in

) = 45 ft



5652 ft _______ 45 ft

= 1256


must buy 13 strands


C inner

= πd asymp 314 ( 150 ) = 471 ft


C outer

= πd asymp 314 ( 154 ) = 48356 ft








smaller gear





314 ( 75 ) - 314 ( 732 ) = 314 ( 018 ) asymp 057

057 m asymp 187 ft

LESSON 92

Your Turn

4 A = π r 2 A = π ( 10 ) 2

A asymp 314 ( 10 ) 2


A asymp 314 f t 2

Guided Practice

1 r = d __ 2 = 14 ___

2 = 7 m

A = π r 2 A = π ( 7 ) 2

A asymp 314 ( 7 ) 2

A asymp 314 sdot 49

A asymp 1539 m 2

2 A = π r 2 A = π ( 12 ) 2

A asymp 314 ( 12 ) 2


A asymp 4522 m m 2

3 r = d __ 2 = 20 ___

2 = 10 yd

A = π r 2 A = π ( 10 ) 2

A asymp 314 ( 10 ) 2


A asymp 314 y d 2

4 A = π r 2 A = π ( 8 ) 2

A asymp 314 ( 8 ) 2

A asymp 314 sdot 64

A asymp 20096 i n 2

5 r = d __ 2 = 12 ___

2 = 6 cm

A = π r 2 A = π ( 6 ) 2

A asymp 314 ( 6 ) 2

A asymp 314 sdot 36

A asymp 11304 c m 2

6 r = d __ 2 = 13 ___

2 = 65 in

A = π r 2 A = π ( 65 ) 2

A asymp 314 ( 65 ) 2


A asymp 13267 i n 2

7 C = 4π = 2πr

4π ___ 2π

= 2πr ___ 2π

r = 2

A = π r 2 A = π ( 2 ) 2


8 C = 12π = 2πr

12π ____ 2π

= 2πr ___ 2π

r = 6

A = π r 2 A = π ( 6 ) 2


9 C = π __ 2 = 2πr

π __ 2 divide 2π = 2πr ___

2π

π __ 2 sdot 1 ___

2π = r

1 __ 4 = r

A = π r 2

A = π ( 1 __ 4 ) 2 = π ( 1 ___

16 )

A = π ___ 16

square units

10 A = π r 2 = 64π

π r 2 ___ π = 64π ____ π

r 2 = 64

r = 8

C = 2πr

= 2π ( 8 )

=16π yd

11 A = π r 2


12 r = d __ 2 = 10 ___

2 = 5 in

A = π r 2 A = π ( 5 ) 2

A asymp 314 ( 5 ) 2

A asymp 314 sdot 25

A asymp 785 i n 2

13 A = π r 2 A = π ( 16 ) 2

A asymp 314 ( 16 ) 2


A asymp 80384 c m 2


diameter 36 in

r = d __ 2 = 36 ___

2 = 18 in

A semicircle

= 1 __ 2 π r 2

A semicircle

= 1 __ 2 π ( 18 ) 2

A semicircle

asymp 1 __ 2 ( 314 ) ( 18 ) 2

A semicircle


A asymp 50868 i n 2




A = π r 2 A = π ( 3 ) 2

A asymp 314 ( 3 ) 2



A r = 75 mi

- A r = 50 mi

π ( 75 ) 2 - π ( 50 ) 2



greater







s 2 minus π r 2 = 1 2 2 minus π ( 6 ) 2

= 144 minus π ( 36 )

asymp 144 minus 11304 = 3096










16π in 2





about $20

_____ π ( 9 ) 2



_____ π ( 6 ) 2

asymp $009






A = π r 2 = π ( 8 ) 2

= π ( 64 )

asymp 20096


201 mi 2




A new

minus A old

= π ( 10 ) 2 - π ( 8 ) 2

= π ( 1 0 2 - 8 2 ) = π ( 100 - 64 )

= π ( 36 ) asymp 11304


more area









A


A whole target

=

π ( 15 ) 2 ______

π ( 75 ) 2

= ( 15 ) 2

_____ ( 75 ) 2

= 225 _____ 5625

= 004


LESSON 93

Your Turn


two right triangles





A = ℓw = 11 sdot 4 = 44 f t 2


A = 1 __ 2 bh = 1 __



A = 1 __ 2 bh = 1 __

2 sdot 3 sdot 3 = 45 f t 2


44 + 3 + 45 = 515 f t 2


semicircle



or 10 ___ 2 = 5 m


A = s 2 = 1 0 2 = 100 m 2


A = 1 __ 2 π r 2

A asymp 1 __ 2 sdot 314 sdot ( 5 ) 2


A asymp 3925 m 2


100 + 3925 = 13925 m 2







4 __ 2 = 2 ft


A = ℓw = 5 sdot 4 = 20 f t 2


A = π r 2 A asymp 314 sdot ( 2 ) 2



two areas

20 + 1256 = 3256 f t 2



( 3256 f t 2 ) ( $28 ____

f t 2 ) = $91168


Guided Practice


a parallelogram



2 ( 4 ) ( 2 ) = 4




2 parallelogram

15 cm 2


4 + 15 + 15 = 34 cm 2


2 Method 1

A 1 = ℓw A

2 = ℓw

= 12 sdot 9 = 20 sdot 9 = 108 = 180


Method 2

A 1 = ℓw A

2 = ℓw

= 9 sdot 8 = 12 sdot 8 = 72 = 216






1 + b

2 )

A = 1 __ 2 ( 5 ) ( 7 + 4 )

A = 1 __ 2 ( 5 ) ( 11 ) = 275 f t 2



275 + 16 = 435 ft 2


find the cost

( 435 f t 2 ) ( $225 _____

f t 2 ) = $9788


simpler figures




A asymp 1 __ 2 sdot 314 sdot ( 13 ) 2


A asymp 26533 i n 2


676 + 26533 = 94133 in 2






A = 1 __ 2 sdot 6 sdot 7

A = 1 __ 2 sdot 42

A = 21 f t 2


40 + 21 = 61 f t 2


square foot

( 61 f t 2 ) ( $250 _____

f t 2 ) = $15250

7

O 42-2-4

2

-4

y

A (-2 4) B (0 4)

C (2 1)D (5 1)

E (5 -2)F (-2 -2)










Area of trapezoid

A = 1 __ 2 h ( b

1 + b

2 )

A = 1 __ 2 ( 3 ) ( 4 + 2 )

A = 1 __ 2 ( 3 ) ( 6 ) = 9 square units











A = 1 __ 2 sdot 8 sdot 8

A = 1 __ 2 sdot 64

A = 32 m 2


A asymp 1 __ 4 sdot 314 sdot ( 8 ) 2


A asymp 5024 f t 2


64 + 32 + 5024 = 14624 m 2









48 + 1256 = 6056 cm 2






A = 1 __ 2 sdot 1 sdot 1

A = 1 __ 2 sdot 1

A = 05 f t 2


3 + 05 = 35 ft 2





( 42 f t 2 ) ( $125 _____

f t 2 ) = $5250


area of triangle

325 ft 2 - 75 ft 2 = 25 ft 2



square is 5 ft






20 ( 15 ) or 300 carrots








triangle



A = 1 __ 2 sdot 12 sdot 8

A = 1 __ 2 sdot 96

A = 48 i n 2


144 + 48 = 192 in 2










420 - 176625 = 243375 in 2 or 243 3 __

8 i n 2










A asymp 1 __ 2 sdot 314 sdot ( 20 ) 2


A asymp 628 i n 2


1600 + 628 = 2228 in 2






40 + 2 sdot 4 = 48 in




total of 40 + 4 = 44 in






A asymp 1 __ 2 sdot 314 sdot ( 24 ) 2


A asymp 90432 i n 2


the sum

2112 + 90432 asymp 3016 in 2

LESSON 94

Your Turn


B = l times w

= 9 times 2

= 18 square inches


P = 2 ( 9 ) + 2 ( 2 )

= 18 + 4 = 22 inches


S = Ph + 2B

S = 22 ( 1 1 __ 2 ) + 2 ( 18 )

= 33 + 36

= 69



B = times w

= 12 times 12

= 144 square inches


P = 4 ( 12 )

= 48 inches


S = Ph + 2B

S = 48 ( 12 ) + 2 ( 144 )

= 576 + 288

= 864 square inches


B = l times w

= 8 times 8

= 64 square inches


P = 4 ( 8 )

= 32 inches


S = Ph + 2B

S = 32 ( 8 ) + 2 ( 64 )

= 256 + 128

= 384 square inches








Guided Practice



Height = 7 ft

Base area = 1 __ 2 ( 3 ) ( 8 ) = 12 ft 2

Surface area

S = ( 18 ft ) ( 7 ft ) + 2 ( 12 ft 2 ) = 150 ft 2


B = l times w

= 25 times 25

= 625 m 2


P = 4 ( 25 )

= 10 m


S = Ph + 2B

S = 10 ( 25 ) + 2 ( 625 )

= 25 + 125

= 375


S = 375 m 2


B = l times w

= 11 times 9

= 99 m 2


prism

P = 2 ( 11 ) + 2 ( 9 )

= 22 + 18

= 40 m


S = Ph + 2B

S = 40 ( 7 ) + 2 ( 99 )

= 280 + 198

= 478


S = 478 m 2


A = ( 25 ) ( 25 ) = 625



= 375 + 478 -2 ( 625 ) = 503 m 2




surface




B = l times w

= 10 times 3

= 30 in 2


P = 2 ( 10 ) + 2 ( 3 )

= 20 + 6

= 26 in


S = Ph + 2B

S = 26 ( 4 ) + 2 ( 30 )

=104 + 60

= 164 in 2



B = l times w

= 20 times 15

= 300 cm 2


P = 2 ( 20 ) + 2 ( 15 )

= 40 + 30

= 70 cm


S = Ph + 2B

S = 70 ( 9 ) + 2 ( 300 )

= 630 + 600

= 1230 cm 2


1230 - 300 = 930 cm 2



Convert cm 2 to mm

2


2 ________

1 cm 2 = 93000 mm

2


93000 divide 25 = 3720




= 2 + 3 = 5 in 2


Perimeter = 3 + 3 + 1 + 2 + 2 + 1

= 12 in


S = Ph + 2B

S = 12 ( 3 ) + 2 ( 5 )

= 36 + 10

= 46 in 2



Perimeter = 25 + 25 + 3 = 8 ft

Base area = 1 __ 2 ( 2 ) ( 3 ) = 3 ft 2


= 8 ( 4 ) + 2 ( 3 )

= 32 + 6 = 38 ft 2


Perimeter = 2 ( 3 ) + 2 ( 4 ) = 14 ft



= 14 ( 2 ) + 2 ( 12 )

= 28 + 24 = 52 ft 2



Surface area = 38 + 52 - 12 - 12 = 66 ft 2







1 + b

2 ) h

1 __ 2 ( 16 + 48 ) 12 = 384 in

2


P = 48 + 20 + 16 + 20 = 104 in


S = Ph + 2B

S = 104 ( 24 ) + 2 ( 384 )

= 2496 + 768

= 3264 in 2



B = l times w

= 7 times l

= 7 ft 2


P = 2 ( 7 ) + 2 ( 1 )

= 14 + 2

= 16 ft


S = Ph + 2B

S = 16 ( 2 ) + 2 ( 7 )

= 32 + 14

= 46 f t 2


B = l times w

= 1 times 1

= 1 ft 2


P = 2 ( 1 ) + 2 ( 1 )

= 2 + 2 = 4 ft


S = Ph + 2B

S = 4 ( 3 ) + 2 ( 1 )

= 12 + 2

= 14 ft 2



Surface area = 46 + 14 - 1 - 1 = 58 ft 2



58 divide 25 = 232


needed


3 times 679 = 2037




B = l times w

= 27 times 24

= 648 cm 2


P = 2 ( 27 ) + 2 ( 24 )

= 54 + 48

= 102 cm


S = Ph + 2B

S = 102 ( 10 ) + 2 ( 648 )

= 1020 + 1296

= 2316 cm 2






2 ( 2l + 2w ) = 2P


New S = 2Ph + 2 ( 4B )


doubles



B = l times w

= 25 times 25

= 625 ft 2


P = 4 ( 25 )

= 10 ft


S = Ph + 2B

S = 10 ( 35 ) + 2 ( 625 )

= 35 + 135

= 485 ft 2



485 - 625 = 4225 ft 2



4225 _____ 485

times 100 asymp 87




15


r = 2 in

9 in


A = πr 2

asymp 31 4 ( 2 ) 2 = 1256 in 2


C = πd

asymp 314 ( 4 ) = 1256 in 2




S = Ch + 2B

asymp 1256 ( 9 ) + 2 ( 1256 ) = 13816 in 2





1500 times 1382 = 207300 in 2



( 207300 in 2 ) 1 ft 2 _______

144 in 2 asymp 1440 ft 2






show

LESSON 95

Your Turn


B = 1 __ 2 bh

= 1 __ 2 ( 24 ) 7

= 84 m 2


V = Bh

= ( 84 ) ( 22 )

= 1848 m 3



B = 1 __ 2 ( b 1 + b 2 ) h

= 1 __ 2 ( 8 + 12 ) 10

= 1 __ 2 ( 20 ) 10 = 100 cm

2


V = Bh

= ( 100 ) ( 22 )

= 2200 cm 3




B = bh

= ( 13 ) 13

= 169 in 2


V = Bh

= ( 169 ) ( 30 )

= 5070 in 3



B = 1 __ 2 bh

= 1 __ 2 ( 9 ) 13

= 585 in 2


V = Bh

= ( 585 ) ( 30 )

= 1755 in 3


5070 + 1755 = 6825 in 3


Guided Practice

1 B = 1 __ 2 bh = 1 __

2 ( 8 ) ( 3 ) = 12 ft 2

V = Bh = ( 12 times 7 ) ft 3 = 84 ft 3

2 B = 1 __ 2 ( b 1 + b 2 ) h = 1 __

2 ( 15 + 5 ) 3 = 30 m

2

V = Bh = ( 30 times 11 ) m 3 = 330 m 3


B = bh

= ( 4 ) 6 = 24 ft 2


V = Bh

= ( 24 ) ( 12 ) = 288 ft 3



B = 1 __ 2 bh

= 1 __ 2 ( 6 ) 4 = 12 ft 2


V = Bh

= ( 12 ) ( 6 ) = 72 ft 3



288 + 72 = 360 ft 3



B = bh

= ( 40 ) ( 50 ) = 2000 ft 2


V = Bh

= ( 2000 ) ( 15 ) = 30000 ft 3


B = 1 __ 2 bh

= 1 __ 2 ( 40 ) ( 10 ) = 200 ft 2


V = Bh

= ( 200 ) ( 50 ) = 10000 ft 3


30000 + 10000 = 40000 ft 3



B = 1 __ 2 ( b 1 + b 2 ) h

= 1 __ 2 ( 10 + 12 ) 5

= 1 __ 2 ( 22 ) 5 = 55 cm

2


V = Bh

= ( 55 ) ( 7 ) = 385 cm 3







V = Bh

= ( 35 ) ( 5 ) = 175 in 3




B = 1 __ 2 bh

= 1 __ 2 ( 7 ) ( 6 ) = 21 in

2


V = Bh

= ( 75 ) ( 7 ) = 525 in 3



B = 1 __ 2 bh

= 1 __ 2 ( 8 ) ( 4 ) = 16 ft 2


V = Bh

= ( 16 ) ( 24 ) = 384 ft 3



B = 1 __ 2 ( b 1 + b 2 ) h

= 1 __ 2 ( 7 + 5 ) 4

= 1 __ 2 ( 12 ) 4 = 24 in

2


V = Bh

= ( 24 ) ( 8 ) = 192 in 3



V = Bh

= ( 20 ) ( 15 ) = 300 in 3


300 cubic inches


given B = 234 in 3


V = Bh

= ( 234 ) ( 3 ) = 702 in 3



B = bh

= ( 3 ) ( 3 ) = 9 in 2


V = Bh

= ( 9 ) ( 3 ) = 27 in 3


702 + 27 = 972 in 3



B = bh

= ( 75 ) 375 = 28125 m 2


V = Bh

= ( 28125 ) ( 75 ) asymp 21094 cm 3


prism


15 - 75 = 75


B = bh

= ( 75 ) 375 = 28125 m 2


V = Bh

= ( 28125 ) ( 375 ) asymp 10547 cm 3


21094 + 10547 = 31641 m 3




V = Bh

= ( 21 ) ( 8 ) = 168 cm 3



260 - 168 = 92 cm 3


V = Bh

= ( 7 ) ( 14 ) = 98 cm 3



260 - 168 = 92 cm 3


a height of 14 cm

V = Bh

92 = B ( 14 )

92 ___ 14

= B ( 14 ) _____ 14

6 8 ___ 14

= B asymp 657





V = Bh

= ( 36 ) ( 5 ) = 180 in 3



prism V = Bh

= ( 32 ) ( 6 ) = 192 in 3





V = Bh

286 = B ( 8 )

286 ____ 8 = B ( 8 )

3575 = B


trapezoidal prism

1 __ 2 ( 2 + b 2 ) 13 = 3575

1 __ 2 ( 2 + b 2 ) ( 13 ___

13 ) = 3575 _____

13

( 2 ) 1 __ 2 ( 2 + b 2 ) = ( 2 ) 275

2 + b 2 = 55

_ -2 _ -2

b 2 = 35 ft



B = 1 __ 2 bh

= 1 __ 2 ( 10 ) 6 = 30 cm

2


V = Bh

= ( 30 ) ( 25 ) = 75 cm 3



_____ cm

3 )

asymp ( 75 cm 3 ) ( 86 g

_____ cm

3 ) = 645 g


about 645 g







of 120 cm 3

V = Bh

V = [ 1 __ 2 ( b 1 + b 2 ) h 1 ] h 2

120 ≟ [ 1 __ 2 ( 2 + 6 ) 4 ] 75

= [ 1 __ 2 ( 8 ) 4 ] 75

= [ 16 ] ( 75 ) = 120


V = Bh

V = [ 1 __ 2 ( b 1 + b 2 ) h 1 ] h 2

120 ≟ [ 1 __ 2 ( 1 + 7 ) 25 ] 12

= [ 1 __ 2 ( 8 ) 25 ] 12

= [ 10 ] 12 = 120






MODULE 9

Ready to Go On




2 d = 12 cm d = 6 cm so r = 12 ___ 2 = 6 ft



A asymp 11304 ft 2





A asymp 1 __ 2 sdot 314 sdot ( 8 ) 2


A asymp 10048 m 2


A = 1 __ 2 sdot 16 sdot 10

A = 1 __ 2 sdot 160

A = 80 m 2


80 + 10048 = 18048 m 2





A = 20 sdot 45

A = 90 c m 2

Area of rectangle

A = ℓw = 20 sdot 55 = 110 c m 2


90 + 110 = 200 cm 2



1 __ 2 ( 4 ) 3 = 6 cm 2


P = 3 + 4 + 5 = 12 cm


S = Ph + 2B

S = 12 ( 10 ) + 2 ( 6 )

thinsp=120 + 12

thinsp= 132 cm 2


V = Bh

= ( 6 ) 10

= 60 cm 3




1 __ 2 ( 4 ) 15 = 3 yd 2


( 4 ) 2 = 8 yd 2



P = 4 + 2 + 25 + 25 + 2 = 13 yd


S = Ph + 2B

S = 13 ( 25 ) + 2 ( 11 )

thinsp= 325 + 22

thinsp= 545 yd 2


is given

B = 234 yd 3


V = Bh

= ( 11 ) 25

= 275 yd 3






unit


Are You Ready

1 x ___16

=45___40

40x=720

40x ____40

=720____40

   x=18

2 x __5=1__

4

4x=5

4x ___4

=5__4

  x=5__4=125

3 25___10

=x ___10

125=10x

125____10

=10x ____10

125=x

4 x __6

=2__9

9x= 12

9x ___9

=12___9

   x=12___9=4__

3

5 4748495152575960range=60-47=13

6 4566689121213range=13-4=9

7 95979799100106108115range=115-95=20

8 121319273539476671range=71-12=59

9 mean=3+5+7+3+6+4+8+6+9+5_________________________________10

=56

10 mean=81+94+113+67+62+75____________________________6

=82

LESSON 101

Your Turn




Guided Practice




Jimmy 80

Darnell 90

Ping 75

Zach 85

Jamar 80

BSampleanswer

75+80+90+75+85+80___________________________6

=485____6

asymp81

Meanasymp81



Stan 80 Marcus 90

Alejandro 90 Tio 85

BSampleanswer

85+80+90+85+90+85____________________________6

=515____6 =86

Mean=size86




















b 35___60

= x ____100

xasymp58


=58



LESSON 102

Your Turn


______________________sizeofsample



6___50

= x_____3500

6sdot70______50sdot70

= x _____3500

420_____3500

= x_____3500


Guided Practice

1

6 7 8 9 10 11 12 13 14 1550 1 2 3 4


6 7 7 107 114 4 54

Leastvalue

4

Lower quartile

4

Median

65

Upper quartile

7

Greatestvalue11

Drawaboxplot

10 1550





______________________sizeofsample



4___60

= x_____4200

4sdot70______60sdot70

= x_____4200

280_____4200

= x_____4200






8___50

= x_____4500

8sdot90______50sdot90

= x_____4500

720_____4500

= x_____4500



divide060

divide060







_______________________________________ size of sample

=



4 ___ 50

= x ____ 600

4 sdot 12 ______ 50 sdot 12

= x ____ 600

48 ____ 600

= x ____ 600

x = 48



_______________________________________________ size of sample

=



2 ___ 20

= x ____ 130

2 sdot 65 _______ 20 sdot 65

= x ____ 130

13 ____ 130

= x ____ 130

x = 13



________________ size of sample



12 ___ 60

= x _____ 1200

12 sdot 20 ______ 60 sdot 20

= x _____ 1200

240 _____ 1200

= x _____ 1200

x = 240


shelters


__________________________ size of sample



12 ___ 72

= x ______ 10800

12 sdot 150 _______ 72 sdot 150

= x ______ 10800

1800

______ 10800

= x ______ 10800

x = 1800



_______ 2 = 25


14 Order the data

11 12 12 12 13 13 13 14 14 14 15 17 18 18

19 22



12 ___ 16

= x ____ 100

12 sdot 625 ________ 16 sdot 625

= x ____ 100

75 ____ 100

= x ____ 100

x = 75



15

6 7 8 9 1050 1 2 3 4


fewer siblings




















9 a 56 + 43 + 62 + 63 + 33 + 34 + 38 + 51 + 59 + 59

___________________________________________ 10

= 498


b 498 sdot 64 = 31872



10 55 + 57 + 57 + 58 + 59 + 59 + 59 + 59 + 59 + 61 + 62 + 62 + 63 + 64 + 66

_________________________________________________________________ 15

= 60






accurately

LESSON 103

Guided Practice

1 (1 600) 20

2 50 51 600








5 Shop A 10 ___ 50

times 500 = 100

Shop B 23 ____ 100

times 500 = 115

Shop C 7 ___ 25

times 500 = 140








fewest bagels










count of 75


MODULE 10

Ready to Go On




service


__________________________________________ size of sample


18 ____ 270

= x ______ 30330

18 sdot 337 ____

3 ________

270 sdot 337 ____ 3

= x ______ 30330

2022

______ 30330

= x ______ 30330

x = 2022


languages





= defective players

______________ shipment

2 ___ 10

= x _____ 5000

2 middot 500 _______ 10 middot 500

= x _____ 5000

1000

_____ 5000

= x _____ 5000

x = 1000


defective


the shipment





Are You Ready

0875

1 8 ⟌ _

7000

_ -6 400

600

_ -560

40

_ -40

0

0875 875

08

2 5 ⟌ _

40

_ -4 0

0

08 80

025

3 4 ⟌ _

100

_ -80

20

_ -20

0

025 25

03

4 10 ⟌ _

30

_ -3 0

0

03 30

5 4 6 7 7 9 11 15 17

7 + 9

_____ 2 = 8

Median = 8

Mode = 7

6 36 37 40 43 44 49 50 51 56

Median = 44

Mode none

7 9 + 16 + 13 + 14 + 10 + 16 + 17 + 9

________________________________ 8

= 13

Mean = 13

8 108 + 95 + 104 + 96 + 97 + 106 + 94

________________________________ 7 = 100

Mean = 100

LESSON 111

Your Turn








in order

1 4 4 4 5 5 5 6 6 6 6 7 7 8 11


range 10 h



range for exercise

Guided Practice




one area




no data


4 Class A

4 4 4 4 4 5 5 5 6 6 12 13 13 13 13 14 14

median 6

Class B

3 4 4 4 5 5 5 5 6 6 7 7 7 7 7 8 8 9

median 6








at 8 letters




3 + 4 + 4 + 5 + 5 + 6 + 7 + 7 + 8 + 8 + 8 + 9

________________________________________ 12

74 ___ 12

asymp 617

Mean asymp 617

3 3 4 5 5 6 7 7 8 8 8 9


average

6 + 7

_____ 2 = 13 ___

2 = 65

Median 65

Range 9 - 3 = 6


the left


interval













LESSON 112

Your Turn



Guided Practice


2 Median79

3 Range88-72=16 IQR85-75=10






























does not




LESSON 113

Your Turn

1 Team 1

Mean

44 + 47 + 67 + 89 + 55 + 76 +85 + 80 + 87 + 69 + 47 + 58 = 804

804 divide 12 = 67


ǀ 44 - 67 ǀ = 23 ǀ 47 - 67 ǀ = 20

ǀ 67 - 67 ǀ = 0 ǀ 89 - 67 ǀ = 22

ǀ 55 - 67 ǀ = 12 ǀ 76 - 67 ǀ = 9

ǀ 85 - 67 ǀ = 18 ǀ 80 - 67 ǀ = 13

ǀ 87 - 67 ǀ = 20 ǀ 69 - 67 ǀ = 2

ǀ 47 - 67 ǀ = 20 ǀ 58 - 67 ǀ = 11


23 + 20 + 0 + 22 + 12 + 9 +18 + 13 + 20 + 2 + 20 + 11 = 170


Team 2

Mean

40 + 32 + 52 + 75 + 65 + 70 +72 + 61 + 54 + 43 + 29 + 32 = 625



ǀ 40 - 521 ǀ = 121 ǀ 32 - 521 ǀ = 201

ǀ 52 - 521 ǀ = 01 ǀ 75 - 521 ǀ = 229

ǀ 65 - 521 ǀ = 129 ǀ 70 - 521 ǀ = 179

ǀ 72 - 521 ǀ = 199 ǀ 61 - 521 ǀ = 89

ǀ 54 - 521 ǀ = 19 ǀ 43 - 521 ǀ = 91

ǀ 29 - 521 ǀ = 231 ǀ 32 - 521 ǀ = 201


121 + 201 + 01 + 229 +129 + 179 + 199 + 89 +19 + 91 + 231 + 201 = 169


Difference in means

67 - 521 = 149



MAD


distributions

Guided Practice

1 Class 1 mean

12 + 1 + 6 + 10 + 1 + 2 + 3 +10 + 3 + 8 + 3 + 9 + 8 + 6 + 8 = 90

90 divide 15 = 6

Class 2 mean

11 + 14 + 11 + 13 + 6 + 7 + 8 + 6 +8 + 13 + 8 + 15 + 13 + 17 + 15 = 165

165 divide 15 = 11


ǀ 12 - 6 ǀ = 6 ǀ 1 - 6 ǀ = 5 ǀ 6 - 6 ǀ = 0

ǀ 10 - 6 ǀ = 4 ǀ 1 - 6 ǀ = 5 ǀ 2 minus 6 ǀ = 4

ǀ 3 - 6 ǀ = 3 ǀ 10 - 6 ǀ = 4 ǀ 3 - 6 ǀ = 3

ǀ 8 - 6 ǀ = 2 ǀ 3 - 6 ǀ = 3 ǀ 9 - 6 ǀ = 3

ǀ 8 - 6 ǀ = 2 ǀ 6 - 6 ǀ = 0 ǀ 8 - 6 ǀ = 2

6 + 5 + 0 + 4 + 5 + 4 + 3 + 4 +3 + 2 + 3 + 3 + 2 + 0 + 2 = 46



ǀ 11 - 11 ǀ = 0 ǀ 14 - 11 ǀ = 3 ǀ 11 - 11 ǀ = 0

ǀ 13 - 11 ǀ = 2 ǀ 6 - 11 ǀ = 5 ǀ 7 - 11 ǀ = 4

ǀ 8 - 11 ǀ = 3 ǀ 6 - 11 ǀ = 5 ǀ 8 - 11 ǀ = 3

ǀ 13 - 11 ǀ = 2 ǀ 8 - 11 ǀ = 3 ǀ 15 - 11 ǀ = 4

ǀ 13 - 11 ǀ = 2 ǀ 17 - 11 ǀ = 6 ǀ 15 - 11 ǀ = 2

0 + 3 + 0 + 2 + 5 + 4 + 3 + 5 +3 + 2 + 3 + 4 + 2 + 6 + 2 = 44



11 minus 6 = 5




comparison


different samples


5 23 + 38 + 39 + 48 + 55 + 56 + 71 +86 + 57 + 53 + 43 + 31 = 600

600 divide 12 = 50

ǀ 23 - 50 ǀ = 27 ǀ 38 - 50 ǀ = 12

ǀ 39 - 50 ǀ = 11 ǀ 48 - 50 ǀ = 2

ǀ 55 - 50 ǀ = 5 ǀ 56 - 50 ǀ = 6

ǀ 71 - 50 ǀ = 21 ǀ 86 - 50 ǀ = 36

ǀ 57 - 50 ǀ = 7 ǀ 53 - 50 ǀ = 3

ǀ 43 - 50 ǀ = 7 ǀ 31 - 50 ǀ = 19

27 + 12 + 11 + 2 + 5 + 6 + 21 +36 + 7 + 3 + 7 + 19 = 156

156 divide 12 = 13



6 ǀ 23 - 8 ǀ = 15 ǀ 38 - 23 ǀ = 15

ǀ 39 - 24 ǀ = 15 ǀ 48 - 33 ǀ = 15

ǀ 55 - 40 ǀ = 15 ǀ 56 - 41 ǀ = 15

ǀ 71 - 56 ǀ = 15 ǀ 86 - 71 ǀ = 15

ǀ 57 - 42 ǀ = 15 ǀ 53 - 38 ǀ = 15

ǀ 43 - 28 ǀ = 15 ǀ 31 - 16 ǀ = 15




7 50 - 15 = 35




8 50 - 35 = 15




9

0 4 8 12 16 20 24 28 32 36 40 44

Medians

School B

School A

0 4 8 12 16 20 24 28 32 36 40 44

Means

School B

School A




10 State A 48 - 38 = 10


State B 50 - 42 = 8

8 divide 4 = 2





well


Median 665


Median 77

77 - 665 = 105

105 divide 6 = 175


ranges













not very similar

MODULE 11

Ready to Go On


5 + 6 + 6 + 7 + 7 + 7 + 7 + 8 + 8 + 8 + 8 + 9 + 9 + 10

________________________________________________ 14

= 105 ____ 14

= 75 mi


6 + 6 + 7 + 7 + 8 + 8 + 8 + 8 + 9 + 9 + 9 + 10 + 10 + 10

__________________________________________________ 14

= 115 ___ 14

asymp 82 mi




5 6 6 7 7 7 7 8 8 8 8 9 9 10


average

7 + 8

_____ 2 = 15 ___

2 = 75

Median 75


6 6 7 7 8 8 8 8 9 9 9 10 10 10




Median 8













7 + 11 + 11 + 12 + 9 + 12 + 8 + 10

______________________________ 8

= 10


21 + 24 + 19 + 19 + 22 + 23 + 24 + 24

__________________________________ 8 = 22




12 ___ 5

= 24




groups



Are You Ready

1 6 ___ 10

= 6 divide 2 ______ 10 divide 2

= 3 __ 5

2 9 ___ 15

= 9 divide 3 ______ 15 divide 3

= 3 __ 5

3 16 ___ 24

= 16 divide 8 ______ 24 divide 8

= 2 __ 3

4 9 ___ 36

= 9 divide 9 ______ 36 divide 9

= 1 __ 4

5 45 ___ 54

= 45 divide 9 ______ 54 divide 9

= 5 __ 6

6 30 ___ 42

= 30 divide 6 ______ 42 divide 6

= 5 __ 7

7 36 ___ 60

= 36 divide 12 _______ 60 divide 12

= 3 __ 5

8 14 ___ 42

= 14 divide 14 _______ 42 divide 14

= 1 __ 3

075

9 4 ⟌ _

300

_ -2 80

20

_ -20

0

075

0875

10 8 ⟌ _

7000

_ -6400

600

_ -560

40

_ -40

0

0875

015

11 20 ⟌ _

300

_ -2 00

100

_ -100

0

015

038

12 50 ⟌ _

1900

_ -15 00

4 00

_ -4 00

0

038

13 67 = 67 ____ 100

= 067

14 31 = 31 ____ 100

= 031

15 7 = 7 ____ 100

= 007

16 146 = 100 + 46

= 100 ____ 100

+ 46 ____ 100

= 1 + 046

= 146

17 013 = 13

18 055 = 55

19 008 = 8

20 116 = 116

LESSON 121

Your Turn







is 10 ___ 20

or 1 __ 2





3


UNIT

6



P(5) + P(not 5) = 1

1 __ 8 + P(not 5) = 1

P(not 5) = 7 __ 8




1 __ 2 + P(odd) = 1

P(odd) = 1 __ 2


Guided Practice













impossible 0
















= 1 __ 4


P(5) + P(not 5) = 1

1 __ 6 + P(not 5) = 1

P(not 5) = 5 __ 6




1 __ 3 + P(not blue) = 1




P(4) + P(not 4) = 1

1 __ 5 + P(not 4) = 1

P(not 4) = 4 __ 5




4 ___ 52

+ P(not queen) = 1

P(not blue) = 48 ___ 52

= 12 ___ 13









selecting


or 2 ___ 13



9 ___ 12



or 1 __ 4



or 1 __ 4













or 5 __ 7



have red hair




or 4 __ 7





coin is 9 ___ 16














landing on blue

LESSON 122

Your Turn


Red 10 ___ 30

= 1 __ 3

Yellow 14 ___ 30

= 7 ___ 15

Blue 6 ___ 30

= 1 __ 5






Guided Practice


A 14 ___ 40

= 7 ___ 20

= 035 = 35

B 7 ___ 40

= 0175 = 175

C 11 ___ 40

= 0275 = 275

D 8 ___ 40

= 1 __ 5 = 020 = 20







4 6 ___ 10








= 8 ___ 48

= 1 __ 6





chosen is 19 ___ 20


1 ___ 20

+ P(not Ryan) = 1

P(not Ryan) = 19 ___ 20


patterns




times



get a hit next time


is 4 ___ 10





or about 417


7 ___ 12



or 417











pocket


LESSON 123

Your Turn



= 60 ____ 400

= 3 ___ 20

= 15



= 12 ___ 75

or 4 ___ 25

Guided Practice




= 50 ____ 400

or 1 __ 8











number of trials








= 33 ____ 330

= 1 ___ 10



= 60 ____ 400

= 3 ___ 20


= 55 + 60 + 23

____________ 400

= 138 ____ 400

= 69 ____ 200


and 4 color choices


P(7th grade + 100 pages) = 85 ____ 250

= 17 ___ 50




7th grade




likely





12 P(male + open toe) = 11 ____ 300











heads and 3 or 4

LESSON 124

Your Turn








Guided Practice








too high

5 98 ____ 100

= x ___ 40

= 39 ___ 40

or 39 times




6 18 ____ 100

= x _____ 5000

= 900 _____ 5000



accepted

times04

times04

times50

times50





events


8 4 ____ 100

= x ____ 200

= 8 ____ 200



9 Yes 6th grade 2 ____ 100

= x ____ 250

= 5 ____ 250

or 5 students

7th grade 4 ____ 100

= x ____ 200

= 8 ____ 200

or 8 students

8th grade 8 ____ 100

= x ____ 150

= 12 ____ 150

or 12 students



10 6 ____ 100

= x ____ 300

= 18 ____ 300










1 ___ 30

= x ____ 180




normal gas pump







4 ____ 100

= x _____ 2400

= 96 _____ 2400



MODULE 12

Ready to Go On

1 H1 H2 T1 T2

2 6 ___ 10

= 3 __ 5

3 13 ___ 20




because 3 ___ 10

= x ___ 80

= 24 ___ 80

or 24 times




times15

times15

times24

times24

times2

times2

times3

times3

times2

times2

times25

times25

times8

times8



Simulations

Are You Ready

075

1 4 ⟌ _

300

_ -2 80

20

_ -20

0

075 = 75

04

2 5 ⟌ _

20

_ -2 0

0

04 = 40

09

3 10 ⟌ _

90

_ -9 0

0

09 = 90

035

4 20 ⟌ _

700

_ -6 00

1 00

_ -1 00

0

035 = 35

0875

5 8 ⟌ _

7000

_ thinsp-6 400

600

_ -560

40

_ -40

0

0875 = 875

005

6 20 ⟌ _

100

_ -1 00

0

005 = 5

076

7 25 ⟌ _

1900

_ -17 50

1 50

_ -1 50

0

076 = 76

046

8 50 ⟌ _

2300

_ -20 50

3 00

_ -3 00

0

046 = 46

9 1 - 1 __ 5 = 5 __

5 - 1 __

5

= 4 __ 5

10 1 - 2 __ 9 = 9 __

9 - 2 __

9

= 7 __ 9

11 1 - 8 ___ 13

= 13 ___ 13

- 8 ___ 13

= 5 ___ 13

12 1 - 3 ___ 20

= 20 ___ 20

- 3 ___ 20

= 17 ___ 20

13 8 ___ 15

times 5 __ 8 =

18 ___ 315

times 5 1 ___

8 1

= 1 __ 3

14 2 __ 9 times 3 __

4 =

12 __ 39

times 3 1 ___

4 2

= 1 __ 6

15 9 ___ 16

times 12 ___ 13

= 9 ___ 416

times 12 3 _____

13

= 27 ___ 52

16 7 ___ 10

times 5 ___ 28

= 17 ___

210 times 5

1 ____

28 4

= 1 __ 8

LESSON 131

Your Turn






= 2 __ 6 = 1 __

3



probability


Guided Practice

1

Basket A Basket B


= 16

7 + 4 + 9

= 20


P(win) =

Number of red balls


3 ___

16 4 ___

20 = 1 __

5


16 use


1 __ 5 = 16 ___

80

3 ___ 16

= 15 ___ 80

Therefore 16 ___ 80

gt 15 ___ 80

so 1 __ 5 gt 3 ___

16


winning




= 6 ___ 11




= 5 ___ 11




= 2 __ 6 = 1 __

3


close


by 20




= 2 __ 6

= 1 __ 3 033 or 33



= 8 ___ 12

= 2 __ 3 067 or 67



= 4 ___ 14

= 2 __ 7 029 or 29


= 26 ___ 52

= 1 __ 2 050 or 50


= 12 - 5 ______ 12

= 7 ___ 12

058 or 58



7 adventure)

P(not a comedy)


= 5 + 7 _________

5 + 7 + 8 = 12 ___

20

= 3 __ 5 060 or 60






= 2 __ 6

= 1 __ 3 033 or 33







= 6 ___ 16

or 3 __ 8







5 ______ 5 + 15

= 5 ___ 20

= 1 __ 4

times16

times16

times5

times5




P(seventh grader) =



= 20 ___ 35

= 4 __ 7


P(eighth grader) =



= 15 ___ 35

= 3 __ 7



more likely










= 8 ___ 20


14 ___ 40

or 7 ___ 20



marble is 8 ___ 20

- 7 ___ 20

= 1 ___ 20



= 10 ___ 20


= 8 ___ 20



marble is 10 ___ 20

- 8 ___ 20

= 2 ___ 20

= 1 ___ 10




= 2 ___ 20


= 5 ___ 20



marble is 5 ___ 20

- 2 ___ 20

= 3 ___ 20



LESSON 132

Your Turn

3 P(ham sandwich) =



= 4 ___ 12

= 1 __ 3




= 6 ___ 12

= 1 __ 2




0 0 0 0

0 0 0 1

0 0 1 0

0 0 1 1


second digit

0 1 0 0

0 1 0 1

0 1 1 0

0 1 1 1


second digit

1 0 0 0

1 0 0 1

1 0 1 0

1 0 1 1


second digit

1 1 0 0

1 1 0 1

1 1 1 0

1 1 1 1



0 0 1 1

0 1 0 1

0 1 1 0

1 0 0 1

1 0 1 0

1 1 0 0





= 6 ___ 16

= 3 __ 8


Guided Practice

1

1 2 3 4 5 6

11 sdot 1

= 1

1 sdot 2

= 2

1 sdot 3

= 3

1 sdot 4

= 4

1 sdot 5

= 5

1 sdot 6

= 6

22 sdot 1

= 2

2 sdot 2

= 4

2 sdot 3

= 6

2 sdot 4

= 8

2 sdot 5

= 10

2 sdot 6

= 12

33 sdot 1

= 3

3 sdot 2

= 6

3 sdot 3

= 9

3 sdot 4

= 12

3 sdot 5

= 15

3 sdot 6

= 18

44 sdot 1

= 4

4 sdot 2

= 8

4 sdot 3

= 12

4 sdot 4

= 16

4 sdot 5

= 20

4 sdot 6

= 24

55 sdot 1

= 5

5 sdot 2

= 10

5 sdot 3

= 15

5 sdot 4

= 20

5 sdot 5

= 25

5 sdot 6

= 30

66 sdot 1

= 6

6 sdot 2

= 12

6 sdot 3

= 18

6 sdot 4

= 24

6 sdot 5

= 30

6 sdot 6

= 36





= 15 ___ 36




= 23 ___ 36

4 H

HHH HHT

H

H

Coin 1

List

Coin 2

Coin 3 T

T

HTH HTT

H T

T

H

H T

THH THT

T

H T

TTH TTT

Coin 1

List

Coin 2

Coin 3




= 1 __ 8


HHT HTH THH



= 3 __ 8




10

Checkered

Red

Checkered

Red

Blue

Black

Checkered

Red

Checkered

Red

Blue

Black

Checkered

Red

Checkered

Red

Blue

Black

Shirt Pants Shoes

Yellow

Red

Green




= 6 ___ 12

= 1 __ 2


Shirt Pants Shoes






= 4 ___ 12

= 1 __ 3



Rhee Pamela

Rhee A

Rhee B

Rhee C

Pamela A

Pamela B

Pamela C

A B

A C

B C



P(Rhee and Pamela)


= 1 ___ 10




1 2 3 4 5 6

11 + 1

= 2

1 + 2

= 3

1 + 3

= 4

1 + 4

= 5

1 + 5

= 6

1 + 6

= 7

22 + 1

= 3

2 + 2

= 4

2 + 3

= 5

2 + 4

= 6

2 + 5

= 7

2 + 6

= 8

33 + 1

= 4

3 + 2

= 5

3 + 3

= 6

3 + 4

= 7

3 + 5

= 8

3 + 6

= 9

44 + 1

= 5

4 + 2

= 6

4 + 3

= 7

4 + 4

= 8

4 + 5

= 9

4 + 6

= 10

55 + 1

= 6

5 + 2

= 7

5 + 3

= 8

5 + 4

= 9

5 + 5

= 10

5 + 6

= 11

66 + 1

= 7

6 + 2

= 8

6 + 3

= 9

6 + 4

= 10

6 + 5

= 11

6 + 6

= 12


are 10 less than 6



= 10 ___ 36

= 5 ___ 18


diagram

Khakis

Shorts

Shirt Pants Shoes

Collared Jeans

Sneakers

Flip-flops

Sandals

Sneakers

Flip-flops

Sandals

Sneakers

Flip-flops

Sandals

Khakis

Shorts

T-shirt Jeans

Sneakers

Flip-flops

Sandals

Sneakers

Flip-flops

Sandals

Sneakers

Flip-flops

Sandals







= 4 ___ 18

= 2 __ 9






outcomes



Therefore




= 7 ___ 30






diagram

Carrots

Sweet potato

Pasta

Peas

Asparagus





Carrots

Sweet potato

Peas

Asparagus





Carrots

Sweet potato

Peas

Asparagus





Carrots

Sweet potato

Peas

Asparagus





Salmon

Beef

Pork



salmon Therefore


= 1 __ 4





Carrots

Sweet potato

PastaPeas

Asparagus

Carrots

Sweet potato

Peas

Asparagus

Carrots

Sweet potato

Peas

Asparagus

Carrots

Sweet potato

Peas

Asparagus

Salmon

Beef

Pork


salmon Therefore


= 1 __ 4















codes













12453 12534 12543 13245 13254 13425

13452 13524 13542 14235 14253 14325

14352 14523 14532 15234 15243 15324













114 115 221 223 224 225 331 332 334 335

441 442 443 445 551 552 553 554 There























LESSON 133

Your Turn




3






heads is 1 __ 2

1 __ 2 = x ___

18

1 __ 2 = x ___

18

x = 9

about 9 times


P(red) = 8 ___ 17

P(not red) = 1 - 8 ___ 17

= 9 ___ 17




Therefore




Guided Practice






3 House 1 __

3



1 __ 3 = x ___

18

1 __ 3 = x ___

18

x = 6














P(hazel) = 9 ___ 28

P(brown) = 10 ___ 28

P(blue) = 7 ___ 28

P(green) = 2 ___ 28






unknown quantity




P(white or gray) = 3 __ 9 = 1 __

3


prediction is then








Y GRR

R R

RR





card is 12 ___ 52


52 use the least


52 Given

that 12 ___ 52

lt 26 ___ 52





P(ace) = 4 ___ 52

= 1 ___ 13


prediction is then


times 39 = 3



P(red card) = 26 ___ 52

= 1 __ 2








times6

times6

times9

times9


1 2 3 4 5 6

1 2 3 4 5 6 7

2 3 4 5 6 7 8

3 4 5 6 7 8 9

4 5 6 7 8 9 10

5 6 7 8 9 10 11

6 7 8 9 10 11 12




P(sum of 8) = 5 ___ 36

P(sum of 11) = 2 ___ 36



gt 2 ___ 36




= 1 __ 4




1 __ 4 times 180 = 45





so P(sum of 3) = 3 ___ 36

= 1 ___ 12


prediction is then


middot 36 = 3





time









that is not green



green is 3 + 9 _________

3 + 8 + 9 = 12 ___



20 = 12 ___

40






6 = 1 ___

12



P(5 or heads) = 1 __ 6 + 1 __

2 - 1 __

6 times 1 __

2 = 7 ___

12





LESSON 134

Your Turn



1 0 0 1 No

2 0 1 No

3 1 No

4 0 1 No

5 1 No

6 0 0 0 1 Yes

7 0 0 1 No

8 0 1 No

9 1 No

10 0 0 0 0 1 Yes




or 20



1 1 0 1 1 0 3

2 0 1 0 0 1 2

3 0 0 0 0 1 1

4 0 0 1 1 0 2

5 1 1 1 1 1 5

6 1 0 0 0 0 1

7 1 0 1 1 0 3

8 1 0 1 0 0 2

9 0 1 1 1 1 4

10 0 0 0 0 0 0



= 70


Guided Practice







numbers each time

2


1 10 3 5 1 2

2 10 4 6 5 0

3 3 2 10 3 3

4 2 10 4 4 1

5 7 3 6 3 2

6 8 4 8 5 0

7 6 2 2 8 2

8 6 5 2 4 1

9 2 2 3 2 4

10 6 3 1 5 2




8 ___ 10

= 80









= 10




= 20














1 3 1

2 4 2 2

3 2 1

4 1 1

5 2 1

6 4 5 3 2

7 4 2 2

8 4 5 2 1

9 4 4 3 3

10 5 1 2


1 + 2 + 1 + 1 + 1 + 2 + 2 + 1 + 3 + 2

_________________________________ 10

= 16 ___ 10

= 1 3 __ 5

















MODULE 13

Ready to Go On


= 12 ___________________ 12 + 12 + 15 + 9 + 12

= 12 ___ 60

= 1 __ 5 020 or 20




= 13 + 13

_______ 52

= 26 ___ 52

= 1 __ 2 050 or 50








or

40





Table of Contents

UNIT 6 Probability


Lesson 122 81

Lesson 123 82

Lesson 124 82


Lesson 132 86

Lesson 133 89

Lesson 134 91



Are You Ready


2 a $700 profit 700



1 1

5 183

_ + 78

261

261

5 16 17

6 677

_ -288

389

389

1 1

7 1188

_ +902

2090

2090

1 15 14

8 2647

_ -1885

762

762

9

-8-10 -4-6 -2 2 4 6 8 100 10

-8-10 -4-6 -2 2 4 6 8 100 11

-8-10 -4-6 -2 2 4 6 8 100 12

-8-10 -4-6 -2 2 4 6 8 100

LESSON 11

Your Turn

7 -8 + ( -1 ) = -9

8 -3 + ( -7 ) = -10

9 -48 + ( -12 ) = -60

10 -32 + ( -38 ) = -70

11 109 + 191 = 300

12 -40 + ( -105 ) = -145

13 -150 + ( -1500 ) = -1650

14 -200 + ( -800 ) = -1000

Guided Practice



c -5 + ( -1 ) = -6



c -2 + ( -7 ) = -9

3 -5 + ( -2 ) = -7

-8-7-6-5 -2-1 0-4-3 4 -1 + ( -3 ) = -4

-5-4-3-2 1 2 3-1 0 5 -3 + ( -7 ) = -10

-10 -9-8-7 -4-3-2-6-5 6 -4 + ( -1 ) = -5

-5-4-3-2 1 2 3-1 0 7 -2 + ( -2 ) = -4

-5-4-3-2 1 2 3-1 0 8 -6 + ( -8 ) = -14

-16 -12 -4 0-8 9 -5 + ( -4 ) = -9

10 -1 + ( -10 ) = -11

11 -9 + ( -1 ) = -10

12 -90 + ( -20 ) = -110

13 -52 + ( -48 ) = -100

14 5 + ( 198 ) = 203

15 -4 + ( -5 ) + ( -6 ) = -15

16 -50 + ( -175 ) + ( -345 ) = -570




UNIT

1



18 a

-4

-6

-8

-2

0

2

-5 + (-3)-3 + (-5)

b No -5 + ( -3 ) is -8 and -3 + ( -5 ) is also -8


score is -11


21 -14 + ( -5 ) + ( -12 ) + ( -23 ) = -54 The total


22 a -10 + ( -8 ) = -18

b -6 + ( -2 ) = -8


23 -100 + ( -75 ) + ( -85 ) = -260


24 a -25 + ( -45 ) + ( -75 ) = -145 Jan withdrew

$145

b -35 + ( -55 ) + ( -65 ) = -155 Julie withdrew

$155








six pairs is 8

LESSON 12

Your Turn

7 -51 + 23

ǀ -51 ǀ - ǀ 23 ǀ = 28

-51 + 23 = -28

8 10 + ( -18 )

ǀ -18 ǀ - ǀ 10 ǀ = 8

10 + ( -18 ) = -8

9 13 + ( -13 )

ǀ 13 ǀ - ǀ -13 ǀ = 0

10 25 + ( -26 )

ǀ -26 ǀ - ǀ 25 ǀ = 1

25 + ( -26 ) = -1

Guided Practice

1 9 + ( -3 ) = 6

2 3 4 5 8 9 106 7 2 -2 + 7 = 5

-3-2-1 0 3 4 51 2 3 -15 + 4 = -11

-18 -16 -12 -10-14 4 1 + ( -4 ) = -3

-5-4-3-2 1 2 3-1 0 5 -4 + 5 = 1

6 -6 + 6 = 0

7 2 + ( -5 ) = -3

8 -3 + 7 = 4

9 -8 + 14 = 6

10 7 + ( -5 ) = 2

11 5 + ( -21 ) = -16

12 14 + ( -14 ) = 0

13 0 + ( -5 ) = -5

14 32 + ( -8 ) = 24





16 -15 + 71 = 56

17 -53 + 45 = -8

18 -79 + 79 = 0

19 -25 + 50 = 25

20 18 + ( -32 ) = -14

21 5 + ( -100 ) = -95

22 -12 + 8 + 7 = 3

23 -8 + ( -2 ) + 3 = -7


24 15 + ( -15 ) + 200 = 200

25 -500 + ( -600 ) + 1200 = 100
















is 8 feet deep








LESSON 13

Your Turn

4 -7 - 2 = -7 + ( -2 )

-7 + ( -2 ) = -9

5 -1 - ( -3 ) = -1 + 3

-1 + 3 = 2

6 3 - 5 = 3 + ( -5 )

3 + ( -5 ) = -2

7 -8 - ( -4 ) = -8 + 4

-8 + 4 = -4

Guided Practice







3 -4 - 5 = -4 + ( -5 ) = -9

0-1-2-3-4-5-6-7-8-9 4 1 - 4 = 1 + -4 = -3

0 1 2 3 4-1-2-3-4 5 8 - 11 = 8 + ( -11 ) = -3

6 -3 - ( -5 ) = -3 + 5 = 2

7 15 - 21 = 15 + ( -21 ) = -6

8 -17 - 1 = -17 + ( -1 ) = -18

9 0 - ( -5 ) = 0 + 5 = 5

10 1 - ( -18 ) = 1 + 18 = 19

11 15 - 1 = 14

12 -3 - ( -45 ) = -3 + 45 = 42

13 19 - ( -19 ) = 19 + 19 = 38

14 -87 - ( -87 ) = -87 + 87 = 0


example 6 - 8 = 6 + ( -8 ) = -2




25 - ( -4 ) = 25 + 4 = 29





-127 - ( -225 ) = -127 + 225 = 98



temperature 90degF

90 - ( -2 ) = 92






-425 - ( -275 ) = -425 + 275 = -150



in temperature

Gas A -8 - ( -21 ) = -8 + 21 = 13

13degC increase

Gas B 12 - ( -12 ) = 12 + 12 = 24

24degC increase

Gas C -15 - ( -19 ) = -15 + 19 = 4

4degC increase













-11 + 4 = -7




LESSON 14

Your Turn




Guided Practice


2 -23+5-7=-18-7  =-25-25degF

3 50-40+87-30=10+87-30  =97-30  =6767points

4 -6+15+15=-6+30  =24

5 9- 4- 17= 9- 21  =-12

6 50-42+10=8+10  =18

7 6+13+7-5=19+2  =21

8 65+43-11=108-11  =97

9 -35-14+45+31=-49+76  =27

10 -12+6-4=-6-4  =-10-34-3+39=-37+39  = 2  -10lt2( -12+6-4)lt( -34-3+39)

11 21-3+8=18+8  =26-14+ 31- 6= 17- 6  =11 26gt11( 21-3+8)gt( -14+31-6)



13 a 5-1+6-1=9






b 45gt-55Barry

17 a 300to400


18 100-18+22-53=51$51

19 45-17-22+18=24$24






MODULE 1

Ready to Go On

1 -8+( -6)=-14

2 -4+( -7)=-11

3 -9+( -12)=-21





4 5 + ( -2 )

ǀ 5 ǀ - ǀ -2 ǀ = 3

5 + ( -2 ) = 3

5 -8 + 4

ǀ -8 ǀ - ǀ 4 ǀ = 4

-8 + 4 = -4

6 15 + ( -8 )

ǀ 15 ǀ - ǀ -8 ǀ = 7

15 + ( -8 ) = 7

7 2 - 9 = 2 + ( -9 )

2 + ( -9 ) = -7

8 -3 - ( -4 ) = -3 + 4-3 + 4 = 1

9 11 - ( -12 ) = 11 + 12

11 + 12 = 23

10 -15 + 9 - 4 = -6 - 4

= -10


11 24 + 8 - 12 - 9 = 24 + 8 - ( 12 + 9 ) = 32 - 21

= 11




after she pays them

-10 + ( -5 ) = -15 $15 decrease



Are You Ready

1 9 times 3 = 27

2 7 times 10 = 70

3 9 times 8 = 72

4 15 times 10 = 150

5 6 times 9 = 54

6 10 times 23 = 230

7 9 times 9 = 81

8 10 times 20 = 200

9 54 divide 9 = 6

10 42 divide 6 = 7

11 24 divide 3 = 8

12 64 divide 8 = 8

13 90 divide 10 = 9

14 56 divide 7 = 8

15 81 divide 9 = 9

16 110 divide 11 = 10

17 12 + 8 divide 212 + 4

16

18 15 - ( 4 + 3 ) times 2

15 - 7 times 2

15 - 14

1

19 18 - ( 8 - 5 ) 2

18 - ( 3 ) 2

18 - 9

9

20 6 + 7 times 3 - 5

6 + 21 - 5

27 - 5

22

21 9 + ( 2 2 + 3 ) 2 times 2

9 + ( 4 + 3 ) 2 times 2

9 + ( 7 ) 2 times 2

9 + 49 times 2

9 + 98

107

22 6 + 5 - 4 times 3 divide 2

6 + 5 - 12 divide 2

6 + 5 - 6

11 - 6

5

LESSON 21

Your Turn


will be negative


-3 ( 5 ) = -15


will be positive

ǀ -10 ǀ times ǀ -2 ǀ = 10 times 2 = 20

( -10 ) ( -2 ) = 20


0 ( -22 ) = 0


will be positive

8 ( 4 ) = 32

Guided Practice

1 -1 ( 9 ) = -9

2 14 ( -2 ) = -28

3 ( -9 ) ( -6 ) = 54

4 ( -2 ) ( 50 ) = -100

5 ( -4 ) ( 15 ) = -60

6 -18 ( 0 ) = 0

7 ( -7 ) ( -7 ) = 49

8 -15 ( 9 ) = -135

9 ( 8 ) ( -12 ) = -96

10 -3 ( -100 ) = 300

11 0 ( -153 ) = 0

12 -6 ( 32 ) = -192

13 7 ( -75 ) = -525 -$525



15 6 ( -2 ) = -12 -12degF








19 5 ( -4 ) = -20 $20 decrease





22 9 ( -6 ) = -54 -54 ( 2 ) = -108 Casey has $108

less in his savings

23 7 ( -8 ) = -56 7 ( -5 ) = -35





160 points


25 a 3 ( 3 ) ( -3 ) = 9 ( -3 ) = -27

b 3 ( -3 ) ( -3 ) = -9 ( -3 ) = 27

c -3 ( -3 ) ( -3 ) = 9 ( -3 ) = -27

d 3 ( 3 ) ( 3 ) ( -3 ) = 9 ( 3 ) ( -3 ) = 27 ( -3 ) = -81

e 3 ( 3 ) ( -3 ) ( -3 ) = 9 ( -3 ) ( -3 ) = -27 ( -3 ) = 81

f 3 ( -3 ) ( -3 ) ( -3 ) = -9 ( -3 ) ( -3 ) = 27 ( -3 ) = -81




negative



3 ( 3 ) ( -3 ) ( -3 ) = 9 ( -3 ) ( -3 ) = 81 the sign of the

product is positive


26 -1 ( 3 ) ( 1 ) 1 ( -3 ) ( 1 ) -1 ( -3 ) ( -1 )









negative

LESSON 22

Your Turn


0 divide ( -6 ) = 0


will be negative

38 divide ( -19 ) = -2


will be positive

-13 divide ( -1 ) = 13



Guided Practice

1 -14 ____ 2 = -7

2 21 divide ( -3 ) = -7

3 26 ____ -13

= -2

4 0 divide ( -4 ) = 0

5 -45 ____ -5 = 9

6 -30 divide ( 10 ) = -3

7 -11 ____ -1

= 11

8 -31 divide ( -31 ) = 1

9 0 ___ -7 = 0

10 -121 _____ -11

= 11

11 84 divide ( -7 ) = -12

12 500 ____ -25

= -20


undefined

14 -63 ____ -21

= 3

15 -40 divide ( 4 ) = -10 $10

16 -22 divide ( 11 ) = -2 2 points

17 -75 divide ( -15 ) = 5 5 targets

18 -99 divide ( -9 ) = 11 11 times





20 -24 divide ( 12 ) = -2 $2







is -200 ft _______ 10 min



= -15 ftmin







-20 divide 5 = -4 and -20 times 5 = -100

-100 lt -4



negative





incorrectly

29 a divide ( -3 ) = 8

a = -24

8 divide b = -4






integers

LESSON 23

Your Turn


3 ( -30 ) + 200 = -90 + 200

= 110

2 -6 ( 13 ) - 21 = -78 - 21

= -99

4 ( -12 ) divide 6 + 2 = -2 + 2

= 0

5 -87 divide ( -3 ) -9 = 29 - 9

= 20

6 40 divide ( -5 ) + 30 = -8 + 30

= 22

7 -39 divide 3 -15 = -13 - 15

= -28



moved further back

9 ( -10 ) divide 2 - 2 = -5 - 2 = -7

( -28 ) divide 4 + 1 = -7 + 1 = -6

10 42 divide ( -3 ) + 9 = -14 + 9 = -5

( -36 ) divide 9 - 2 = -4 - 2 = -6

Guided Practice

1 -6 ( -5 ) + 12 = 30 + 12

= 42

2 3 ( -6 ) - 3 = -18 - 3

= -21

3 -2 ( 8 ) + 7 = -16 + 7

= -9

4 4 ( -13 ) + 20 = -52 + 20

= -32

5 -4 ( 0 ) - 4 = 0 - 4

= -4

6 -3 ( -5 ) - 16 = 15 - 16

= -1

7 7 ( -5 ) + 20 = -35 + 20

= -15

15 dollars less

8 7 ( -10 ) + ( -100 ) = -70 + ( -100 )

= -170

170 fewer points

9 6 ( -4 ) + 10 = -24 + 10

= -14

Ned lost 14 points

10 4 ( -12 ) + 10 = -48 + 10

= -38

$38 less

11 -3 ( -2 ) + 3 = 6 + 3

= 9

3 ( -4 ) + 9 = -12 + 9

= -3

9 gt -3

-3 ( -2 ) + 3 gt 3 ( -4 ) + 9

12 -8 ( -2 ) -20 = 16 -20

= -4

3 ( -2 ) + 2 = - 6 + 2

= -4

-4 = -4

-8 ( -2 ) -20 = 3 ( -2 ) + 2

13 -7 ( 5 ) - 9 = -35 - 9

= -44

-3 ( 20 ) + 10 = -60 + 10

= -50

-44 gt -50

-7 ( 5 ) -9 gt -3 ( 20 ) + 10

14 -16 ( 0 ) -3 = 0 -3

= -3

-8 ( -2 ) -3 = 16 -3

= 13

-3 lt 13

-16 ( 0 ) -3 lt -8 ( -2 ) -3





16 -12 ( -3 ) + 7 = 36 + 7

= 43

17 -42 divide ( -6 ) + 5 -8 = 7 + 5 -8

= 12 -8

= 4

18 10 ( -60 ) -18 = -600 -18

= -618

19 ( -11 ) ( -7 ) + 5 - 82 = 77 + 5 - 82

= 82 - 82

= 0

20 35 divide ( -7 ) + 6 = -5 + 6

= 1

21 -13 ( -2 ) - 16 - 8 = 26 - 16 - 8

= 10 - 8

= 2

22 a 5 ( 2 ) -12 + 3 = 10 -12 + 3

= -2 + 3

= 1

b -3 ( 2 ) -1 + 6 + 7 = -6 -1 + 6 + 7

= -7 + 6 + 7

= -1 + 7

= 6


the game

23 5 ( -4 ) -8 = -20 - 8 = -28

24 -36 divide ( -4 ) + 9 = 9 + 9 = 18


25 a 4 ( -35 ) -9 = -140 -9

= -149

$149 less

b Yes $200 - $149 = $51 $51 gt $50 so Arleen

has enough money

26 a 2 ( -10 ) + 3 = -20 + 3= -17

b 7 + 2 + ( -7 ) = 2




7 of clubs





had change








MODULE 2

Ready to Go On


will be negative

( -2 ) ( 3 ) = -6


will be positive

( -5 ) ( -7 ) = 35



( 8 ) ( -11 ) = -88

4 ( -3 ) ( 2 ) ( -2 ) = ( -6 ) ( -2 ) = 12

5 5 ( -3 ) = -15 -15degC

6 -63 ____ 7 = -9

7 -15 ____ -3

= 5

8 0 ____ -15

= 0

9 96 ____ -12

= -8

10 -24 divide 6 = -4 -4 Ib

11 ( -4 ) ( 5 ) + 8 = -20 + 8

= -12

12 ( -3 ) ( -6 ) -7 = 18 -7

= 11

13 -27 ____ 9 - 11 = -3 - 11

= -14

14 -24 ____ -3

- ( -2 ) = 8 + 2

= 10




( -3 ) ( 5 ) + 10 = -15 + 10 = -5 He had $05 less

than before



Are You Ready

1 9 ___ 14

times 7 __ 6 =

3

2

9 ___ 14

times 7 __ 6 1

2

= 3 __ 4

2 3 __ 5 times 4 __

7 = 12 ___

35

3 11 ___ 8

times 10 ___ 33

= 1

4

11 ___ 8 times 10 ___

33 5

3

= 5 ___ 12

4 4 __ 9 times 3 =

3

4 __ 9 times 3 __

1 1

= 4 __ 3 or 1 1 __

3

5 1 __ 2 divide 1 __

4 = 1 __

2 times 4 __

1

=

1 1 __ 2 times 4 __

1 2

= 2 __ 1 = 2

6 3 __ 8 divide 13 ___

16 = 3 __

8 times 16 ___

13

= 1 3 __ 8 times 16 ___

13 2

= 6 ___ 13

7 2 __ 5 divide 14 ___

15 = 2 __

5 times 15 ___

14

= 1

1 2 __ 5 times 15 ___

14 3

7

= 3 __ 7

8 4 __ 9 divide 16 ___

27 = 4 __

9 times 27 ___

16

= 1

1 4 __ 9 times 27 ___

16 3

4

= 3 __ 4

9 3 __ 5 divide 5 __

6 = 3 __

5 times 6 __

5

= 18 ___ 25

10 1 __ 4 divide 23 ___

24 = 1 __

4 times 24 ___

23

= 1 1 __ 4 times 24 ___

23 6

= 6 ___ 23

11 6 divide 3 __ 5 = 6 __

1 times 5 __

3

= 2

6 __ 1 times 5 __

3 1

= 10 ___ 1 = 10

12 4 __ 5 divide 10 = 4 __

5 times 1 ___

10

= 2

4 __ 5 times 1 ___

10 5

= 2 ___ 25

13 21 - 6 divide 3

21 - 2

19

14 18 + ( 7 - 4 ) times 3

18 + 3 times 3

18 + 9

27

15 5 + ( 8 - 3 ) 2

5 + ( 5 ) 2

5 + 25

30

16 9 + 18 divide 3 + 10

9 + 6 + 10

15 + 10

25

17 60 - ( 3 - 1 ) 4 times 3

60 - ( 2 ) 4 times 3

60 - 16 times 3

60 - 48

12

18 10 - 16 divide 4 times 2 + 6

10 - 4 times 2 + 6

10 - 8 + 6

2 + 6

8

LESSON 31

Your Turn

0 _

571428

4 7 ⟌ _


_ -35

50

_ -49

10

_ -7

30

_ -28

20

_ -14

60

_ -56




-0 _

571428 or -0571428571428hellip


0 _ 3

5 3 ⟌ _


_ -3




0333hellip

045

6 20 ⟌ _

900

_ -8 0

1 00

_ -1 00

0

-045

7 -2 3 __ 4 = -thinsp 4 times 2 + 3

_________ 4 = -11 ____

4

275

4 ⟌ _

1100

_ -8

30

_ -28

20

_ -20

0

-275 terminating

8 7 1 __ 3 =

3 times 7 + 1 _________

3 = 22 ___

3

7 _ 3

3 ⟌ _


_ -21





Guided Practice

06

1 5 ⟌ _

30

_ -3 0

0

06 terminating

089

2 100 ⟌ _

8900

_ -80 0

9 00

_ -9 00

0

-089 terminating


4 ___ 12

= 4 times 1 _____ 4 times 3

= 1 __ 3

0 _ 3

3 ⟌ _


_ -3





0 _

25

4 99 ⟌ _


_ -19 8

520

_ -495




25 or


0 _ 7

5 9 ⟌ _


_ -63





036

6 25 ⟌ _

900

_ -7 5

1 50

_ -1 50

0

-036 terminating

004

7 25 ⟌ _

100

_ -1 00

0

004 terminating

01420 _

45

8 176 ⟌ _

250000000

_ -17 6

7 40

_ -7 04

360

_ -352

80

_ -0


_ -704

960

_ -880




-01420 _


0012

9 1000 ⟌ _

12000

_ -10 00

2 000

_ -2 000

0

0012 terminating


10 -11 1 __ 6 = -thinsp 6 times 11 + 1

_________ 6 = -67 ____

6

111 _ 6

6 ⟌ _

67000

_ -6

07

_ -6

1 0

_ -6


_ -36




- 67 ___ 6

-111 _ 6 or -111666hellip

11 2 9 ___ 10

= 10 times 2 + 9

__________ 10

= 29 ___ 10

29

10 ⟌ _

290

_ -20

9 0

_ -9 0

0

29 ___ 10

29

12 -8 23 ____ 100

= - 100 times 8 + 23

____________ 100

= -823 _____ 100

823

100 ⟌ _

82300

_ -800

23 0

_ -20 0

3 00

_ -3 00

0

-823 _____ 100

-823

13 7 3 ___ 15

= 15 times 7 + 3

__________ 15

= 108 ____ 15

72

15 ⟌ _

1080

_ -105

3 0

_ -3 0

0

108 ____ 15

72

14 54 3 ___ 11

= 11 times 54 + 3

__________ 11

= 597 ____ 11

54 _

27

11 ⟌ _

597000

_ -55

47

_ -44


_ -22

80

_ -77




597 ____ 11

54 _

27 or 542727hellip

15 -3 1 ___ 18

= -thinsp 18 times 3 + 1 __________

18 = -55 ____

18

30 _ 5

18 ⟌ _

55000

_ -54

1 0

_ -0


_ -90




-55 ____ 18

-30 _ 5 or -30555hellip

16 3 2 __ 3 =

3 times 3 + 2 _________

3 = 11 ___

3

3 _ 6

3 ⟌ _

1100

_ -9


_ -1 8





17 -2 7 __ 8 = -

8 times 2 + 7 _________

8 = -23 ____

8

2875

8 ⟌ _

23000

_ -16

7 0

_ -6 4

60

_ -56

40

_ -40

0

-2875 lb




3 ___ 47








= 5 ___ 11

0 _

45

11 ⟌ _


_ -4 4

60

_ -55




5 ___ 11

0 _


20 hockey players


= 6 ___ 10

06

10 ⟌ _

60

_ -6 0

0

6 ___ 10

06 terminating

21 polo players


= 4 ___ 11

036

11 ⟌ _


_ -3 3

70

_ -66




4 ___ 11

0 _


22 lacrosse players


= 10 ___ 15

= 5 times 2 _____ 5 times 3

= 2 __ 3

0 _ 6

3 ⟌ _


_ -1 8




10 ___ 15


23 football players


= 11 ___ 11

= 1

11 ___ 11

1 terminating







25 a -4 7 __ 8 = -thinsp 8 times 4 + 7

_________ 8 = - 39 ___

8

b 4875

8 ⟌ _

39000

_ -32

7 0

_ -6 4

60

_ -56

40

_ -40

0

-4875








is equal

to 85 ___ 16


is

equal to 127 ____ 24

or 52916hellip ft




















090625











0121212hellip


LESSON 32

Your Turn

2

50 1 2 3 4

3 + 1 1 __ 2 = 4 1 __

2

3

0-7 -6 -5 -4 -3 -2 -1

-25 + ( -45 ) = -7

6

0 1 2-5-6-7-8 -4 -3-2-1

-8 + 5 = -3

7

10-1

1 __ 2 + ( - 3 __

4 ) = - 1 __

4

8

3 4 5 6 7 80 1 2-3-2-1

-1 + 7 = 6

9

3 4 50 1 2-5-4 -3-2-1

2 1 __ 2 + ( -2 1 __

2 ) = 0

10

3 4 50 1 2-5-4 -3-2-1

-45 + 45 = 0

11

1-1 0

3 __ 4 + ( - 3 __

4 ) = 0


12 -15 + 35 + 2

-15 + 55

55 - 15

4

13 3 1 __ 4 + ( -2 ) + ( -2 1 __

4 )

3 1 __ 4 + ( -4 1 __

4 )

3 1 __ 4 - 4 1 __

4

-1

14 -275 + ( 325 ) + 5

-6 + 5

-1

15 15 + 8 + ( -3 )

23 + 3

20

Guided Practice

1

3 4 50 1 2-5-4 -3-2-1

-3 + ( -15 ) = -45

2

0 54321-5-4-3-2-1

15 + 35 = 5

3

0 105-1 -05

1 __ 4 + 1 __

2 = 3 __

4

4

0 54321-5-4-3-2-1

-1 1 __ 2 + ( -1 1 __

2 ) = -3

5

0 54321-5-4-3-2-1

3 + ( -5 ) = -2

6

0 54321-5-4-3-2-1

-15 + 4 = 25

7 -2150 + 2150 = 0 $0

8 -874 + 874 = 0 $0

9 275 + ( -2 ) + ( -525 )

275 + ( -725 )

- ( 725 - 275 )

-45

10 -3 + 1 1 __ 2 + 2 1 __

2 = -3 + 4 = 1

11 124 + 92 + 1

-124 + 102

- ( 124 - 102 )

-22

12 -12 + 8 +13

-12 + 21

21 - 12

9

13 45 + ( -12 ) + ( -45 )

45 + ( -45 ) + ( -12 )

0 + ( -12 )

-12

14 1 __ 4 + ( - 3 __

4 ) = - ( 3 __

4 - 1 __

4 ) = - 2 __

4 = - 1 __

2


15 -4 1 __ 2 + 2 = - ( 4 1 __

2 - 2 ) = -2 1 __

2

16 -8 + ( -1 1 __ 8 ) = -9 1 __

8


The sum is 2



19 -$225 + $1500 = $1500 - $225 = $1275

20 -3525 m + ( -85 ) = -4375 m

21 4 3 __ 4 mi + ( -3 1 __

4 mi ) = 1 2 __

4 mi = 1 1 __

2 mi


23 30 + 15 - 25 = 45 - 25 = 20 pts

24 January

Income - Expenses

$1205 - $129060

- ( $129060 - $1205 ) -$8560

February

Income - Expenses

$1183 - $134544

-($134544 - $1183)

-$16244


February

25 June

Income - Expenses

$2413 - $210623

$30677

July

Income - Expenses

$2260 - $195850

$30150

August

Income - Expenses

$2183 - $184512

$33788


$33788 in August






the end of August

Income = $1205 + $1183 + $1664 + $2413

$2260 + $2183 = $10908

Expenses = $129060 + $134544 + $1664 +$210623 + $195850 + $184512

= $1020989

Profit = $10908 - $1020989 + $250

= $94811


28 a 7 ( 10 ) + 3 ( -15 ) = 70 - 45 = 25 pts

b 2 ( 10 ) + 8 ( -15 ) = 20 - 120 = -100 pts








the positive number







LESSON 33

Your Turn

1

-9 -8 -7 -6 -5 -4

-65 - 2 = -85

2

42 30-1 1

1 1 __ 2 - 2 = - 1 __

2

3

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0

-225 - 55 = -775

6

1 2-1 0

025 - ( -150 ) = 175

7

1-1 0

- 1 __ 2 - ( - 3 __

4 ) = 1 __

4

Guided Practice

1

1312111098765 14 15

5 - ( -8 ) = 13

2

-9 -8 -7 -6 -5 -4 -3

3 1 __ 2 - 4 1 __

2 = -8


3

-15 -13 -11 -9 -5-7

-7 - 4 = -11

4

-6 -5 -4 -3 -2 -1 0 1

-05 - 35 = -4

5 -14 - 22 = -36

6 -125 - ( -48 )

-125 + 48

- ( 125 - 48 )

-77

7 1 __ 3 - ( - 2 __

3 ) = 1 __

3 + 2 __

3 = 1

8 65 - ( -14 ) = 65 + 14 = 79

9 - 2 __ 9

- ( -3 )

- 2 __ 9

+ 3

3 - 2 __ 9

2 9 __ 9 - 2 __

9

2 7 __ 9

10 24 3 __ 8

- ( -54 1 __ 8 )

24 3 __ 8

+ 54 1 __ 8

78 4 __ 8

78 1 __ 2

11 -1 m + ( 105 m ) = -15 m


12 -12 1 __ 2 + ( -5 ) = -17 1 __

2

17 1 __ 2

or 175 yards


533 ft - ( -10 ft ) = 533 ft + 10 ft = 543 ft

14 -4500 + (-3015) = -7515 $7515






16 -126degC - 75degC = -201degC

17 -2565 ft - 165 ft + 1245 ft = -297 ft


18 -9500 ft - ( -26000 ft ) = 16500 ft

19 29035 ft - ( -36198 ft ) = 65233 ft

70000 ft - ( -26000 ft ) = 96000 ft


96000 ft - ( 65233 ft ) = 30767 ft


b 78degF - 32degF


21 a -$1258 + ( -$3072 ) = -$4330

b -$4330 + ( -$25 ) = -$6830

c $6830 since -$6830 + $6830 = 0



23 a 5 ft - 72 ft + 22 ft

b 5 ft - 72 ft + 22 ft

5 ft + 22 ft - 72 ft

72 ft - 72 ft



24 a Yes

$425 + $089 + $1099

= $1613 lt $20

b $20 - $1613 = $387 left over





- 7 ___ 16

- 1 __ 4 - 5 ___

16 = ( - 7 ___

16 ) + ( - 1 __

4 ) + ( - 5 ___

16 )

( - 7 ___ 16

) + ( - 5 ___ 16

) + ( - 1 __ 4 ) by CPA

( -7 + ( -5 ) __________

16 ) + ( - 1 __

4 )

( -12 ____ 16

) + ( - 1 __ 4 )

( - 4 times 3 _____ 4 times 4

) + ( - 1 __ 4 )

( - 3 __ 4 ) + ( - 1 __

4 )

( -3 + ( -1 ) __________

4 )

( -4 ___ 4 ) = -1





and c __ d

Both fractions









LESSON 34

Your Turn

1

-8 -7 -6 -5 -2 -1 0-4 -3

2 ( -35 ) = -7

2

-2 -1 0 1 2 3 4-4 -3

-3 ( -125 ) = 375

4 ( - 3 __ 4 ) ( - 4 __

7 ) ( - 2 __

3 ) = -



= - 2 __ 7

5 ( - 2 __ 3 ) ( - 3 __

4 ) ( 4 __


__________ 13 times 41 times 5


= 2 __ 5

6 ( 2 __ 3 ) ( - 9 ___

10 ) ( 5 __

6 ) = -


____________ 13 times 210 times 63


= - 1 __ 2

Guided Practice

1

-5 -2 -1 0-4 -3

5 ( - 2 __ 3 ) = 5 __

1 times ( - 2 __

3 )

= - 5 times 2 _____ 1 times 3

= - 10 ___ 3

= -3 1 __ 3

2

-1 -05 0-2 -15

3 ( - 1 __ 4 ) = 3 __

1 times - 1 __

4

= - 3 times 1 _____ 1 times 4

= - 3 __ 4

3

0 1 2-2 -1

-3 ( - 4 __ 7 ) = 3 __

1 times 4 __

7

= 3 times 4 _____ 1 times 7

= 12 ___ 7

= 1 5 __ 7

4

-2 -1 0 1 2 3 4-4 -3

- 3 __ 4 ( -4 ) = 3 __

4 times 4 __

1

= 3 times 41

______ 14 times 1

= 3 times 1 _____ 1 times 1

= 3 __ 1

= 3

5 4 ( -3 ) = -12

6 -18 ( 5 ) = -9

7 -2 ( -34 ) = 68

8 054 ( 8 ) = 432

9 -5 ( -12 ) = 6

10 -24 ( 3 ) = -72

11 1 __ 2 times 2 __

3 times 3 __

4 = ( 1 times 21

______ 12 times 3

) ( 3 __ 4 )

= ( 1 __ 3 ) ( 3 __

4 )

= 1

1 __ 3 times 3 __

4 1

= 1 __ 4

12 - 4 __ 7 ( -thinsp 3 __

5 ) ( - 7 __

3 ) = ( - 4 times 3 _____

7 times 5 ) ( - 7 __

3 )

= 12 ___ 35

( - 7 __ 3 )

= - 4

5 12 times 7 ______ 35 times 3

1

1

= - 4 times 1 _____ 5 times 1

= - 4 __ 5

13 ( - 1 __ 8 ) times 5 times 2 __

3 = ( - 1 __

8 ) times 5 __

1 times 2 __

3


__________ 48 times 1 times 3


= - 5 ___ 12


14 ( - 2 __ 3

) ( 1 __ 2 ) ( - 6 __


__________ 13 times 21 times 7


= 2 __ 7


16 18 ( -100 ) = -1800 or a $1800 change









amount

b 200 + 6 ( -1998 )

= 200 - 11988

= 8012 $8012





which is 6

20 8 ( -3 1 __ 4 ) = -8 ( 13 ___

4 )

= - 1

8 __ 1 times 13 ___

4 1

= - 2 times 13 ______ 1 times 1

= - 26 ___ 1





(below the surface)

22 5 + ( -3 ) ( 15 )

= 5 + ( -45 )

= 05 cups left





a positive



25 Total score is

2 times ( 6 ) + 16 times ( 05 )

+ 7 times ( -05 ) + 2 times ( -15 )

= 12 + 8 - 35 - 3

= 20 - 65

= 135 pts




= 12 + 5 ( -68 )

= 12 + ( -34 )

= -22degC

27 a b c d

+ + + +

+ + - +

+ - + +

- + + +

- - - +

- - + -

- + - -

+ - - -









LESSON 35

Your Turn

3 28 ___ -4

= - 28 ___ 4 = -07

4 -664 ______ -04

= 664 ____ 04

= 166

5 - 55 ___ 05

= - 55 ___ 5 = -11

6 -4256 _______ 112

= -38


per minute

7 - 5 __

8 ___

- 6 __ 7 = - 5 __

8 divide - 6 __

7

= - 5 __ 8 times - 7 __

6

= 35 ___ 48

8 - 5 ___

12 ____

2 __ 3 = - 5 ___

12 divide 2 __

3

= - 5 ___ 12

times 3 __ 2

= - 15 ___ 24

= - 5 __ 8


9 -4__5

___1__2 =-4__5divide1__

2

=-4__5times2__1

=-8__5

=-13__5

Guided Practice

1 072_____-09=-72___

9 =-08

2 -1__5

___7__5 =-1__

15times5

1__

7=-1times1_____

1times7=-1__7

3 56___-7=-56___7=-8

4 251____4 divide(-3__

8)=251____

4 times-8__

3

=-251times82________

14times3


=-502____3

5 75____-1__5

=-75___1times5__

1=-75times5______

1times1=-375

6 -91____-13=91___

13=7

7 -3__7

___9__4 =-

13__7times4__93


=-4___21

8 - 12____003

=-1200_____

3 =-400


changeindays

=-35L______4day

=-0875 L____day

or-0875Lperday


changeindays

=-$4575________5day



numberofminutes

=-044mi________08min

=-44mi______8min

=-055mileperminute



13 5___-2__

8=-5__

1times8__

24

1=-5times4_____

1times1=-20

14 51__3divide(-11__

2)


2

=-16___3divide3__

2

=-16___3times2__

3


=-32___9

15 -120_____-6 =120____

6 =20

16 -4__5

___-2__

3=

24__5times3__

21=2times3_____

5times1=6__

5

17 103divide(-103)=-103____1 times 1____

103

=-103times1________1times103

=-103____103

=-103____103

=-01

18 -04_____80

=-04___80

=-0005

19 1divide9__5=1__

1times5__

9=5__

9

20 -1___4 ___

23___24

=-1__

14times246

___23


=-6___23

21 -1035_______-23 =1035_____

23 =45


= 21h______7days

=3 h____day


times3days=9hours




=-4times15+3___________4 times1__

9

yd___run

=-763___4 times1__

91yd

___run

=-153__

4yd______

9runs

=-153__4times1__

9

yd___run

=-7__4or-13__

4yardsperrun





_____________________________________ 4

= 414degC ______ 4

= -1035degC per day

25 a total profit


= $1750

______ 7 days

= $250 per day

b $150

_____ day


c total change


= - $490

______ 7 days

= -$70 per day


= 996 m ______ 12 s

= 83 ms





- 3 __

4 ___

4 __ 3

= - 3 __

4 times 3 __

4 = - 9 ___

16



= -629 m





-85degF divide 15 d

= - 1785 ____ 315

degF __ d

= - 17 ___ 3 degF __

d or -5 2 __

3 degF __


d


every day





definition

LESSON 36

Your Turn


3 times 2 1 __ 2 = 7 1 __

2


30 - 7 1 __ 2 = 22 1 __

2


22 1 __ 2 divide 4 = 5 5 __

8











12 3 __ 5 = 126

= 0126


750 times 0126 = 945

750 + 945 = 8445


8445 times 0126 asymp 10641

8445 + 10641 = 95091


95091 times 0126 asymp 11981

95091 + 11981 = 107072


Guided Practice











78 times 3 = 234


234 divide 4 = 585




12 - 3 1 __ 2 = 8 1 __

2

Find half the width

8 1 __ 2 divide 2 = 4 1 __

4


of the page


11 times 1 __ 3 = 3 2 __

3

10 times 3 __ 4 = 7 1 __

2

3 2 __ 3 + 7 1 __

2 = 11 1 __

6


box

11 1 __ 6 lt 12





41 3 __ 4 divide 2 = 20 7 __

8


50 - 20 7 __ 8 = 29 1 __

8




( 78 + 10 ) = 88


88 = 88 ____ 100

= 44 ___ 50


Donovan

44 - 39 = 5


Donovan







19 ___ 37


15 times ( - 1 __ 2 ) = -075







-79 9 ___ 10

divide ( -188 ) = 425


19 1 __ 8 - 1275 - 425 = 2 1 __

8


-28 9 ___ 10

- ( -79 9 ___ 10

) = 51


51 divide 2 1 __ 8 = 24


ascent was 24 ftmin

15 Sample answer



the result by 037



(276 + 159)037 = (276)(037) + (159)(037)




make errors








MODULE 3

Ready to Go On

1 4 1 __ 5 =

5 times 4 + 1 _________

5 = 21 ___

5

42

5 ⟌ _

210

_ -20

1 0

_ -1 0

0

42


2 12 14 ___ 15

= 15 times 12 + 14

___________ 15

= 194 ____ 15

129 _ 3

15 ⟌ _

194000

_ -15

44

_ -30

14 0

_ -13 5

50 first 50

_ -45

50 second 50



129 _ 3 or 12933

3 5 5 ___ 32

= 32 times 5 + 5

__________ 32

= 165 ____ 32

515625

32 ⟌ _

16500000

_ -160

5 0

_ -3 2

1 80

_ -1 60

200

_ -192

80

_ -64

160

_ -160

0

515625

4 45 + 71 = 116

5 5 1 __ 6 + ( -3 5 __

6 ) = 4

6+1 ____

6 -3 5 __

6

= 1 2 __ 6

= 1 1 __ 3

6 - 1 __ 8 -6 7 __

8 = - 1 __

8 + ( -6 7 __

8 )

= -6 8 __ 8

= -7

7 142 - ( -49 ) = 142 + 49

= 191

8 -4 ( 7 ___ 10

) = - 4 __ 1 times 7 ___

10

= - 24 times 7 _______ 1 times 105

= - 2 times 7 _____ 1 times 5

= - 14 ___ 5 or -2 4 __

5

9 -32 ( -56 ) ( 4 ) = 32 times 56 times 4

= 7168

10 - 19 ___ 2 divide 38 ___

7 = -

119 times 7 _______ 2 times 382

= - 1 times 7 _____ 2 times 2

= - 7 __ 4

11 -3201 _______ -33

= 3201 _____ 33

97

33 ⟌ _

3201

_ -297

23 1

_ -23 1

0

97


second day

$8360 + $1535 = $9895


-4 3 __ 4 = -475 or -00475




price

$9895 times -00475 asymp -$47

$9895 - $47 = $9425






prices



Are You Ready

1 3 __ 4 divide 4 __

5 = 3 __

4 times 5 __

4

= 15 ___ 16

2 5 __ 9 divide 10 ___

11 = 5 __

9 times 11 ___

10

= 1

5 __ 9 times 11 ___

10 2

= 11 ___ 18

3 3 __ 8 divide 1 __

2 = 3 __

8 times 2 __

1

= 4

3 __ 8 times 2 __

1 1

= 3 __ 4

4 16 ___ 21

divide 8 __ 9 = 16 ___

21 times 9 __

8

=thinsp 2

7 16 ___ 21

times 9 __ 8 3

1

= 6 __ 7

5 B ( -4 1 )

6 C ( 3 0 )

7 D ( 5 4 )

8 E ( -2 -2 )

9 F ( 0 0 )

10 G ( 0 -4 )

LESSON 41

Your Turn

3 1 __ 6 acre divide ( 1 __

4 hour ) = 1 __

6 times 4 __

1

= 3


2

= 1 times 2 _____ 3 times 1


4 3 cups divide ( 3 __ 4 cups ) = 3 __

1 divide 3 __

4

= 3 __ 1 times 4 __

3

= 1


1

= 1 times 4 _____ 1 times 1

= 4 cups


5 = 3 __

4 times 5 __

1 = 15 ___

4 = 3 3 __

4


6 = 2 ___

1 3 times 6

2 __

1 = 4 __

1 = 4






flavor

Guided Practice

1

Distance (mi) 8 1 __ 2 17 25 1 __

2 34 42 1 __

2

Time (h) 1 __ 2 1 1 1 __

2 2 2 1 __

2

2 3 1 __ 2 miles divide ( 1 1 __

4 hours ) = 7 __

2 divide 5 __

4 mi ___ h

= 7 times 4 _____ 2 times 5

= 1 7 times 4 _____ 2 times 5

2

= 7 times 2 _____ 1 times 5

= 14 ___ 5 mi ___

h


3 5 __ 8 page divide ( 2 __

3 minute ) = 5 __

8 times 3 __

2

= 15 ___ 16

page per minute

4 1 __ 6 foot divide ( 1 __

3 hour ) = 1 __

6 times 3 __

1

= 2 1 times 3 _____ 6 times 1

1

= 1 times 1 _____ 2 times 1


5 5 __ 8 sq ft divide ( 1 __

4 hour ) = 5 __

8 times 4 __

1

= 2 5 times 4 _____ 8 times 1

1

= 5 times 1 _____ 2 times 1

= 5 __ 2 or 2 1 __



UNIT

2



1 divide 1 __

3

= 240 ____ 1 times 3 __

1

= 720 ____ 1



1 divide 1 __

2

= 325 ____ 1 times 2 __

1

= 650 ____ 1




1 __ 4 cup divide ( 2 __

3 serving ) = 1 __

4 times 3 __

2

= 3 __ 8

cup _______

serving


1 __ 3 cup divide ( 3 __

4 serving ) = 1 __

3 times 4 __

3

= 4 __ 9

cup _______

serving




72 and 4 __

9 = 32 ___

72




the rate


1 __ 2 hour

= 1 __




$10 divide ( 35 hours ) = 10 ___ 35

$ __



$125 divide ( 1 __ 2 hours ) = 125 ____

05 $ __





multiply by 60


= 005 ____ 1

$ ____


1 h

= $3 per hour



one


8 cup






originally

c 1 __ 2 divide 1 __

8 = 1 ___

1 2 times 8

4 __

1 = 4 __

1 = 4


sunflower seeds

11 10 songs


= 5 songs ____________

1 commercials


6 mi divide ( 1 __ 2 h ) = 6 __

1 times 2 __

1

= 12 miles per hour

Jessersquos rate


4

= 2 __ 1 times 4 __

1 mi ___ h

= 8 miles per hour

b Terrance

50 mi divide ( 12 mi ___ h ) = 50 ___

1 times 1 ___

12

= 50 ___ 12

h

= 4 1 __ 6 h

= 4 10 ___ 60

h


Jesse

50 mi divide ( 8 mi ___ h ) = 50 ___

1 times 1 __

8

= 50 ___ 8 h

= 6 1 __ 4 h

= 6 15 ___ 60

h



4

= 8 __ 1 times 4 __

3

= 32 ___ 3





13 1 ___ 10

h = 6 ___ 60

h = 6 min

300 words _________ 6 min

= 50 words per min

1 ___ 12

h = 5 ___ 60

h = 5 min

300 words _________ 5 min

= 60 words per min










b For the 10-pack



For the 12-pack








2 day ) = 1 room _____

day so at the same





LESSON 42

Your Turn


was not constant




= 12 ___ 1 = 36 ___

3 = 60 ___




s or s = 12a

Guided Practice

1 45 ___ 1 = 45 90 ___

2 = 45 135 ____

3 = 45 180 ____

4 = 45


2 k = y __ x = 10 ___

2 = 5 y = 5x

3 k = y __ x = 2 __

8 = 1 __

4 y = 1 __

4 x


of proportionality


5 k = y __ x = 74 ___

4 = 1850 y = 1850x

6 $1099

_______ 05 days

= $2198 per day


($1850)

8 100 ft _____ 08 s

= 1000 _____ 8 ft __ s = 125 ft __ s

500 ft _____ 31 s

= 5000 _____ 31


1875 ft ______ 15 s

= 1875 ______ 15





9 $3125

______ 5 h


______ 8 h

= $625 per







12 y = $625 ( 3 ) = $1875

13 300 ft _____ 2 min

= 6750

_____ 45


150 ft _____ min

times 60 min ______ 1 h


14 y = 150x



hours




same factor




of corn

LESSON 43

Your Turn

1 No because 11 ___ 1 ne 16 ___





b k = 60 mi _____ 4 h

= 15 mi ___ h


distance in miles

Guided Practice

1

Time (h) 3 5 9 10

Pages 195 325 585 650


per hour

2

Time (h) 2 3 5 8

Earnings 15 2250 3750 60








5 k = 28 ft ____ 8 s

= 7 __ 2 ft __ s = 35 ft __ s y = 7 __



6 k = $2 ______

8 items = 1 __

4

$ _____

items = 025

$ _____

items so y = 1 __

4 x or


y = cost in dollars


origin



0 minutes





x or 2 __ 5 x




5 = 48




2

2

4

6

8

10

4 6 8 10Time (min)

Dis

tanc

e (m

i)

A

B

O








equation

15 a

2

8

16

24

32

40

4 6 8 10DVDs

Cost

($)

O



cost $20






18 k = 8 ft ___ 4 s










because 65 ___ 1 ne 85 ___

2





distance column

MODULE 4

Ready to Go On

1 $140

_____ 18 ft 2


2 $299

_____ 14 lb


3 $56 ______


$3205

______ 15 gal


4 $160

_____ 5 g


$315

_____ 9 g




3


6 k = $9

___ 8euro

= $27 ____

24euro = 9 __

8 $ __

euro or 1125

$ __

euro So y = 9 __

8 x or





_______ pt

or k = 25 servings

_______ pt

Therefore

y = 5 __ 2




2

2

4

6

8

10

4 6 8 10Pints

Serv

ings

Frozen Yogurt

O





constant rate



Are You Ready

1 22 = 22 ____ 100

= 022

2 75 = 75 ____ 100

= 075

3 6 = 6 ____ 100

= 006

4 189 = 100 + 89

= 100 ____ 100

+ 89 ____ 100

= 1 + 089

= 189

5 059 = 59

6 098 = 98

7 002 = 2

8 133 = 133

9 64

_ timesthinsp05

320

32

10 30

_ timesthinsp007

210

21

11 160

_ timesthinsp015

800

_ +1600

2400

24

12 62

_ timesthinsp032

124

_ +thinsp1860

1984

1984

13 4

_ timesthinsp12

8

_ +thinsp40

48

48

14 1000

_ timesthinsp006

6000

60

LESSON 51

Your Turn

2 x = ( $64 - 52 )

__________ $52

x = $12

____ $52

asymp 23

4 x = ( 18 - 12 )

________ 18

x = 6 ___ 18

asymp 33

5 x = ( 16 - 10 )

________ 16

x = 6 ___ 16

= 375

8 010 times $499 = $4990

$499 + $4990 = $54890

9 030 times $499 = $14970

$499 - $14970 = $34930

Guided Practice

1 x = ( $8 - $5 )

_________ $5

x = $3

___ $5

= 60

2 x = ( 30 - 20 )

_________ 20

x = 10 ___ 20

= 50

3 x = ( 150 - 86 )

__________ 86

x = 64 ___ 86

asymp 74

4 x = ( $389 - $349 )

______________ $349

x = $040

_____ $349

asymp 11

5 x = ( 14 - 13 )

________ 13

x = 1 ___ 13

asymp 8

6 x = ( 16 - 5 )

________ 5

x = 11 ___ 5 = 220

7 x = ( 64 - 36 )

_________ 36

x = 28 ___ 36

asymp 78

8 x = ( 80 - 64 )

_________ 80

x = 16 ___ 80

= 20

9 x = ( 95 - 68 )

_________ 95

x = 27 ___ 95

asymp 28


10 x=( 90-45)_________

90

x=45___90

=50

11 x=( 145-132)__________

145

x=13____145

asymp9

12 x=( 64-21)_________

64

x=43___64

asymp67

13 x=( 16-0)________

16

x=16___16

=100

14 x=( 3-1__

2)_______

3

x=21__

2___

3 asymp83

15 010times$900=$090 $900+$090=$990

16 025times48=12 48-12=36cookies

17 020times340=68 $340-68=272pages

18 050times28=14 28+14=42members

19 004times$29000=$1160 $29000-$1160=$27840

20 130times810=1053 810+1053=1863songs

21 030times20=6 20+6=26miles



ItemOriginal

PriceNew Price

Percent Change

Increase or





24 a 55

x=( 8-3)_______

8 =5__

8=625

x=( 12-7)________

12 =5___

12asymp417



x=( 12-3)________

3

x=9__3=300increase



b $100_____5 =$020each$100_____

4 =$025each



=25

26 Percenterror=( 136-133)___________

136 times100

=03____136

times100asymp2







LESSON 52

Your Turn

2 a 1c+01c11c

b s=11times$28=$3080

3 a 200

b 1c+2c3c

5 a

1b - 024b

1b024b

b 1b-024b=076b

6 a 1p-005p095p

b 095p=$1425




Guided Practice

1 a 035s

b 1s + 035s 135s

c 135 times $3200 = $4320

d 035 times $3200 = $1120


Price

2 Hat $18 15 $270 $2070

3 Book $2250 42 $945 $3195

4 Shirt $3375 75 $2531 $5906

5 Shoes $7499 33 $2475 $9974

6 Clock $4860 100 $4860 $9720

7 Painting $18500 125 $23125 $41625

8 $4500 - 022 ( $4500 ) = $3510

9 $8900 - 033 ( $8900 ) = $5963

10 $2399 - 044 ( $2399 ) = $1343

11 $27999 - 075 ( $27999 ) = $7000





13 a 046b

b 1b - 046b 054b

c 054 times $2900 = $1566

d 046 times $2900 = $1334


Sale Price $201

Regular Price $419

Sale Price $245

Regular Price $279

Sale Price $115

Regular Price $309

Sale Price $272

Regular Price $377

Sale Price $224


$050


$9950


$350

16 p = 127 ( $7400 ) = $9398

s = 127 ( $4800 ) = $6096

j = 127 ( $32500 ) = $41275

2 ( 9398 ) + 3 ( $6096 ) + $41275 = $78359









greater




the coat

LESSON 53

Your Turn

1 005 times $2000 = $100 $100 + $2000 = $2100

3 005 times $40000 = $2000

$2000 times 4 years = $8000

$40000 + $8000 = $48000


Total $2200 + $16875 = $236875

Guided Practice

1 005 times $3000 = $150

2 015 times $7000 = $1050

3 0004 times $10000 = $040

4 15 times $2200 = $3300

5 001 times $8000 = $080

6 20 times $500 = $1000

7 a 007 times $4399 = $308

b $4399 + $308 = $4707

8 115 times $7550 = $8683

9 007 times $2000 = $140


10 003 times $550 = $1650

$1650 times 10 years = $165

$550 + $165 = $715

11 a 090 times $20 = $18

b 1085 times $18 = $1953

12 020 times $2999 = $600 tip

00625 times $2999 = $187 tax

$2999 + $600 + $187 = $3786 total



to the price


14 $3275 + $3988 = $7263 total meal cost

014 times $7263 = $1017 tip

$7263 + $1017 = $8280 total with tip


$7865 times 020 = $1573 tip

$7865 + $1573 - $1180 = $8258 total


0075 times $29375 = $2203 tax

$29375 + $2203 = $31578 total with tax


17 $7999 times 012 = $960 discount

$7999 - $960 = $7039 price before tax





19 $4500 + 00725 = $32625 commission

$750 + $32625 = $107625 total income


$475 + $3850 = $51350 total income










nearest inch

22 a $4998 times 05 = $2499 50 discount

$2499 - $1000 = $1499 $10 discount

b $4998 - $1000 = $3998 $10 discount

$3998 times 05 = $1999 50 discount


$8550 + $1599 = $10149 total


$95 + $1439 = $10939 total



d $10149 times 008 = $812 tax

$10149 + $812 = $10961 total

24 a Store 1 $22 divide 2 = $11

Store 2 $1299 times 09 = $1169




b Store 3 $2098 times 045 = $944






to $2050 per month


____________ 137

times 100 = 05 ____ 137

asymp 36

MODULE 5

Ready to Go On

1 x = ( 63 - 36 )

_________ 36

x = 27 ___ 36

= 75 increase

2 x = ( 50 - 35 )

_________ 50

x = 15 ___ 50

= 30 decrease

3 x = ( 72 - 40 )

_________ 40

x = 32 ___ 40

= 80 increase

4 x = ( 92 - 69 )

_________ 92

x = 23 ___ 92

= 25 decrease

5 $60 times 015 = $9

$60 + $9 = $69

6 $32 times 0125 = $4

$32 + $4 = $36

7 $50 times 022 = $11

$50 - $11 = $39

8 $125 times 030 = $3750

$12500 - $3750 = $8750


$325 + $312 = $637 total income

10 $5310

______ $1735

asymp 31



$700 times 020 = $140

$700 + $140 = $840


5 less than Priya

$840 times 005 = $042

$840 - $042 = $798





$45 times 026 = $1170

$45 + $1170 = $5670






Are You Ready

1 5 + x

2 11 - n

3 -9 ___ y

4 2x - 13

5 2x + 3

= 2 ( 3 ) + 3

= 6 + 3

= 9

6 -4x + 7

= -4 ( 1 ) + 7

= -4 + 7

= 11

7 15x - 25

= 15 ( 3 ) - 25

= 45 - 25

= 2

8 04x + 61

= 04 ( -5 ) + 61

= -20 + 61

= 41

9 2 __ 3 x - 12

= 2 __ 3

( 18 ) - 12

= 2 __ 3

times ( 18 ___ 1 ) - 12

= 36 ___ 3 - 12

= 0

10 - 5 __ 8

x + 10

= - 5 __ 8 ( -8 ) + 10

= - 5 __ 8 times- 8 __

1 + 10

= - 5 ___ 1 8

times- 8 1 __

1 + 10

= - 5 __ 1 times- 1 __

1 + 10

= 5 + 10

= 15

11 1 __ 2 divide 1 __

4

= 1 times 4 _____ 2 times 1

= 1 times 4 2 ______

1 2 times 1

= 1 times 2 _____ 1 times 1

= 2

12 3 __ 8 divide 13 ___

16

= 3 __ 8 times 16 ___

13

= 3 times 16 2 _______

1 8 times 13

= 3 times 2 ______ 1 times 13

= 6 ___ 13

13 2 __ 5 divide 14 ___

15

= 2 __ 5 times 15 ___

14

= 1 2 times 15

3 ________

1 5 times 14 7

= 1 times 3 _____ 1 times 7

= 3 __ 7

14 4 __ 9 divide 16 ___

27

= 4 __ 9 times 27 ___

16

= 1 4 times 27

3 ________

1 9 times 16 4

= 1 times 3 _____ 1 times 4

= 3 __ 4

LESSON 61

Your Turn

2 ( 3x + 1 __ 2 ) + ( 7x - 4 1 __

2 )

= 3x + 7x + 1 __ 2 - 4 1 __

2

= 10x - 4

3 ( -025x - 3 ) - ( 15x + 14 ) = -025x - 3 - 15x - 14

= -175x - 44

4 02(3b - 15c) + 6c

= 06b - 3c + 6c

= 06b + 3c

5 2 __ 3 (6e + 9f - 21g) - 7f

= 4e + 6f - 14g - 7f

= 4e - f - 14g

6 5x - 3(x - 2) - x

= 5x - 3x + 6 - x

= x + 6

7 83 + 34y - 05(12y - 7)

= 83 + 34y - 6y + 35

= 118 - 26y


UNIT

3


Guided Practice


14 + 12n + 23 + 16n

14 + 23 + 12n + 16n

37 + 28n


37 + 28n

2 37 + 28n

37 + 28 ( 9 )

= 37 + 252

= 289

3 14 + 5(x + 3) - 7x = 14 + 5x + 15 - 7x

= 29 - 2x

4 3 ( t - 4 ) - 8 ( 2 - 3t ) = 3t - 12 - 16 + 24t

= 27t - 28

5 63c - 2 ( 15c + 41 ) = 63c - 3c - 82

= 33c - 82

6 9 + 1 __ 2 ( 7n - 26 ) - 8n = 9 + 35n - 13 - 8n

= -4 - 4 1 __ 2 n

7 2x + 12

2 ( x + 6 )

8 12x + 24

12 ( x + 2 )

9 7x + 35

7 ( x + 5 )







15 ( 100 + 5d ) + 20 ( 50 + 7d ) = 15 ( 100 ) + 15 ( 5d ) + 20 ( 50 ) + 20 ( 7d )

= 1500 + 75d + 1000 + 140d

= 1500 + 1000 + 75d + 140d

= 2500 + 215d


New width 60 + w


2(96 + l) + 2(60 + w)

=2(96) + 2l + 2(60) + 2w

192 + 2l + 120 + 2w

192 + 120 + 2l + 2w

312 + 2l + 2w

13 Width 3


Factors 3 and x + 2

Product 3 ( x + 2 ) = 3x + 6

14 Width 4



Product 4 ( 2x - 1 ) = 8x - 4




and 6 times 4 ) So 6 ( 9 ) = 6 ( 5 ) + 6 ( 4 )


6x = ( x + 3 ) + ( 2x + 4 ) +

6x = 3x + 7 +

-3x = _ -3x

3x = 7 +

_ -7 = _ -7

3x - 7 =



10x + 6 = 2 ( 3x - 3 ) + 2 ( )

10x + 6 = 6x - 6 + 2

_ -6x = _ -6x

4x + 6 = - 6 + 2

_ + 6 = _ + 6

4x + 12 = 2

( 4x + 12 ) divide 2 = ( 2 ) divide 2

2x + 6 =


18 a P = 2l + 2w


2(2x + 6) + 2(x)

= 4x + 12 + 2x

= 6x + 12


2(3x - 14) + 2( 1 __ 2 x + 32)

= 6x - 28 + x + 64

= 7x + 36

b (7x + 36) - (6x + 12)

= 7x + 36 - 6x - 12

= x + 24


Let x = 36

2x + 6 = 2 ( 36 ) + 6

= 72 + 6

= 78


Let x = 36

1 __ 2 x + 32 = 1 __

2 ( 36 ) + 32

= 18 + 32

= 50


Let x = 36

3x - 14 = 3 ( 36 ) - 14

= 108 - 14

= 94





( x ) ( x ) = x 2

( x ) 1 = x

( 1 ) 1 = 1


x

x

1

11

1 1

x2 x x x

x 1 1 1x 1 1 1

Area =

x 2 + x + x + x + x + x + 1 + 1 + 1 + 1 + 1 + 1

= x 2 + 5x + 6

( x + 3 ) ( x + 2 ) = x 2 + 5x + 6




1160 = 1334 So 58 ( 23 ) = 58 ( 3 ) + 58 ( 20 )


8 ( 1000 - 3 ) = 8000 - 24 = 7976


Property 8 ( 900 + 90 + 7 ) = 7200 + 720 + 56 =

7976

LESSON 62

Your Turn

1 49 + z = -9

_ -49 _ -49

z = -139

2 r - 171 = -48

_ +171 _ +171

r = 123

3 -3c = 36

-3c ____ -3

= 36 ___ -3

c = -12

5 x - 15 = 525

_ +15 _ +15

x = 675


6 x ___ 35

= -12

x ___ 35

( 35 ) = -12 ( 35 )

x = -42


7 25x = 75

25x ____ 25

= 75 ___ 25

x = 3


Guided Practice



x + ( -134 ) = -17 or x - 134 = -17

x - 134 = -17

_ +134 _ +134

x = 117


warmer



-1 1 __ 2 x = -9

( - 2 __ 3 ) ( - 3 __

2 x ) = ( - 2 __

3 ) ( -9 )

x = 18 ___ 3

x = 6


3 -2x = 34

-2x ____ -2

= 34 ___ -2

x = -17

4 y - 35 = -21

_ + 35 _ + 35

y = 14

y = 14

5 2 __ 3 z = -6

( 3 __ 2 ) 2z ___

3 = ( 3 __

2 ) ( -6 )

z = -9





x - 870737 = 203215

_ +870737 _ +870 737

x = 2902887



2825131 - x = 2320106

_ -2825131 _ -2825131

-x = - 505025

x = 505025




2825131 - x = 1119421

_ -2825131 _ -2825131

-x = -1705710

x = 1705710



1250 - 935 = 315

Use an equation


descends

( -22 1 __ 2 ) x = -315

( - 45 ___ 2 ) x = -315

( - 2 ___ 45

) ( - 45 ___ 2 ) x = -315 ( - 2 ___

45 )

x = 14



4106 - 3205 = 901




34x = 901

34x ____ 34

= 901 ____ 34

x = 265 = 26 1 __ 2




- 25 + x = -07

_ + 25 _ + 25

x = 18





181 - x = -07

_ - 181 _ -181

-x = -188

x = 188





125 + x = 181

_ -125 _ -125

x = 56



their next play

-26 1 __ 3

+ x = 10

+26 1 __ 3

______

+26 1 __ 3

______

x = 36 1 __ 3



( -2 1 __ 2 ) x = -156

( -25 ) x = -156

( -25 _____ -25

) x = -156 ______ -25

x = 624



rate and the time


x __ 5 = 455

( 5 ) x __ 5 = 455 ( 5 )

x = 2275


Sample answer


to $22750



below sea level



lower elevation

20 -4x = -48

( -4x ____ -4

) = -48 _____ -4

x = 12

- 1 __ 4 x = -48

( -4 ) ( - 1 __ 4 ) x = -48 ( -4 )

x = 192

192 ____ 12

= 16








$21085

LESSON 63

Your Turn


purchased






Equation 150 - 35x = 45





Guided Practice

1

+ + ++ ++

+++ + +

+++

2

----

+ ++ ++

- - -

























place 28 +1-tiles


bicycle





Equation 85d + 55 = 123






Equation 125r + 675 = 3175








Equation 45n + 60 = 285




means + 45





1 _ 2

bull n + 45 = 172

Equation 1 __ 2 n + 45 = 172





uniforms equipment


Equation 295u + 548 = 2023





weeks


Equation 500 - 20x = 220






Total bill $88


shirts bill















10 + 5c = 25

10 - 10 + 5c = 25 - 10

5c = 15

5c ___ 5 = 15 ___

5

c = 3

3 children



10 + 5 ( 5 ) = $35














bought

LESSON 64

Your Turn


+ ++ +

+ ++ ++ +

+ ++ ++ +

++


+ ++ +

+ ++ ++ +

+ ++ ++ +

++


++

+ ++ +

++


++ ++


+ + ++ + ++ +

+++

+++

__



+ + ++ + ++

++ +

+++

+++

__


+ + ++++ + +++


+ + +++


++++

______

______

____



++++

+

++

+

++

______

______

____


++++

____


++ __



____

________

++



________

________

++

____


________

________

We get -y = -1

____


tile to each side

++

__ ++ __


++++

__


+++

6 3n + 10 = 37


3n + 10 = 37

-10 ____

-10 ____

3n = 27

3n ___ 3 = 27 ___

3

n = 9


7 n __ 4 - 5 = 15


n __ 4 - 5 = 15

+5 ___

+5 ___

n __ 4 = 20

n __ 4 ( 4 ) = 20 ( 4 )

n = 80

The number is 80

8 -20 = 5 __ 9 ( x - 32 )


-20 = 5 __ 9 ( x - 32 )

-20 = 5 __ 9 x - 160 ____

9

+ 160 ____ 9

______

+ 160 ____ 9

______

- 20 ___ 9 = 5 __

9 x

- 20 ___ 9 divide ( 5 __

9 ) = 5 __

9 x divide ( 5 __

9 )

4 20 times 9

1 _______

9 1 times 5

1 = x

- 4 __ 1 = x

-4 = x


9 120 - 4x = 92


120 - 4x = 92

-120 _____

-120 _____

- 4x = -28

-4x ____ -4

= -28 ____ -4

x = 7



Guided Practice





++++

+ +++++++++


++++

++++++++


++ + + + +




Solve the equation

2 ( 18 ) + 2w = 58

36 + 2w = 58

36 - 36 + 2w = 58 - 36

2w = 22

2w ___ 2 = 22 ___

2

w = 11


4 1200 minus 25x = 500


1200 - 25x = 500

_ -1200 _ -1200

-25x = -700

-25x _____ -25

= -700 _____ -25

x = 28






equation


6 9s + 3 = 57

9s + 3 - 3 = 57 - 3

9s = 54

9s ___ 9 = 54 ___

9

s = 6

7 4d + 6 = 42

4d + 6 - 6 = 42 - 6

4d = 36

4d ___ 4 = 36 ___

4

d = 9

8 115 - 3y = -485

115 - 115 - 3y = -485 - 115

thinsp-3y = -60

-3y

____ -3

= -60 ____ -3

y = 20

9 k __ 2 + 9 = 30

k __ 2 + 9 - 9 = 30 - 9

k __ 2 = 21

2 sdot k __ 2 = 2 sdot 21

k = 42

10 g

__ 3 - 7 = 15

g

__ 3 - 7 + 7 = 15 + 7

g

__ 3 = 22

3 sdot g

__ 3 = 3 sdot 22

g = 66

11 z __ 5 + 3 = -35

z __ 5 + 3 - 3 = -35 - 3

z __ 5 = -38

5 sdot z __ 5 = 5 ( -38 )

z = -190

12 -9h - 15 = 93

-9h - 15 + 15 = 93 + 15

-9h = 108

-9h ____ -9 = 108 ____

-9

h = -12

13 - 1 __ 3 (n + 15) = -2

- 1 __ 3 n - 5 = -2

- 1 __ 3 n - 5 + 5 = -2 + 5

- 1 __ 3 n = 3

-3 sdot - 1 __ 3 n = -3 sdot 3

n = -9

14 -17 + b __ 8 = 13

-17 + 17 + b __ 8 = 13 + 17

b __ 8 = 30

8 sdot b __ 8 = 8 sdot 30

b = 240


15 7 ( c - 12 ) = -21

7c - 84 = -21

_ +84 _ +84

7c = 63

7c ___ 7 = 63 ___

7

c = 9

16 -35 + p

__ 7 = -52

-35 + 35 + p

__ 7 = -52 + 35

p

__ 7 = -17

7 sdot p

__ 7 = -17 sdot 7

p = -119

17 46 = -6t - 8

46 + 8 = -6t - 8 + 8

54 = -6t

54 ___ -6

= -6t ____ -6

t = -9





2 (a + $26) = $264

Solve the equation

2 ( a + 26 ) = 264

2 ( a + 26 )

_________ 2 = 264 ____

2

a + 26 = 132

a + 26 - 26 = 132 - 26

a = 106






Solve the equation

2t - 6 = 20

2t - 6 + 6 = 20 + 6

2t = 26

2t __ 2 = 26 ___

2

t = 13


20 -35 = 5 __ 9 ( x - 32 )

-35 = 5 __ 9 x - 160 ____

9

+ 160 ____ 9

______

+ 160 ____ 9

- 155 ____ 9 = 5 __

9 x

thinsp- 155 ____ 9 divide ( 5 __

9 ) = 5 __

9 x divide ( 5 __

9 )

-thinsp 31

155 times 9

1

= x

9 1

times 5

1

- 31 ___ 1 = x

-31 = x




Solve the equation

-a + 40 = 28

-a + 40 - 40 = 28 - 40

-a = -12

-a ___ -1

= -12 ____ -1

a = 12






Solve the equation

2c + 11 = 73

2c + 11 - 11 = 73 - 11

2c = 62

2c ___ 2 = 62 ___

2

c = 31




price paid


1 __ 2

middot p -6 = 88

Solve the equation

1 __ 2 p - 6 = 88

1 __ 2 p - 6 + 6 = 88 + 6

1 __ 2 p = 94

2 sdot 1 __ 2 p = 2 sdot 94

p = 188



24 115 minus 8n = 19


115 - 8n = 19

_ -115 _ -115

-8n = -96

-8n _____ -8

= -96 _____ -8

n = 12


25 -55x + 056 = -164

-55x + 056 - 056 = -164 - 056

-55x = -22

-55x ______ -22

= -22 _____ -22

x = 04

26 -42x + 315 = -651

-42x + 315 - 315 = -651 - 315

-42x = -966

-42x ______ -42

= -966 ______ -42

x = 23

27 k ___ 52

+ 819 = 472

k ___ 52

+ 819 - 819 = 472 - 819

k ___ 52

= -347

52 sdot k ___ 52

= 52 ( -347 )

k = -18044




divide 2 by 3

3x + 2 = 15

3x ___ 3 + 2 __

3 = 15 ___

3

x + 2 __ 3 = 5

- 2 __ 3

___

- 2 __ 3

___

x = 5 - 2 __ 3

x = 5 times3

___ 1

times3 - 2 __

3

x = 15 ___ 3 - 2 __

3

x = 13 ___ 3 or 4 1 __

3


31 a 2(x + 40) = 234


2x + 80 = 234

2x + 80 - 80 = 234 - 80

2x = 154

2x ___ 2 = 154 ____

2

x = 77

Trey saved $77






32 F = 18c + 32

F - 32 = 18c + 32 - 32

F - 32 = 18c

F - 32 ______ 18

= 18c ____ 18

F - 32 ______ 18

= c

33 P = 2 ( ℓ + w ) P = 2ℓ + 2w

P - 2ℓ = 2ℓ - 2ℓ + 2w

P - 2ℓ = 2w

P - 2ℓ ______ 2 = 2w ___

2

P - 2ℓ ______ 2 = w

34 ax + b = c

ax + b - b = c - b

ax = c - b

ax ___ a = c - b ______ a

x = c - b ______ a

MODULE 6

Ready to Go On




15n + 60 + 12n + 95



2 h + 97 = -97

_ -97 _ -97

h = -194

3 - 3 __ 4 + p = 1 __

2

+ 3 __ 4 + 3 __

4

p = 1 __ 2 + 3 __

4

p = 1 times2

___ 2

times2 + 3 __

4

p = 2 __ 4 + 3 __

4

p = 5 __ 4

4 -15 = -02k

-15 _____ -02

= -02k ______ -02

75 = k


5 y ___

-3 = 1 __

6

y ___

-3 ( -3 ) = 1 __

6 ( -3 )

y = 1 __ 6 times -3 ___

1

y = -3 ___ 6

y = -1 ___ 2

6 - 2 __ 3

m = -12

- 2 __

3 m _____

- 2 __ 3 = -12 ____

- 2 __ 3

m = -12 divide - 2 __ 3

m = -12 ____ 1 divide - 2 __

3

m = -12 ____ 1 times - 3 __

2

m = -36 ____ -2

m = 18

7 24 = - t ___ 45

24 ( 45 ) = - t ___ 45

( 45 )

108 = -t

-108 = t







2 middot d + 15 = 33


9 5n + 8 = 43

5n + 8 - 8 = 43 - 8

5n = 35

5n ___ 5 = 35 ___

5

n = 7

10 y __

6 - 7 = 4

y __

6 - 7 + 7 = 4 + 7

y __

6 = 11

6 sdot y __

6 = 6 sdot 11

y = 66

11 8w - 15 = 57

8w - 15 + 15 = 57 + 15

8w = 72

8w ___ 8 = 72 ___

8

w = 9

12 g

__ 3 + 11 = 25

g

__ 3 + 11 - 11 = 25 - 11

g

__ 3 = 14

3 sdot g

__ 3 = 3 sdot 14

g = 42

13 f __ 5 - 22 = -25

f __ 5 - 22 + 22 = -25 + 22

f __ 5 = -03

5 sdot f __ 5 = 5 ( -03 )

f = -15

14 - 1 __ 4 (p + 16) = 2

- 1 __ 4 p - 4 = 2

- 1 __ 4 p - 4 + 4 = 2 + 4

- 1 __ 4 p = 6

-4 sdot - 1 __ 4 p = 6 sdot -4

p = -24




situation



Are You Ready

1 9w = -54

9w ___ 9 = -54 ____

9

w = -6

2 b - 12 = 3

thinsp _ + 12 = _ + 12

b = 15

3 n __ 4

= -11

4 times n __ 4

= 4 ( -11 )

n = -44

4-7


75 4 6

8 3 - (-5)

3 + 5

8

9 -4 - 5

-9

10 6 - 10

-4

11 -5 - (-3)

-5 + 3

-2

12 8 - (-8)

8 + 8

16

13 9 - 5

4

14 -3 - 9

-12

15 0 - (-6)

0 + 6

6

LESSON 71

Your Turn


_ +5 _ +5

y ge minus2

-4-5 -3 -2-1 0 1 2 3 4 5


minus1 ge -8


2 le 16

5 21 gt 12 + x

_ -12 _ minus12

9 gt x

x lt 9

10 2 3 4 5 6 7 8 9 10


21 gt 12 + 8

21 gt 12 + 8

21 gt 20

6 -10y lt 60

-10y

_____ -10

lt 60 ____ -10

y gt -6

-10-9 -8 -7 -6 -5 -4 -3 -2-1 0 1


-10y lt 60

-10(-5) lt 60

50 lt 60

7 7 ge - t __ 6

7(-6) le - t __ 6 (-6)

-42 le t

t ge -42

-46 -45 -44 -43 -42 -41 -40-47


7 ge - t __ 6

7 ge - ( -36 ____

6 )

7 ge 6



35m le 315

35m ____ 35

le 315 ____ 35

m le 9



Guided Practice

1 -5 le -2

_ +7 _ +7

2 le 5

2 -6 lt -3

-6 ___ -3

gt -3 ___ -3

2 gt 1

3 7 gt -4

_ -7 _ -7

0 gtthinsp -11


4 -1 ge -8

-1 ( -2 ) le -8 ( -2 )

2 le 16

5 n - 5 ge -2

_ +5 _ +5

n ge 3

-5 -4 -3 -2-1 0 3 4 51 2


n - 5 ge -2

4 - 5 ge -2

-1 ge -2

6 3 + x lt 7

_ -3 _ -3

x lt 4

-2-1 0 3 4 5 6 7 81 2


3 + x lt 7

3 + 3 lt 7

6 lt 7

7 -7y le 14

-7y

____ -7 ge 14 ___ -7

y ge -2

-5-6-7 -4 -3 -2-1 0 1 2 3


-7y le 14

-7 ( -1 ) le 14

7 le 14

8 b __ 5 gt -1

b __ 5 ( 5 ) gt -1 ( 5 )

b gt -5

-5-6-7-8 -4 -3 -2-1 0 1 2


b __ 5 gt -1

0 __ 5 gt

-1

0 gt -1

9 a -4t ge -80

b -4t ge -80

-4t ____ -4

le -80 ____ -4

t le 20








number


11 x - 35 gt 15

_ + 35 _ +35

x gt 50

100 20 30 40 50 60 70 80 90100


x - 35 gt 15

51 minus 35 gt 15

16 gt 15

12 193 + y ge 201

_ -193 _ minus193

y ge 8

10 2 3 4 5 6 7 8 9 10


193 + y ge 201

193 + 9 ge 201

202 ge 201

13 - q

__ 7 ge -1

- q

__ 7 ( -7 ) le -1 ( -7 )

q le 7

8 9 105 6 70 1 2 3 4


- q

__ 7 ge -1

- -14 ____ 7 ge

-1

2 ge -1

14 -12x lt 60

-12x _____ -12

gt 60 ____ -12

x gt -5

0-10-9 -8 -7 -6 -5 -4 -3 -2-1


-12x lt 60

-12 ( -4 ) lt 60

48 lt 60

15 5 gt z -3

_ +3 _ +3

8 gt z

z lt 8

10 2 3 4 5 6 7 8 9 10


5 gt z - 3

5 gt 7 - 3

5 gt 4


16 05 le y __

8

05 ( 8 ) le y __

8 ( 8 )

4 le y

y ge 4

8 9 105 6 70 1 2 3 4


05 le y __

8

05 le 8 __

8

05 le 1



12 + x le 28

_ -12 _ -12

x le 16




w __ 7 lt 35

w __ 7 ( 7 ) lt 35 ( 7 )

w lt 245





6s le 42

6s ___ 6 le 42 ___

6

s le 7




3025 + x ge 50

_ -3025 _ -3025

x ge 1975




155w ge 1705

155w ______ 155

ge 1705 _____ 155

w ge 11




thinsp-12t lt -120

-12t _____ -12

gt -120 _____ -12

t gt 10






3s le 10

3s ___ 3 le 10 ___

3

s le 3 1 __ 3


pounds



m ___ 05

le 55

m ___ 05

( 05 ) le 55 ( 05 )

m le 275




125x le 3

125x _____ 125

le 3 ____ 125

x le 24



buy 25 pounds







not true





prism

V = lwh



( 13 ) ( 1 __ 2 ) h lt 65

65h lt 65

65h ____ 65

lt 65 ___ 65

h lt 10





LESSON 72Your Turn


raise



Target amount $6000



must raise equal to




can go on

Starting amount $40

Admission price $6




equal to




are looking for




10 is added to 3x



than 30








looking for












Guided Practice

1

- -- -

-

lt

++++++

+ + ++ + +

+

2

---

gt

+ + ++ + +

+ + ++ + +

+ + +


raise








1250 + 92a ge 7000




greater than 32







inequality






3a + 28 gt 200




cheese to has


075n + 129 le 700












120 + 32n le 720




month month


2100 + 005s ge 2400






668 + 7n gt 2000


day



buys to a month


$7 + $10 middot c le $100

7 + 10c le 100






$22 + $17 middot n le $80

22 + 17n le 80














is given by

95 + 86 + 89 + 3s

________________ 6


tests



95 + 86 + 89 + 3s

________________ 6 ge 90 or

95 + 86 + 89 + 3s ge 540 or

270 + 3s ge 540












So -m gt 0

25 n gt 1 __ n if n gt 1


n = 1 __ n if n = 1

LESSON 73

Your Turn


++

++++

+++

++++

++++

+++

gt


++

++++

+++

++++

++++

+++

gt

- -- -- --

- -- -- --


++

++++

gt


++

++++

gt



+ + +gt


+++++

----

+++++

+ +++++

ge


+++++

----

+++++

+ ++

++++

+++

++++

ge


+++++

+++++

+ +++++

++++

ge


+++++

+++++

+ +++++

++++

ge


+ + + +ge


5 - p

__ 6 le 4

5 - 5 - p

__ 6 le 4 - 5

thinsp- p

__ 6 le -1

thinsp-6 ( - p

__ 6 ) ge -6 ( -1 )

p ge 6


arrow

0 1 4 5 72 3 6 8 9 10



3v - 8 gt 22

v = 9 v = 10 v = 11

3 ( 9 ) - 8 gt 22 3 ( 10 ) - 8 gt 22 3 ( 11 ) - 8 gt 22


results

3 ( 9 ) - 8 gt 22 3 ( 10 ) - 8 gt

22 3 ( 11 ) - 8 gt

22

27 - 8 gt 22 30 - 8 gt

22 33 - 8 gt

22

19 gt 22 22 gt

22 25 gt

22


v = 11


5h + 12 le -3

h = -3 h = -4 h = -5

5 ( -3 ) + 12 le -3 5 ( -4 ) + 12 le -3 5 ( -5 ) + 12 le -3


results

5 ( -3 ) + 12 le -3 5 ( -4 ) + 12 le

-3 5 ( -5 ) + 12 le

-3

-15 + 12 le -3 -20 + 12 le

-3 -25 + 12 le

-3

-3 le -3 -8 le

-3 -13 le

-3

true true true

h = -3 h = -4 h = -5


Guided Practice




5d - 13 lt 32

5d - 13 + 13 lt 32 + 13

5d lt 45

5d ___ 5 lt 45 ___

5

d lt 9


20 6 84 10 12 14 16 18 20


-4b + 9 le -7

-4b + 9 - 9 le -7 - 9

-4b le -16

-4b ____ -4

ge -16 ____ -4

b ge 4


20 6 84 10 12 14 16 18 20


2m + 18 gt - 4

m = -12 m = -11 m = -10

2 ( -12 ) + 18 gt -4 2 ( -11 ) + 18 gt -4 2 ( -10 ) + 18 gt -4


results

2 ( -12 ) + 18 gt -4 2 ( -11 ) + 18 gt

- 4 2 ( -10 ) + 18 gt

- 4

- 24 + 18 gt -4 - 22 + 18 gt

- 4 - 20 + 18 gt

- 4

- 6 gt - 4 - 4 gt

- 4 - 2 gt

- 4


m = -10


- 6y + 3 ge 0

y = 1 y = 1 __ 2 y = 0

-6 ( 1 ) + 3 ge 0 -6 ( 1 __ 2 ) + 3 ge 0 -6 ( 0 ) + 3 ge 0


results

-6 ( 1 ) + 3 ge 0 - 6 ( 1 __

2 ) + 3 ge

0 - 6 ( 0 ) + 3 ge

0

-6 + 3 ge 0 -3 + 3 ge

0 0 + 3 ge

0

-3 ge 0 0 ge

0 3 ge

0

not true true true

y = 1 __ 2

y = 0


65 - 4t ge 15

65 - 65 - 4t ge 15 - 65

-4t ge -5

-4t ____ -4

le -5 ___ -4

t le 125


0 05 1 15 2 25



time






8 2s + 5 ge 49

2s + 5 - 5 ge 49 - 5

2s ge 44

2s ___ 2 ge 44 ___

2

s ge 22

10 14 1612 18 20 22 24 26 28 30

9 -3t + 9 ge -21

-3t + 9 - 9 ge -21 -9

-3t ge -30

-3t ____ -3

le -30 ____ -3

t le 10


10 55 gt -7v + 6

55 - 6 gt -7v + 6 - 6

49 gt - 7v

49 ___ -7 lt -7v ____ -7

v gt -7

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0

11 21 1 __ 3 gt 3m - 2 2 __

3

21 1 __ 3 + 2 2 __

3 gt 3m - 2 2 __

3 + 2 2 __

3

24 gt 3m

24 ___ 3 gt 3m ___

3

8 gt m or m lt 8

0 1 4 5 72 3 6 8 9 10

12 a ___ -8

+ 15 gt 23

a ___ -8

+ 15 - 15 gt 23 - 15

a ___ -8

gt 8

-8 ( a ___ -8

) lt -8 ( 8 )

a lt -64

-70 -68 -66 -64 -62 -60


13 f __ 2 - 22 lt 48

f __ 2 - 22 + 22 lt 48 + 22

f __ 2 lt 70

2 ( f __ 2 ) lt 2 ( 70 )

f lt 140

100 110 120 130 140 150

14 -25 + t __ 2 ge 50

-25 + 25 + t __ 2 ge 50 + 25

t __ 2 ge 75

2 ( t __ 2 ) ge 2 ( 75 )

t ge 150

130 140 150 160 170 180

15 10 + g ___

-9 gt 12

10 - 10 + g ___

-9 gt 12 - 10

g ___

-9 gt 2

-9 ( g ___

-9 ) lt -9 ( 2 )

g lt -18

-20 -18 -14 -12 -10-16

16 252 le -15y + 12

252 - 12 le -15y + 12 - 12

24 le - 15y

24 ____ -15

ge -15y

_____ -15

y le -16

-20 -18 -14 -12 -10-16

17 -36 ge -03a + 12

-36 - 12 ge -03a + 12 - 12

-48 ge -03a

-48 _____ -03

le -03a ______ -03

a ge 16

10 11 12 13 14 16 17 18 19 2015

18 80 - 2w ge 50

80 - 80 - 2w ge 50 - 80

- 2w ge -30

-2w ____ -2

le -30 ____ -2

w le 15



11 12 13 14 and 15


7n - 25 ge 65

7n - 25 + 25 ge 65 + 25

7n ge 90

7n ___ 7 ge 90 ___

7

n ge 12 6 __ 7


be a whole number





21 a

10 3 42 5 6 7 8 9 10

b

10 3 42 5 6 7 8 9 10














MODULE 7

Ready to Go On

1 n + 7 lt -3

thinsp _ -7

_ -7

n lt -10

2 5p ge -30

5p

___ 5 ge -30 ____

5

p ge -6

3 14 lt k + 11

_ -11 _ -11

3 lt k

4 d ___ -3

le minus6

( -3 ) ( d ) ge ( -3 ) ( -6 )

d ge 18


5 c - 25 le 25

_ +25 _ +25

c le 5

6 12 ge -3b

12 ___ -3

le -3b _____ -3

-4 le b




562 + n ge 650

_ -562 _ -562

n ge 88


-20 - 20t ge -100

9 2s + 3 gt 15

_ -3 _ -3

2s gt 12

2s ___ 2

gt 12 ___ 2

s gt 6

10 - d ___ 12

- 6 lt 1

_ +6 _ +6

- d ___ 12

lt 7

12 ( - d ___ 12

) lt 12 ( 7 )

-d lt 84

d gt -84

11 -6w - 18 ge 36

_ +18 _ +18

thinsp-6w ge 54

-6w _____ -6

le 54 ___ -6

w le -9

12 z __ 4 + 22 le 38

_ -22 _ -22

z __ 4 le 16

4 ( z __ 4 ) le 4 ( 16 )

z le 64

13 b __ 9 - 34 lt -36

_ +34 _ +34

b __ 9 lt -2

9 ( b __ 9 ) lt 9 ( -2 )

b lt -18

14 -2p + 12 gt 8

-12 ____

-12 ____

-2p gt -4

-2p

____ -2 lt -4 ___

-2

p lt 2






Are You Ready

1 3x + 4 = 10

3x + 4 - 4 =10 - 4

3x = 6

3x ___ 3 = 6 __

3

x = 2

2 5x - 11 = 34

5x - 11 + 11 = 34 + 11

5x = 45

5x ___ 5 = 45 ___

5

x = 9

3 -2x + 5 = -9

-2x + 5 - 5 = -9 - 5

-2x = -14

-2x ____ -2

= -14 ____ -2

x = 7

4 -11 = 8x + 13

-11 - 13 = 8x + 13 - 13

-24 = 8x

-24 ____ 8 = 8x ___

8

-3 = x

5 4x - 7 = -27

4x - 7 + 7 = -27 + 7

4x = -20

4x ___ 4 = -20 ____

4

x = -5

6 1 __ 2 x + 16 = 39

1 __ 2 x + 16 - 16 = 39 - 16

1 __ 2 x = 23

( 2 ) 1 __ 2 x = ( 2 ) 23

x = 46

7 12 = 2x - 16

12 + 16 = 2x - 16 + 16

28 = 2x

28 ___ 2 = 2x ___

2

14 = x

8 5x - 15 = -65

5x - 15 + 15 = -65 + 15

5x = -50

5x ___ 5 = -50 ____

5

x = -10

9 x __ 5 = 18 ___

30


30x = 90

30x ____ 30

= 90 ___ 30

x = 3

10 x ___ 12

= 24 ___ 36


36x = 288

36x ____ 36

= 288 ____ 36

x = 8

11 3 __ 9 = x __

3


9 = 9x

9 __ 9 = 9x ___

9

1 = x

12 14 ___ 15

= x ___ 75


1050 = 15x

1050 _____ 15

= 15x ____ 15

70 = x

13 8 __ x = 14 ___ 7


56 = 14x

56 ___ 14

= 14x ____ 14

4 = x

14 14 ___ x = 2 __ 5


70 = 2x

70 ___ 2 = 2x ___

2

35 = x

15 5 __ 6 = x ___

15


75 = 6x

75 ___ 6 = 6x ___

6

125 = x


UNIT

4


16 81 ___ 33

= x ____ 55


4455 = 33x

4455 _____ 33

= 33x ____ 33

135 = x

LESSON 81

Your Turn


= 22 ft


= 10 ft


Guided Practice

1

Blueprint

length (in)3 6 9 12 15 18

Actual

length (ft)5 10 15 20 25 30



= 15 in







= 25 m


= 15 m


4 a


scales



the drawing


6 a 2 in times 40 cm ______ 1 in

= 80 cm

15 in times 40 cm ______ 1 in

= 60 cm


b 80 cm times 60 cm = 4800 c m 2

c 80 cm times 1 in _______ 254 cm

asymp 315 in

60 cm times 1 in _______ 254 cm

asymp 236 in


315 in by 236 in



= 24 units


= 15 units


15 units




larger



r = 810 m ______ 54 ft

r = 150 m ______ 1 ft



= 648 in



b = 162 bricks



h = 30 ft times 126 cm _______ 1 ft

h = 378 cm



_________ 63 cm

n = 6 toothpicks



asymp 5 swabs






s = 10 cm times 2 ft _____ 1 cm

s = 20 ft










original size


2

LESSON 82

Guided Practice















triangle






6 cm

3 cm120˚








same angle measures








between them






LESSON 83

Guided Practice


2 rectangle

3 triangle





















volume is 480 in 3





LESSON 84

Your Turn



intersecting lines




mangFGD and mangDGC



mangBGC and mangCGD



Because lines _

BE and _




mangCGD = 55deg



3x ___ 3 = 126deg ____

3

x = 42deg





Guided Practice




so mangDGE = 30deg





value by 3














measures are equal

mangKMI = mangHMG

84 = 4x

84 ___ 4 = 4x ___

4

x = 21deg



x + 84 - 84 = 180 - 84

x = 96

mangKMH = 96deg



x + 62 - 62 = 180 - 62

x = 118

mangCBE = 118deg



x + 62 - 62 = 90 - 62

x = 28

mangABF = 28deg




x + 28 - 28 = 152

mangCBA = 152deg




2x ___ 2 = 86deg ___

2





6x ___ 6 = 180deg ____

6









_ -48deg268 _ -48deg268

mangK = 41deg3352






greater than 38deg











( 90 - ( 90 - xdeg ) ) = ( 90 - 90 + xdeg ) = xdeg

MODULE 8

Ready to Go On

1

Living


Actual


Blueprint





created




A point is another




mangFGE = 50deg




3 ( mangY ) ________ 3 = 120deg ____

3

mangY = 40deg

mangY = 40deg


rooms or gardens



Are You Ready

1 416

_ times 13

1248

_ +thinsp4160

5408

5408

2 647

_ times thinsp04

2588

2588

3 705

_ times thinsp94

2820

_ +thinsp63450

66270

6627

4 256

_ timesthinsp049

2304

_ +thinsp10240

12544

12544

5 1 __ 2 ( 14 ) ( 10 )

7 ( 10 )

70 i n 2

6 ( 35 ) ( 35 )

1225 ft 2

7 ( 8 1 __ 2 ) ( 6 )

17 ___ 1 2 sdot 6 3 __

1

51 i n 2

8 1 __ 2 ( 125 ) ( 24 )

1 __ 2 ( 24 ) ( 125 )

( 12 ) ( 125 )

15 m 2

LESSON 91

Your Turn

3 d = 11 cm

C = πd

C asymp 314 ( 11 )

C asymp 3454


6 C = πd

44 asymp 314d

44 ____ 314

asymp d

d asymp 1401 yards


rate

1401 divide 7 = 2001


Guided Practice

1 d = 9 in

C asymp 314 ( 9 )

C asymp 2826 in

2 r = 7 cm

C = 2πr

C asymp 2 ( 22 ___ 7 ) ( 7 )

C asymp 44 cm

3 d = 25 m

C = πd

C asymp 314 ( 25 )

C asymp 785 m

4 r = 48 yd

C = 2πr

C asymp 2 ( 314 ) ( 48 )

C asymp 3014 yd

5 r = 75 in

C = 2πr

C asymp 2 ( 314 ) ( 75 )

C asymp 471 in

6 Find the diameter

C = πd

66 asymp 314d

66 ____ 314

asymp 314d _____ 314

21 asymp d

Find the cost


25 times $045 = $1125



r = 05 yd

d = 1 yd


2πr = 788

2πr ___ 2π

= 788 ____ 2π

r asymp 788 _______ 2 ( 314 )

r asymp 1255 ft

d = 2r asymp 2 ( 1255 ft )

d asymp 2510 ft

9 d = 2r so r = d __ 2 asymp 34 ___

2

r asymp 17 in

C = πd asymp 314 ( 34 )

C = 1068 in





11 d = 59 ft

C = πd

C asymp 314 ( 59 )

C asymp 1853 ft

12 r = 56 cm

C = 2πr

C asymp 2 ( 22 ___ 7 ) ( 56 )

C asymp 352 cm

13 d = 35 in

C = πd

C asymp ( 22 ___ 7 ) ( 35 )

C asymp 110 in



15 r = 94 ft

d = 2r = 2 ( 94 )

d = 188 ft

C = πd

C asymp 314 ( 188 )

C asymp 590 ft

16 d = 475 in

r = d __ 2 = 475 ____

2

r = 2375 in

C = πd

C asymp 314 ( 475 )

C asymp 14915 in

17 d = 18 in

r = d __ 2 = 18 ___

2

r = 9 in

C = πd

C asymp 314 ( 18 )

C asymp 5652 in

18 r = 15 ft

C = 2πr

C asymp 2 ( 314 ) ( 15 ) = 942 ft


so ( 942 ) ( 075 ) = 7065 or about $707

19 C = πd

C asymp ( 22 ___ 7 ) ( 63 )

C asymp 198 ft




20 C = πd asymp 314 ( 2 )

C asymp 628 ft

Converting km to ft

2 km sdot ( 3280 ft _______

1 km ) = 6560 ft

6560 ft

_______ 628 ft

= 104459




1 __ 2 C = 1 __

2 πd asymp 1 __

2 sdot 314 ( 025 ) = 03925





Height 180 ft



_______ 2 ( 314 )

asymp 48 ft

Diameter d = 2r = 2 ( 48 ) = 96 ft



plus the diameter

1 __ 2 C = 1 __

2 πd asymp 1 __

2 sdot 314 ( 30 ) = 471



per linear foot

( 771 ft ) ( $925 _____

ft ) = $71318



C = πd asymp 314 ( 18 ) = 5652 ft


inches to feet

( 54 in ) ( 1 ft _____ 12 in

) = 45 ft



5652 ft _______ 45 ft

= 1256


must buy 13 strands


C inner

= πd asymp 314 ( 150 ) = 471 ft


C outer

= πd asymp 314 ( 154 ) = 48356 ft








smaller gear





314 ( 75 ) - 314 ( 732 ) = 314 ( 018 ) asymp 057

057 m asymp 187 ft

LESSON 92

Your Turn

4 A = π r 2 A = π ( 10 ) 2

A asymp 314 ( 10 ) 2


A asymp 314 f t 2

Guided Practice

1 r = d __ 2 = 14 ___

2 = 7 m

A = π r 2 A = π ( 7 ) 2

A asymp 314 ( 7 ) 2

A asymp 314 sdot 49

A asymp 1539 m 2

2 A = π r 2 A = π ( 12 ) 2

A asymp 314 ( 12 ) 2


A asymp 4522 m m 2

3 r = d __ 2 = 20 ___

2 = 10 yd

A = π r 2 A = π ( 10 ) 2

A asymp 314 ( 10 ) 2


A asymp 314 y d 2

4 A = π r 2 A = π ( 8 ) 2

A asymp 314 ( 8 ) 2

A asymp 314 sdot 64

A asymp 20096 i n 2

5 r = d __ 2 = 12 ___

2 = 6 cm

A = π r 2 A = π ( 6 ) 2

A asymp 314 ( 6 ) 2

A asymp 314 sdot 36

A asymp 11304 c m 2

6 r = d __ 2 = 13 ___

2 = 65 in

A = π r 2 A = π ( 65 ) 2

A asymp 314 ( 65 ) 2


A asymp 13267 i n 2

7 C = 4π = 2πr

4π ___ 2π

= 2πr ___ 2π

r = 2

A = π r 2 A = π ( 2 ) 2


8 C = 12π = 2πr

12π ____ 2π

= 2πr ___ 2π

r = 6

A = π r 2 A = π ( 6 ) 2


9 C = π __ 2 = 2πr

π __ 2 divide 2π = 2πr ___

2π

π __ 2 sdot 1 ___

2π = r

1 __ 4 = r

A = π r 2

A = π ( 1 __ 4 ) 2 = π ( 1 ___

16 )

A = π ___ 16

square units

10 A = π r 2 = 64π

π r 2 ___ π = 64π ____ π

r 2 = 64

r = 8

C = 2πr

= 2π ( 8 )

=16π yd

11 A = π r 2


12 r = d __ 2 = 10 ___

2 = 5 in

A = π r 2 A = π ( 5 ) 2

A asymp 314 ( 5 ) 2

A asymp 314 sdot 25

A asymp 785 i n 2

13 A = π r 2 A = π ( 16 ) 2

A asymp 314 ( 16 ) 2


A asymp 80384 c m 2


diameter 36 in

r = d __ 2 = 36 ___

2 = 18 in

A semicircle

= 1 __ 2 π r 2

A semicircle

= 1 __ 2 π ( 18 ) 2

A semicircle

asymp 1 __ 2 ( 314 ) ( 18 ) 2

A semicircle


A asymp 50868 i n 2




A = π r 2 A = π ( 3 ) 2

A asymp 314 ( 3 ) 2



A r = 75 mi

- A r = 50 mi

π ( 75 ) 2 - π ( 50 ) 2



greater







s 2 minus π r 2 = 1 2 2 minus π ( 6 ) 2

= 144 minus π ( 36 )

asymp 144 minus 11304 = 3096










16π in 2





about $20

_____ π ( 9 ) 2



_____ π ( 6 ) 2

asymp $009






A = π r 2 = π ( 8 ) 2

= π ( 64 )

asymp 20096


201 mi 2




A new

minus A old

= π ( 10 ) 2 - π ( 8 ) 2

= π ( 1 0 2 - 8 2 ) = π ( 100 - 64 )

= π ( 36 ) asymp 11304


more area









A


A whole target

=

π ( 15 ) 2 ______

π ( 75 ) 2

= ( 15 ) 2

_____ ( 75 ) 2

= 225 _____ 5625

= 004


LESSON 93

Your Turn


two right triangles





A = ℓw = 11 sdot 4 = 44 f t 2


A = 1 __ 2 bh = 1 __



A = 1 __ 2 bh = 1 __

2 sdot 3 sdot 3 = 45 f t 2


44 + 3 + 45 = 515 f t 2


semicircle



or 10 ___ 2 = 5 m


A = s 2 = 1 0 2 = 100 m 2


A = 1 __ 2 π r 2

A asymp 1 __ 2 sdot 314 sdot ( 5 ) 2


A asymp 3925 m 2


100 + 3925 = 13925 m 2







4 __ 2 = 2 ft


A = ℓw = 5 sdot 4 = 20 f t 2


A = π r 2 A asymp 314 sdot ( 2 ) 2



two areas

20 + 1256 = 3256 f t 2



( 3256 f t 2 ) ( $28 ____

f t 2 ) = $91168


Guided Practice


a parallelogram



2 ( 4 ) ( 2 ) = 4




2 parallelogram

15 cm 2


4 + 15 + 15 = 34 cm 2


2 Method 1

A 1 = ℓw A

2 = ℓw

= 12 sdot 9 = 20 sdot 9 = 108 = 180


Method 2

A 1 = ℓw A

2 = ℓw

= 9 sdot 8 = 12 sdot 8 = 72 = 216






1 + b

2 )

A = 1 __ 2 ( 5 ) ( 7 + 4 )

A = 1 __ 2 ( 5 ) ( 11 ) = 275 f t 2



275 + 16 = 435 ft 2


find the cost

( 435 f t 2 ) ( $225 _____

f t 2 ) = $9788


simpler figures




A asymp 1 __ 2 sdot 314 sdot ( 13 ) 2


A asymp 26533 i n 2


676 + 26533 = 94133 in 2






A = 1 __ 2 sdot 6 sdot 7

A = 1 __ 2 sdot 42

A = 21 f t 2


40 + 21 = 61 f t 2


square foot

( 61 f t 2 ) ( $250 _____

f t 2 ) = $15250

7

O 42-2-4

2

-4

y

A (-2 4) B (0 4)

C (2 1)D (5 1)

E (5 -2)F (-2 -2)










Area of trapezoid

A = 1 __ 2 h ( b

1 + b

2 )

A = 1 __ 2 ( 3 ) ( 4 + 2 )

A = 1 __ 2 ( 3 ) ( 6 ) = 9 square units











A = 1 __ 2 sdot 8 sdot 8

A = 1 __ 2 sdot 64

A = 32 m 2


A asymp 1 __ 4 sdot 314 sdot ( 8 ) 2


A asymp 5024 f t 2


64 + 32 + 5024 = 14624 m 2









48 + 1256 = 6056 cm 2






A = 1 __ 2 sdot 1 sdot 1

A = 1 __ 2 sdot 1

A = 05 f t 2


3 + 05 = 35 ft 2





( 42 f t 2 ) ( $125 _____

f t 2 ) = $5250


area of triangle

325 ft 2 - 75 ft 2 = 25 ft 2



square is 5 ft






20 ( 15 ) or 300 carrots








triangle



A = 1 __ 2 sdot 12 sdot 8

A = 1 __ 2 sdot 96

A = 48 i n 2


144 + 48 = 192 in 2










420 - 176625 = 243375 in 2 or 243 3 __

8 i n 2










A asymp 1 __ 2 sdot 314 sdot ( 20 ) 2


A asymp 628 i n 2


1600 + 628 = 2228 in 2






40 + 2 sdot 4 = 48 in




total of 40 + 4 = 44 in






A asymp 1 __ 2 sdot 314 sdot ( 24 ) 2


A asymp 90432 i n 2


the sum

2112 + 90432 asymp 3016 in 2

LESSON 94

Your Turn


B = l times w

= 9 times 2

= 18 square inches


P = 2 ( 9 ) + 2 ( 2 )

= 18 + 4 = 22 inches


S = Ph + 2B

S = 22 ( 1 1 __ 2 ) + 2 ( 18 )

= 33 + 36

= 69



B = times w

= 12 times 12

= 144 square inches


P = 4 ( 12 )

= 48 inches


S = Ph + 2B

S = 48 ( 12 ) + 2 ( 144 )

= 576 + 288

= 864 square inches


B = l times w

= 8 times 8

= 64 square inches


P = 4 ( 8 )

= 32 inches


S = Ph + 2B

S = 32 ( 8 ) + 2 ( 64 )

= 256 + 128

= 384 square inches








Guided Practice



Height = 7 ft

Base area = 1 __ 2 ( 3 ) ( 8 ) = 12 ft 2

Surface area

S = ( 18 ft ) ( 7 ft ) + 2 ( 12 ft 2 ) = 150 ft 2


B = l times w

= 25 times 25

= 625 m 2


P = 4 ( 25 )

= 10 m


S = Ph + 2B

S = 10 ( 25 ) + 2 ( 625 )

= 25 + 125

= 375


S = 375 m 2


B = l times w

= 11 times 9

= 99 m 2


prism

P = 2 ( 11 ) + 2 ( 9 )

= 22 + 18

= 40 m


S = Ph + 2B

S = 40 ( 7 ) + 2 ( 99 )

= 280 + 198

= 478


S = 478 m 2


A = ( 25 ) ( 25 ) = 625



= 375 + 478 -2 ( 625 ) = 503 m 2




surface




B = l times w

= 10 times 3

= 30 in 2


P = 2 ( 10 ) + 2 ( 3 )

= 20 + 6

= 26 in


S = Ph + 2B

S = 26 ( 4 ) + 2 ( 30 )

=104 + 60

= 164 in 2



B = l times w

= 20 times 15

= 300 cm 2


P = 2 ( 20 ) + 2 ( 15 )

= 40 + 30

= 70 cm


S = Ph + 2B

S = 70 ( 9 ) + 2 ( 300 )

= 630 + 600

= 1230 cm 2


1230 - 300 = 930 cm 2



Convert cm 2 to mm

2


2 ________

1 cm 2 = 93000 mm

2


93000 divide 25 = 3720




= 2 + 3 = 5 in 2


Perimeter = 3 + 3 + 1 + 2 + 2 + 1

= 12 in


S = Ph + 2B

S = 12 ( 3 ) + 2 ( 5 )

= 36 + 10

= 46 in 2



Perimeter = 25 + 25 + 3 = 8 ft

Base area = 1 __ 2 ( 2 ) ( 3 ) = 3 ft 2


= 8 ( 4 ) + 2 ( 3 )

= 32 + 6 = 38 ft 2


Perimeter = 2 ( 3 ) + 2 ( 4 ) = 14 ft



= 14 ( 2 ) + 2 ( 12 )

= 28 + 24 = 52 ft 2



Surface area = 38 + 52 - 12 - 12 = 66 ft 2







1 + b

2 ) h

1 __ 2 ( 16 + 48 ) 12 = 384 in

2


P = 48 + 20 + 16 + 20 = 104 in


S = Ph + 2B

S = 104 ( 24 ) + 2 ( 384 )

= 2496 + 768

= 3264 in 2



B = l times w

= 7 times l

= 7 ft 2


P = 2 ( 7 ) + 2 ( 1 )

= 14 + 2

= 16 ft


S = Ph + 2B

S = 16 ( 2 ) + 2 ( 7 )

= 32 + 14

= 46 f t 2


B = l times w

= 1 times 1

= 1 ft 2


P = 2 ( 1 ) + 2 ( 1 )

= 2 + 2 = 4 ft


S = Ph + 2B

S = 4 ( 3 ) + 2 ( 1 )

= 12 + 2

= 14 ft 2



Surface area = 46 + 14 - 1 - 1 = 58 ft 2



58 divide 25 = 232


needed


3 times 679 = 2037




B = l times w

= 27 times 24

= 648 cm 2


P = 2 ( 27 ) + 2 ( 24 )

= 54 + 48

= 102 cm


S = Ph + 2B

S = 102 ( 10 ) + 2 ( 648 )

= 1020 + 1296

= 2316 cm 2






2 ( 2l + 2w ) = 2P


New S = 2Ph + 2 ( 4B )


doubles



B = l times w

= 25 times 25

= 625 ft 2


P = 4 ( 25 )

= 10 ft


S = Ph + 2B

S = 10 ( 35 ) + 2 ( 625 )

= 35 + 135

= 485 ft 2



485 - 625 = 4225 ft 2



4225 _____ 485

times 100 asymp 87




15


r = 2 in

9 in


A = πr 2

asymp 31 4 ( 2 ) 2 = 1256 in 2


C = πd

asymp 314 ( 4 ) = 1256 in 2




S = Ch + 2B

asymp 1256 ( 9 ) + 2 ( 1256 ) = 13816 in 2





1500 times 1382 = 207300 in 2



( 207300 in 2 ) 1 ft 2 _______

144 in 2 asymp 1440 ft 2






show

LESSON 95

Your Turn


B = 1 __ 2 bh

= 1 __ 2 ( 24 ) 7

= 84 m 2


V = Bh

= ( 84 ) ( 22 )

= 1848 m 3



B = 1 __ 2 ( b 1 + b 2 ) h

= 1 __ 2 ( 8 + 12 ) 10

= 1 __ 2 ( 20 ) 10 = 100 cm

2


V = Bh

= ( 100 ) ( 22 )

= 2200 cm 3




B = bh

= ( 13 ) 13

= 169 in 2


V = Bh

= ( 169 ) ( 30 )

= 5070 in 3



B = 1 __ 2 bh

= 1 __ 2 ( 9 ) 13

= 585 in 2


V = Bh

= ( 585 ) ( 30 )

= 1755 in 3


5070 + 1755 = 6825 in 3


Guided Practice

1 B = 1 __ 2 bh = 1 __

2 ( 8 ) ( 3 ) = 12 ft 2

V = Bh = ( 12 times 7 ) ft 3 = 84 ft 3

2 B = 1 __ 2 ( b 1 + b 2 ) h = 1 __

2 ( 15 + 5 ) 3 = 30 m

2

V = Bh = ( 30 times 11 ) m 3 = 330 m 3


B = bh

= ( 4 ) 6 = 24 ft 2


V = Bh

= ( 24 ) ( 12 ) = 288 ft 3



B = 1 __ 2 bh

= 1 __ 2 ( 6 ) 4 = 12 ft 2


V = Bh

= ( 12 ) ( 6 ) = 72 ft 3



288 + 72 = 360 ft 3



B = bh

= ( 40 ) ( 50 ) = 2000 ft 2


V = Bh

= ( 2000 ) ( 15 ) = 30000 ft 3


B = 1 __ 2 bh

= 1 __ 2 ( 40 ) ( 10 ) = 200 ft 2


V = Bh

= ( 200 ) ( 50 ) = 10000 ft 3


30000 + 10000 = 40000 ft 3



B = 1 __ 2 ( b 1 + b 2 ) h

= 1 __ 2 ( 10 + 12 ) 5

= 1 __ 2 ( 22 ) 5 = 55 cm

2


V = Bh

= ( 55 ) ( 7 ) = 385 cm 3







V = Bh

= ( 35 ) ( 5 ) = 175 in 3




B = 1 __ 2 bh

= 1 __ 2 ( 7 ) ( 6 ) = 21 in

2


V = Bh

= ( 75 ) ( 7 ) = 525 in 3



B = 1 __ 2 bh

= 1 __ 2 ( 8 ) ( 4 ) = 16 ft 2


V = Bh

= ( 16 ) ( 24 ) = 384 ft 3



B = 1 __ 2 ( b 1 + b 2 ) h

= 1 __ 2 ( 7 + 5 ) 4

= 1 __ 2 ( 12 ) 4 = 24 in

2


V = Bh

= ( 24 ) ( 8 ) = 192 in 3



V = Bh

= ( 20 ) ( 15 ) = 300 in 3


300 cubic inches


given B = 234 in 3


V = Bh

= ( 234 ) ( 3 ) = 702 in 3



B = bh

= ( 3 ) ( 3 ) = 9 in 2


V = Bh

= ( 9 ) ( 3 ) = 27 in 3


702 + 27 = 972 in 3



B = bh

= ( 75 ) 375 = 28125 m 2


V = Bh

= ( 28125 ) ( 75 ) asymp 21094 cm 3


prism


15 - 75 = 75


B = bh

= ( 75 ) 375 = 28125 m 2


V = Bh

= ( 28125 ) ( 375 ) asymp 10547 cm 3


21094 + 10547 = 31641 m 3




V = Bh

= ( 21 ) ( 8 ) = 168 cm 3



260 - 168 = 92 cm 3


V = Bh

= ( 7 ) ( 14 ) = 98 cm 3



260 - 168 = 92 cm 3


a height of 14 cm

V = Bh

92 = B ( 14 )

92 ___ 14

= B ( 14 ) _____ 14

6 8 ___ 14

= B asymp 657





V = Bh

= ( 36 ) ( 5 ) = 180 in 3



prism V = Bh

= ( 32 ) ( 6 ) = 192 in 3





V = Bh

286 = B ( 8 )

286 ____ 8 = B ( 8 )

3575 = B


trapezoidal prism

1 __ 2 ( 2 + b 2 ) 13 = 3575

1 __ 2 ( 2 + b 2 ) ( 13 ___

13 ) = 3575 _____

13

( 2 ) 1 __ 2 ( 2 + b 2 ) = ( 2 ) 275

2 + b 2 = 55

_ -2 _ -2

b 2 = 35 ft



B = 1 __ 2 bh

= 1 __ 2 ( 10 ) 6 = 30 cm

2


V = Bh

= ( 30 ) ( 25 ) = 75 cm 3



_____ cm

3 )

asymp ( 75 cm 3 ) ( 86 g

_____ cm

3 ) = 645 g


about 645 g







of 120 cm 3

V = Bh

V = [ 1 __ 2 ( b 1 + b 2 ) h 1 ] h 2

120 ≟ [ 1 __ 2 ( 2 + 6 ) 4 ] 75

= [ 1 __ 2 ( 8 ) 4 ] 75

= [ 16 ] ( 75 ) = 120


V = Bh

V = [ 1 __ 2 ( b 1 + b 2 ) h 1 ] h 2

120 ≟ [ 1 __ 2 ( 1 + 7 ) 25 ] 12

= [ 1 __ 2 ( 8 ) 25 ] 12

= [ 10 ] 12 = 120






MODULE 9

Ready to Go On




2 d = 12 cm d = 6 cm so r = 12 ___ 2 = 6 ft



A asymp 11304 ft 2





A asymp 1 __ 2 sdot 314 sdot ( 8 ) 2


A asymp 10048 m 2


A = 1 __ 2 sdot 16 sdot 10

A = 1 __ 2 sdot 160

A = 80 m 2


80 + 10048 = 18048 m 2





A = 20 sdot 45

A = 90 c m 2

Area of rectangle

A = ℓw = 20 sdot 55 = 110 c m 2


90 + 110 = 200 cm 2



1 __ 2 ( 4 ) 3 = 6 cm 2


P = 3 + 4 + 5 = 12 cm


S = Ph + 2B

S = 12 ( 10 ) + 2 ( 6 )

thinsp=120 + 12

thinsp= 132 cm 2


V = Bh

= ( 6 ) 10

= 60 cm 3




1 __ 2 ( 4 ) 15 = 3 yd 2


( 4 ) 2 = 8 yd 2



P = 4 + 2 + 25 + 25 + 2 = 13 yd


S = Ph + 2B

S = 13 ( 25 ) + 2 ( 11 )

thinsp= 325 + 22

thinsp= 545 yd 2


is given

B = 234 yd 3


V = Bh

= ( 11 ) 25

= 275 yd 3






unit


Are You Ready

1 x ___16

=45___40

40x=720

40x ____40

=720____40

   x=18

2 x __5=1__

4

4x=5

4x ___4

=5__4

  x=5__4=125

3 25___10

=x ___10

125=10x

125____10

=10x ____10

125=x

4 x __6

=2__9

9x= 12

9x ___9

=12___9

   x=12___9=4__

3

5 4748495152575960range=60-47=13

6 4566689121213range=13-4=9

7 95979799100106108115range=115-95=20

8 121319273539476671range=71-12=59

9 mean=3+5+7+3+6+4+8+6+9+5_________________________________10

=56

10 mean=81+94+113+67+62+75____________________________6

=82

LESSON 101

Your Turn




Guided Practice




Jimmy 80

Darnell 90

Ping 75

Zach 85

Jamar 80

BSampleanswer

75+80+90+75+85+80___________________________6

=485____6

asymp81

Meanasymp81



Stan 80 Marcus 90

Alejandro 90 Tio 85

BSampleanswer

85+80+90+85+90+85____________________________6

=515____6 =86

Mean=size86




















b 35___60

= x ____100

xasymp58


=58



LESSON 102

Your Turn


______________________sizeofsample



6___50

= x_____3500

6sdot70______50sdot70

= x _____3500

420_____3500

= x_____3500


Guided Practice

1

6 7 8 9 10 11 12 13 14 1550 1 2 3 4


6 7 7 107 114 4 54

Leastvalue

4

Lower quartile

4

Median

65

Upper quartile

7

Greatestvalue11

Drawaboxplot

10 1550





______________________sizeofsample



4___60

= x_____4200

4sdot70______60sdot70

= x_____4200

280_____4200

= x_____4200






8___50

= x_____4500

8sdot90______50sdot90

= x_____4500

720_____4500

= x_____4500



divide060

divide060







_______________________________________ size of sample

=



4 ___ 50

= x ____ 600

4 sdot 12 ______ 50 sdot 12

= x ____ 600

48 ____ 600

= x ____ 600

x = 48



_______________________________________________ size of sample

=



2 ___ 20

= x ____ 130

2 sdot 65 _______ 20 sdot 65

= x ____ 130

13 ____ 130

= x ____ 130

x = 13



________________ size of sample



12 ___ 60

= x _____ 1200

12 sdot 20 ______ 60 sdot 20

= x _____ 1200

240 _____ 1200

= x _____ 1200

x = 240


shelters


__________________________ size of sample



12 ___ 72

= x ______ 10800

12 sdot 150 _______ 72 sdot 150

= x ______ 10800

1800

______ 10800

= x ______ 10800

x = 1800



_______ 2 = 25


14 Order the data

11 12 12 12 13 13 13 14 14 14 15 17 18 18

19 22



12 ___ 16

= x ____ 100

12 sdot 625 ________ 16 sdot 625

= x ____ 100

75 ____ 100

= x ____ 100

x = 75



15

6 7 8 9 1050 1 2 3 4


fewer siblings




















9 a 56 + 43 + 62 + 63 + 33 + 34 + 38 + 51 + 59 + 59

___________________________________________ 10

= 498


b 498 sdot 64 = 31872



10 55 + 57 + 57 + 58 + 59 + 59 + 59 + 59 + 59 + 61 + 62 + 62 + 63 + 64 + 66

_________________________________________________________________ 15

= 60






accurately

LESSON 103

Guided Practice

1 (1 600) 20

2 50 51 600








5 Shop A 10 ___ 50

times 500 = 100

Shop B 23 ____ 100

times 500 = 115

Shop C 7 ___ 25

times 500 = 140








fewest bagels










count of 75


MODULE 10

Ready to Go On




service


__________________________________________ size of sample


18 ____ 270

= x ______ 30330

18 sdot 337 ____

3 ________

270 sdot 337 ____ 3

= x ______ 30330

2022

______ 30330

= x ______ 30330

x = 2022


languages





= defective players

______________ shipment

2 ___ 10

= x _____ 5000

2 middot 500 _______ 10 middot 500

= x _____ 5000

1000

_____ 5000

= x _____ 5000

x = 1000


defective


the shipment





Are You Ready

0875

1 8 ⟌ _

7000

_ -6 400

600

_ -560

40

_ -40

0

0875 875

08

2 5 ⟌ _

40

_ -4 0

0

08 80

025

3 4 ⟌ _

100

_ -80

20

_ -20

0

025 25

03

4 10 ⟌ _

30

_ -3 0

0

03 30

5 4 6 7 7 9 11 15 17

7 + 9

_____ 2 = 8

Median = 8

Mode = 7

6 36 37 40 43 44 49 50 51 56

Median = 44

Mode none

7 9 + 16 + 13 + 14 + 10 + 16 + 17 + 9

________________________________ 8

= 13

Mean = 13

8 108 + 95 + 104 + 96 + 97 + 106 + 94

________________________________ 7 = 100

Mean = 100

LESSON 111

Your Turn








in order

1 4 4 4 5 5 5 6 6 6 6 7 7 8 11


range 10 h



range for exercise

Guided Practice




one area




no data


4 Class A

4 4 4 4 4 5 5 5 6 6 12 13 13 13 13 14 14

median 6

Class B

3 4 4 4 5 5 5 5 6 6 7 7 7 7 7 8 8 9

median 6








at 8 letters




3 + 4 + 4 + 5 + 5 + 6 + 7 + 7 + 8 + 8 + 8 + 9

________________________________________ 12

74 ___ 12

asymp 617

Mean asymp 617

3 3 4 5 5 6 7 7 8 8 8 9


average

6 + 7

_____ 2 = 13 ___

2 = 65

Median 65

Range 9 - 3 = 6


the left


interval













LESSON 112

Your Turn



Guided Practice


2 Median79

3 Range88-72=16 IQR85-75=10






























does not




LESSON 113

Your Turn

1 Team 1

Mean

44 + 47 + 67 + 89 + 55 + 76 +85 + 80 + 87 + 69 + 47 + 58 = 804

804 divide 12 = 67


ǀ 44 - 67 ǀ = 23 ǀ 47 - 67 ǀ = 20

ǀ 67 - 67 ǀ = 0 ǀ 89 - 67 ǀ = 22

ǀ 55 - 67 ǀ = 12 ǀ 76 - 67 ǀ = 9

ǀ 85 - 67 ǀ = 18 ǀ 80 - 67 ǀ = 13

ǀ 87 - 67 ǀ = 20 ǀ 69 - 67 ǀ = 2

ǀ 47 - 67 ǀ = 20 ǀ 58 - 67 ǀ = 11


23 + 20 + 0 + 22 + 12 + 9 +18 + 13 + 20 + 2 + 20 + 11 = 170


Team 2

Mean

40 + 32 + 52 + 75 + 65 + 70 +72 + 61 + 54 + 43 + 29 + 32 = 625



ǀ 40 - 521 ǀ = 121 ǀ 32 - 521 ǀ = 201

ǀ 52 - 521 ǀ = 01 ǀ 75 - 521 ǀ = 229

ǀ 65 - 521 ǀ = 129 ǀ 70 - 521 ǀ = 179

ǀ 72 - 521 ǀ = 199 ǀ 61 - 521 ǀ = 89

ǀ 54 - 521 ǀ = 19 ǀ 43 - 521 ǀ = 91

ǀ 29 - 521 ǀ = 231 ǀ 32 - 521 ǀ = 201


121 + 201 + 01 + 229 +129 + 179 + 199 + 89 +19 + 91 + 231 + 201 = 169


Difference in means

67 - 521 = 149



MAD


distributions

Guided Practice

1 Class 1 mean

12 + 1 + 6 + 10 + 1 + 2 + 3 +10 + 3 + 8 + 3 + 9 + 8 + 6 + 8 = 90

90 divide 15 = 6

Class 2 mean

11 + 14 + 11 + 13 + 6 + 7 + 8 + 6 +8 + 13 + 8 + 15 + 13 + 17 + 15 = 165

165 divide 15 = 11


ǀ 12 - 6 ǀ = 6 ǀ 1 - 6 ǀ = 5 ǀ 6 - 6 ǀ = 0

ǀ 10 - 6 ǀ = 4 ǀ 1 - 6 ǀ = 5 ǀ 2 minus 6 ǀ = 4

ǀ 3 - 6 ǀ = 3 ǀ 10 - 6 ǀ = 4 ǀ 3 - 6 ǀ = 3

ǀ 8 - 6 ǀ = 2 ǀ 3 - 6 ǀ = 3 ǀ 9 - 6 ǀ = 3

ǀ 8 - 6 ǀ = 2 ǀ 6 - 6 ǀ = 0 ǀ 8 - 6 ǀ = 2

6 + 5 + 0 + 4 + 5 + 4 + 3 + 4 +3 + 2 + 3 + 3 + 2 + 0 + 2 = 46



ǀ 11 - 11 ǀ = 0 ǀ 14 - 11 ǀ = 3 ǀ 11 - 11 ǀ = 0

ǀ 13 - 11 ǀ = 2 ǀ 6 - 11 ǀ = 5 ǀ 7 - 11 ǀ = 4

ǀ 8 - 11 ǀ = 3 ǀ 6 - 11 ǀ = 5 ǀ 8 - 11 ǀ = 3

ǀ 13 - 11 ǀ = 2 ǀ 8 - 11 ǀ = 3 ǀ 15 - 11 ǀ = 4

ǀ 13 - 11 ǀ = 2 ǀ 17 - 11 ǀ = 6 ǀ 15 - 11 ǀ = 2

0 + 3 + 0 + 2 + 5 + 4 + 3 + 5 +3 + 2 + 3 + 4 + 2 + 6 + 2 = 44



11 minus 6 = 5




comparison


different samples


5 23 + 38 + 39 + 48 + 55 + 56 + 71 +86 + 57 + 53 + 43 + 31 = 600

600 divide 12 = 50

ǀ 23 - 50 ǀ = 27 ǀ 38 - 50 ǀ = 12

ǀ 39 - 50 ǀ = 11 ǀ 48 - 50 ǀ = 2

ǀ 55 - 50 ǀ = 5 ǀ 56 - 50 ǀ = 6

ǀ 71 - 50 ǀ = 21 ǀ 86 - 50 ǀ = 36

ǀ 57 - 50 ǀ = 7 ǀ 53 - 50 ǀ = 3

ǀ 43 - 50 ǀ = 7 ǀ 31 - 50 ǀ = 19

27 + 12 + 11 + 2 + 5 + 6 + 21 +36 + 7 + 3 + 7 + 19 = 156

156 divide 12 = 13



6 ǀ 23 - 8 ǀ = 15 ǀ 38 - 23 ǀ = 15

ǀ 39 - 24 ǀ = 15 ǀ 48 - 33 ǀ = 15

ǀ 55 - 40 ǀ = 15 ǀ 56 - 41 ǀ = 15

ǀ 71 - 56 ǀ = 15 ǀ 86 - 71 ǀ = 15

ǀ 57 - 42 ǀ = 15 ǀ 53 - 38 ǀ = 15

ǀ 43 - 28 ǀ = 15 ǀ 31 - 16 ǀ = 15




7 50 - 15 = 35




8 50 - 35 = 15




9

0 4 8 12 16 20 24 28 32 36 40 44

Medians

School B

School A

0 4 8 12 16 20 24 28 32 36 40 44

Means

School B

School A




10 State A 48 - 38 = 10


State B 50 - 42 = 8

8 divide 4 = 2





well


Median 665


Median 77

77 - 665 = 105

105 divide 6 = 175


ranges













not very similar

MODULE 11

Ready to Go On


5 + 6 + 6 + 7 + 7 + 7 + 7 + 8 + 8 + 8 + 8 + 9 + 9 + 10

________________________________________________ 14

= 105 ____ 14

= 75 mi


6 + 6 + 7 + 7 + 8 + 8 + 8 + 8 + 9 + 9 + 9 + 10 + 10 + 10

__________________________________________________ 14

= 115 ___ 14

asymp 82 mi




5 6 6 7 7 7 7 8 8 8 8 9 9 10


average

7 + 8

_____ 2 = 15 ___

2 = 75

Median 75


6 6 7 7 8 8 8 8 9 9 9 10 10 10




Median 8













7 + 11 + 11 + 12 + 9 + 12 + 8 + 10

______________________________ 8

= 10


21 + 24 + 19 + 19 + 22 + 23 + 24 + 24

__________________________________ 8 = 22




12 ___ 5

= 24




groups



Are You Ready

1 6 ___ 10

= 6 divide 2 ______ 10 divide 2

= 3 __ 5

2 9 ___ 15

= 9 divide 3 ______ 15 divide 3

= 3 __ 5

3 16 ___ 24

= 16 divide 8 ______ 24 divide 8

= 2 __ 3

4 9 ___ 36

= 9 divide 9 ______ 36 divide 9

= 1 __ 4

5 45 ___ 54

= 45 divide 9 ______ 54 divide 9

= 5 __ 6

6 30 ___ 42

= 30 divide 6 ______ 42 divide 6

= 5 __ 7

7 36 ___ 60

= 36 divide 12 _______ 60 divide 12

= 3 __ 5

8 14 ___ 42

= 14 divide 14 _______ 42 divide 14

= 1 __ 3

075

9 4 ⟌ _

300

_ -2 80

20

_ -20

0

075

0875

10 8 ⟌ _

7000

_ -6400

600

_ -560

40

_ -40

0

0875

015

11 20 ⟌ _

300

_ -2 00

100

_ -100

0

015

038

12 50 ⟌ _

1900

_ -15 00

4 00

_ -4 00

0

038

13 67 = 67 ____ 100

= 067

14 31 = 31 ____ 100

= 031

15 7 = 7 ____ 100

= 007

16 146 = 100 + 46

= 100 ____ 100

+ 46 ____ 100

= 1 + 046

= 146

17 013 = 13

18 055 = 55

19 008 = 8

20 116 = 116

LESSON 121

Your Turn







is 10 ___ 20

or 1 __ 2





3


UNIT

6



P(5) + P(not 5) = 1

1 __ 8 + P(not 5) = 1

P(not 5) = 7 __ 8




1 __ 2 + P(odd) = 1

P(odd) = 1 __ 2


Guided Practice













impossible 0
















= 1 __ 4


P(5) + P(not 5) = 1

1 __ 6 + P(not 5) = 1

P(not 5) = 5 __ 6




1 __ 3 + P(not blue) = 1




P(4) + P(not 4) = 1

1 __ 5 + P(not 4) = 1

P(not 4) = 4 __ 5




4 ___ 52

+ P(not queen) = 1

P(not blue) = 48 ___ 52

= 12 ___ 13









selecting


or 2 ___ 13



9 ___ 12



or 1 __ 4



or 1 __ 4













or 5 __ 7



have red hair




or 4 __ 7





coin is 9 ___ 16














landing on blue

LESSON 122

Your Turn


Red 10 ___ 30

= 1 __ 3

Yellow 14 ___ 30

= 7 ___ 15

Blue 6 ___ 30

= 1 __ 5






Guided Practice


A 14 ___ 40

= 7 ___ 20

= 035 = 35

B 7 ___ 40

= 0175 = 175

C 11 ___ 40

= 0275 = 275

D 8 ___ 40

= 1 __ 5 = 020 = 20







4 6 ___ 10








= 8 ___ 48

= 1 __ 6





chosen is 19 ___ 20


1 ___ 20

+ P(not Ryan) = 1

P(not Ryan) = 19 ___ 20


patterns




times



get a hit next time


is 4 ___ 10





or about 417


7 ___ 12



or 417











pocket


LESSON 123

Your Turn



= 60 ____ 400

= 3 ___ 20

= 15



= 12 ___ 75

or 4 ___ 25

Guided Practice




= 50 ____ 400

or 1 __ 8











number of trials








= 33 ____ 330

= 1 ___ 10



= 60 ____ 400

= 3 ___ 20


= 55 + 60 + 23

____________ 400

= 138 ____ 400

= 69 ____ 200


and 4 color choices


P(7th grade + 100 pages) = 85 ____ 250

= 17 ___ 50




7th grade




likely





12 P(male + open toe) = 11 ____ 300











heads and 3 or 4

LESSON 124

Your Turn








Guided Practice








too high

5 98 ____ 100

= x ___ 40

= 39 ___ 40

or 39 times




6 18 ____ 100

= x _____ 5000

= 900 _____ 5000



accepted

times04

times04

times50

times50





events


8 4 ____ 100

= x ____ 200

= 8 ____ 200



9 Yes 6th grade 2 ____ 100

= x ____ 250

= 5 ____ 250

or 5 students

7th grade 4 ____ 100

= x ____ 200

= 8 ____ 200

or 8 students

8th grade 8 ____ 100

= x ____ 150

= 12 ____ 150

or 12 students



10 6 ____ 100

= x ____ 300

= 18 ____ 300










1 ___ 30

= x ____ 180




normal gas pump







4 ____ 100

= x _____ 2400

= 96 _____ 2400



MODULE 12

Ready to Go On

1 H1 H2 T1 T2

2 6 ___ 10

= 3 __ 5

3 13 ___ 20




because 3 ___ 10

= x ___ 80

= 24 ___ 80

or 24 times




times15

times15

times24

times24

times2

times2

times3

times3

times2

times2

times25

times25

times8

times8



Simulations

Are You Ready

075

1 4 ⟌ _

300

_ -2 80

20

_ -20

0

075 = 75

04

2 5 ⟌ _

20

_ -2 0

0

04 = 40

09

3 10 ⟌ _

90

_ -9 0

0

09 = 90

035

4 20 ⟌ _

700

_ -6 00

1 00

_ -1 00

0

035 = 35

0875

5 8 ⟌ _

7000

_ thinsp-6 400

600

_ -560

40

_ -40

0

0875 = 875

005

6 20 ⟌ _

100

_ -1 00

0

005 = 5

076

7 25 ⟌ _

1900

_ -17 50

1 50

_ -1 50

0

076 = 76

046

8 50 ⟌ _

2300

_ -20 50

3 00

_ -3 00

0

046 = 46

9 1 - 1 __ 5 = 5 __

5 - 1 __

5

= 4 __ 5

10 1 - 2 __ 9 = 9 __

9 - 2 __

9

= 7 __ 9

11 1 - 8 ___ 13

= 13 ___ 13

- 8 ___ 13

= 5 ___ 13

12 1 - 3 ___ 20

= 20 ___ 20

- 3 ___ 20

= 17 ___ 20

13 8 ___ 15

times 5 __ 8 =

18 ___ 315

times 5 1 ___

8 1

= 1 __ 3

14 2 __ 9 times 3 __

4 =

12 __ 39

times 3 1 ___

4 2

= 1 __ 6

15 9 ___ 16

times 12 ___ 13

= 9 ___ 416

times 12 3 _____

13

= 27 ___ 52

16 7 ___ 10

times 5 ___ 28

= 17 ___

210 times 5

1 ____

28 4

= 1 __ 8

LESSON 131

Your Turn






= 2 __ 6 = 1 __

3



probability


Guided Practice

1

Basket A Basket B


= 16

7 + 4 + 9

= 20


P(win) =

Number of red balls


3 ___

16 4 ___

20 = 1 __

5


16 use


1 __ 5 = 16 ___

80

3 ___ 16

= 15 ___ 80

Therefore 16 ___ 80

gt 15 ___ 80

so 1 __ 5 gt 3 ___

16


winning




= 6 ___ 11




= 5 ___ 11




= 2 __ 6 = 1 __

3


close


by 20




= 2 __ 6

= 1 __ 3 033 or 33



= 8 ___ 12

= 2 __ 3 067 or 67



= 4 ___ 14

= 2 __ 7 029 or 29


= 26 ___ 52

= 1 __ 2 050 or 50


= 12 - 5 ______ 12

= 7 ___ 12

058 or 58



7 adventure)

P(not a comedy)


= 5 + 7 _________

5 + 7 + 8 = 12 ___

20

= 3 __ 5 060 or 60






= 2 __ 6

= 1 __ 3 033 or 33







= 6 ___ 16

or 3 __ 8







5 ______ 5 + 15

= 5 ___ 20

= 1 __ 4

times16

times16

times5

times5




P(seventh grader) =



= 20 ___ 35

= 4 __ 7


P(eighth grader) =



= 15 ___ 35

= 3 __ 7



more likely










= 8 ___ 20


14 ___ 40

or 7 ___ 20



marble is 8 ___ 20

- 7 ___ 20

= 1 ___ 20



= 10 ___ 20


= 8 ___ 20



marble is 10 ___ 20

- 8 ___ 20

= 2 ___ 20

= 1 ___ 10




= 2 ___ 20


= 5 ___ 20



marble is 5 ___ 20

- 2 ___ 20

= 3 ___ 20



LESSON 132

Your Turn

3 P(ham sandwich) =



= 4 ___ 12

= 1 __ 3




= 6 ___ 12

= 1 __ 2




0 0 0 0

0 0 0 1

0 0 1 0

0 0 1 1


second digit

0 1 0 0

0 1 0 1

0 1 1 0

0 1 1 1


second digit

1 0 0 0

1 0 0 1

1 0 1 0

1 0 1 1


second digit

1 1 0 0

1 1 0 1

1 1 1 0

1 1 1 1



0 0 1 1

0 1 0 1

0 1 1 0

1 0 0 1

1 0 1 0

1 1 0 0





= 6 ___ 16

= 3 __ 8


Guided Practice

1

1 2 3 4 5 6

11 sdot 1

= 1

1 sdot 2

= 2

1 sdot 3

= 3

1 sdot 4

= 4

1 sdot 5

= 5

1 sdot 6

= 6

22 sdot 1

= 2

2 sdot 2

= 4

2 sdot 3

= 6

2 sdot 4

= 8

2 sdot 5

= 10

2 sdot 6

= 12

33 sdot 1

= 3

3 sdot 2

= 6

3 sdot 3

= 9

3 sdot 4

= 12

3 sdot 5

= 15

3 sdot 6

= 18

44 sdot 1

= 4

4 sdot 2

= 8

4 sdot 3

= 12

4 sdot 4

= 16

4 sdot 5

= 20

4 sdot 6

= 24

55 sdot 1

= 5

5 sdot 2

= 10

5 sdot 3

= 15

5 sdot 4

= 20

5 sdot 5

= 25

5 sdot 6

= 30

66 sdot 1

= 6

6 sdot 2

= 12

6 sdot 3

= 18

6 sdot 4

= 24

6 sdot 5

= 30

6 sdot 6

= 36





= 15 ___ 36




= 23 ___ 36

4 H

HHH HHT

H

H

Coin 1

List

Coin 2

Coin 3 T

T

HTH HTT

H T

T

H

H T

THH THT

T

H T

TTH TTT

Coin 1

List

Coin 2

Coin 3




= 1 __ 8


HHT HTH THH



= 3 __ 8




10

Checkered

Red

Checkered

Red

Blue

Black

Checkered

Red

Checkered

Red

Blue

Black

Checkered

Red

Checkered

Red

Blue

Black

Shirt Pants Shoes

Yellow

Red

Green




= 6 ___ 12

= 1 __ 2


Shirt Pants Shoes






= 4 ___ 12

= 1 __ 3



Rhee Pamela

Rhee A

Rhee B

Rhee C

Pamela A

Pamela B

Pamela C

A B

A C

B C



P(Rhee and Pamela)


= 1 ___ 10




1 2 3 4 5 6

11 + 1

= 2

1 + 2

= 3

1 + 3

= 4

1 + 4

= 5

1 + 5

= 6

1 + 6

= 7

22 + 1

= 3

2 + 2

= 4

2 + 3

= 5

2 + 4

= 6

2 + 5

= 7

2 + 6

= 8

33 + 1

= 4

3 + 2

= 5

3 + 3

= 6

3 + 4

= 7

3 + 5

= 8

3 + 6

= 9

44 + 1

= 5

4 + 2

= 6

4 + 3

= 7

4 + 4

= 8

4 + 5

= 9

4 + 6

= 10

55 + 1

= 6

5 + 2

= 7

5 + 3

= 8

5 + 4

= 9

5 + 5

= 10

5 + 6

= 11

66 + 1

= 7

6 + 2

= 8

6 + 3

= 9

6 + 4

= 10

6 + 5

= 11

6 + 6

= 12


are 10 less than 6



= 10 ___ 36

= 5 ___ 18


diagram

Khakis

Shorts

Shirt Pants Shoes

Collared Jeans

Sneakers

Flip-flops

Sandals

Sneakers

Flip-flops

Sandals

Sneakers

Flip-flops

Sandals

Khakis

Shorts

T-shirt Jeans

Sneakers

Flip-flops

Sandals

Sneakers

Flip-flops

Sandals

Sneakers

Flip-flops

Sandals







= 4 ___ 18

= 2 __ 9






outcomes



Therefore




= 7 ___ 30






diagram

Carrots

Sweet potato

Pasta

Peas

Asparagus





Carrots

Sweet potato

Peas

Asparagus





Carrots

Sweet potato

Peas

Asparagus





Carrots

Sweet potato

Peas

Asparagus





Salmon

Beef

Pork



salmon Therefore


= 1 __ 4





Carrots

Sweet potato

PastaPeas

Asparagus

Carrots

Sweet potato

Peas

Asparagus

Carrots

Sweet potato

Peas

Asparagus

Carrots

Sweet potato

Peas

Asparagus

Salmon

Beef

Pork


salmon Therefore


= 1 __ 4















codes













12453 12534 12543 13245 13254 13425

13452 13524 13542 14235 14253 14325

14352 14523 14532 15234 15243 15324













114 115 221 223 224 225 331 332 334 335

441 442 443 445 551 552 553 554 There























LESSON 133

Your Turn




3






heads is 1 __ 2

1 __ 2 = x ___

18

1 __ 2 = x ___

18

x = 9

about 9 times


P(red) = 8 ___ 17

P(not red) = 1 - 8 ___ 17

= 9 ___ 17




Therefore




Guided Practice






3 House 1 __

3



1 __ 3 = x ___

18

1 __ 3 = x ___

18

x = 6














P(hazel) = 9 ___ 28

P(brown) = 10 ___ 28

P(blue) = 7 ___ 28

P(green) = 2 ___ 28






unknown quantity




P(white or gray) = 3 __ 9 = 1 __

3


prediction is then








Y GRR

R R

RR





card is 12 ___ 52


52 use the least


52 Given

that 12 ___ 52

lt 26 ___ 52





P(ace) = 4 ___ 52

= 1 ___ 13


prediction is then


times 39 = 3



P(red card) = 26 ___ 52

= 1 __ 2








times6

times6

times9

times9


1 2 3 4 5 6

1 2 3 4 5 6 7

2 3 4 5 6 7 8

3 4 5 6 7 8 9

4 5 6 7 8 9 10

5 6 7 8 9 10 11

6 7 8 9 10 11 12




P(sum of 8) = 5 ___ 36

P(sum of 11) = 2 ___ 36



gt 2 ___ 36




= 1 __ 4




1 __ 4 times 180 = 45





so P(sum of 3) = 3 ___ 36

= 1 ___ 12


prediction is then


middot 36 = 3





time









that is not green



green is 3 + 9 _________

3 + 8 + 9 = 12 ___



20 = 12 ___

40






6 = 1 ___

12



P(5 or heads) = 1 __ 6 + 1 __

2 - 1 __

6 times 1 __

2 = 7 ___

12





LESSON 134

Your Turn



1 0 0 1 No

2 0 1 No

3 1 No

4 0 1 No

5 1 No

6 0 0 0 1 Yes

7 0 0 1 No

8 0 1 No

9 1 No

10 0 0 0 0 1 Yes




or 20



1 1 0 1 1 0 3

2 0 1 0 0 1 2

3 0 0 0 0 1 1

4 0 0 1 1 0 2

5 1 1 1 1 1 5

6 1 0 0 0 0 1

7 1 0 1 1 0 3

8 1 0 1 0 0 2

9 0 1 1 1 1 4

10 0 0 0 0 0 0



= 70


Guided Practice







numbers each time

2


1 10 3 5 1 2

2 10 4 6 5 0

3 3 2 10 3 3

4 2 10 4 4 1

5 7 3 6 3 2

6 8 4 8 5 0

7 6 2 2 8 2

8 6 5 2 4 1

9 2 2 3 2 4

10 6 3 1 5 2




8 ___ 10

= 80









= 10




= 20














1 3 1

2 4 2 2

3 2 1

4 1 1

5 2 1

6 4 5 3 2

7 4 2 2

8 4 5 2 1

9 4 4 3 3

10 5 1 2


1 + 2 + 1 + 1 + 1 + 2 + 2 + 1 + 3 + 2

_________________________________ 10

= 16 ___ 10

= 1 3 __ 5

















MODULE 13

Ready to Go On


= 12 ___________________ 12 + 12 + 15 + 9 + 12

= 12 ___ 60

= 1 __ 5 020 or 20




= 13 + 13

_______ 52

= 26 ___ 52

= 1 __ 2 050 or 50








or

40






Are You Ready


2 a $700 profit 700



1 1

5 183

_ + 78

261

261

5 16 17

6 677

_ -288

389

389

1 1

7 1188

_ +902

2090

2090

1 15 14

8 2647

_ -1885

762

762

9

-8-10 -4-6 -2 2 4 6 8 100 10

-8-10 -4-6 -2 2 4 6 8 100 11

-8-10 -4-6 -2 2 4 6 8 100 12

-8-10 -4-6 -2 2 4 6 8 100

LESSON 11

Your Turn

7 -8 + ( -1 ) = -9

8 -3 + ( -7 ) = -10

9 -48 + ( -12 ) = -60

10 -32 + ( -38 ) = -70

11 109 + 191 = 300

12 -40 + ( -105 ) = -145

13 -150 + ( -1500 ) = -1650

14 -200 + ( -800 ) = -1000

Guided Practice



c -5 + ( -1 ) = -6



c -2 + ( -7 ) = -9

3 -5 + ( -2 ) = -7

-8-7-6-5 -2-1 0-4-3 4 -1 + ( -3 ) = -4

-5-4-3-2 1 2 3-1 0 5 -3 + ( -7 ) = -10

-10 -9-8-7 -4-3-2-6-5 6 -4 + ( -1 ) = -5

-5-4-3-2 1 2 3-1 0 7 -2 + ( -2 ) = -4

-5-4-3-2 1 2 3-1 0 8 -6 + ( -8 ) = -14

-16 -12 -4 0-8 9 -5 + ( -4 ) = -9

10 -1 + ( -10 ) = -11

11 -9 + ( -1 ) = -10

12 -90 + ( -20 ) = -110

13 -52 + ( -48 ) = -100

14 5 + ( 198 ) = 203

15 -4 + ( -5 ) + ( -6 ) = -15

16 -50 + ( -175 ) + ( -345 ) = -570




UNIT

1



18 a

-4

-6

-8

-2

0

2

-5 + (-3)-3 + (-5)

b No -5 + ( -3 ) is -8 and -3 + ( -5 ) is also -8


score is -11


21 -14 + ( -5 ) + ( -12 ) + ( -23 ) = -54 The total


22 a -10 + ( -8 ) = -18

b -6 + ( -2 ) = -8


23 -100 + ( -75 ) + ( -85 ) = -260


24 a -25 + ( -45 ) + ( -75 ) = -145 Jan withdrew

$145

b -35 + ( -55 ) + ( -65 ) = -155 Julie withdrew

$155








six pairs is 8

LESSON 12

Your Turn

7 -51 + 23

ǀ -51 ǀ - ǀ 23 ǀ = 28

-51 + 23 = -28

8 10 + ( -18 )

ǀ -18 ǀ - ǀ 10 ǀ = 8

10 + ( -18 ) = -8

9 13 + ( -13 )

ǀ 13 ǀ - ǀ -13 ǀ = 0

10 25 + ( -26 )

ǀ -26 ǀ - ǀ 25 ǀ = 1

25 + ( -26 ) = -1

Guided Practice

1 9 + ( -3 ) = 6

2 3 4 5 8 9 106 7 2 -2 + 7 = 5

-3-2-1 0 3 4 51 2 3 -15 + 4 = -11

-18 -16 -12 -10-14 4 1 + ( -4 ) = -3

-5-4-3-2 1 2 3-1 0 5 -4 + 5 = 1

6 -6 + 6 = 0

7 2 + ( -5 ) = -3

8 -3 + 7 = 4

9 -8 + 14 = 6

10 7 + ( -5 ) = 2

11 5 + ( -21 ) = -16

12 14 + ( -14 ) = 0

13 0 + ( -5 ) = -5

14 32 + ( -8 ) = 24





16 -15 + 71 = 56

17 -53 + 45 = -8

18 -79 + 79 = 0

19 -25 + 50 = 25

20 18 + ( -32 ) = -14

21 5 + ( -100 ) = -95

22 -12 + 8 + 7 = 3

23 -8 + ( -2 ) + 3 = -7


24 15 + ( -15 ) + 200 = 200

25 -500 + ( -600 ) + 1200 = 100
















is 8 feet deep








LESSON 13

Your Turn

4 -7 - 2 = -7 + ( -2 )

-7 + ( -2 ) = -9

5 -1 - ( -3 ) = -1 + 3

-1 + 3 = 2

6 3 - 5 = 3 + ( -5 )

3 + ( -5 ) = -2

7 -8 - ( -4 ) = -8 + 4

-8 + 4 = -4

Guided Practice







3 -4 - 5 = -4 + ( -5 ) = -9

0-1-2-3-4-5-6-7-8-9 4 1 - 4 = 1 + -4 = -3

0 1 2 3 4-1-2-3-4 5 8 - 11 = 8 + ( -11 ) = -3

6 -3 - ( -5 ) = -3 + 5 = 2

7 15 - 21 = 15 + ( -21 ) = -6

8 -17 - 1 = -17 + ( -1 ) = -18

9 0 - ( -5 ) = 0 + 5 = 5

10 1 - ( -18 ) = 1 + 18 = 19

11 15 - 1 = 14

12 -3 - ( -45 ) = -3 + 45 = 42

13 19 - ( -19 ) = 19 + 19 = 38

14 -87 - ( -87 ) = -87 + 87 = 0


example 6 - 8 = 6 + ( -8 ) = -2




25 - ( -4 ) = 25 + 4 = 29





-127 - ( -225 ) = -127 + 225 = 98



temperature 90degF

90 - ( -2 ) = 92






-425 - ( -275 ) = -425 + 275 = -150



in temperature

Gas A -8 - ( -21 ) = -8 + 21 = 13

13degC increase

Gas B 12 - ( -12 ) = 12 + 12 = 24

24degC increase

Gas C -15 - ( -19 ) = -15 + 19 = 4

4degC increase













-11 + 4 = -7




LESSON 14

Your Turn




Guided Practice


2 -23+5-7=-18-7  =-25-25degF

3 50-40+87-30=10+87-30  =97-30  =6767points

4 -6+15+15=-6+30  =24

5 9- 4- 17= 9- 21  =-12

6 50-42+10=8+10  =18

7 6+13+7-5=19+2  =21

8 65+43-11=108-11  =97

9 -35-14+45+31=-49+76  =27

10 -12+6-4=-6-4  =-10-34-3+39=-37+39  = 2  -10lt2( -12+6-4)lt( -34-3+39)

11 21-3+8=18+8  =26-14+ 31- 6= 17- 6  =11 26gt11( 21-3+8)gt( -14+31-6)



13 a 5-1+6-1=9






b 45gt-55Barry

17 a 300to400


18 100-18+22-53=51$51

19 45-17-22+18=24$24






MODULE 1

Ready to Go On

1 -8+( -6)=-14

2 -4+( -7)=-11

3 -9+( -12)=-21





4 5 + ( -2 )

ǀ 5 ǀ - ǀ -2 ǀ = 3

5 + ( -2 ) = 3

5 -8 + 4

ǀ -8 ǀ - ǀ 4 ǀ = 4

-8 + 4 = -4

6 15 + ( -8 )

ǀ 15 ǀ - ǀ -8 ǀ = 7

15 + ( -8 ) = 7

7 2 - 9 = 2 + ( -9 )

2 + ( -9 ) = -7

8 -3 - ( -4 ) = -3 + 4-3 + 4 = 1

9 11 - ( -12 ) = 11 + 12

11 + 12 = 23

10 -15 + 9 - 4 = -6 - 4

= -10


11 24 + 8 - 12 - 9 = 24 + 8 - ( 12 + 9 ) = 32 - 21

= 11




after she pays them

-10 + ( -5 ) = -15 $15 decrease



Are You Ready

1 9 times 3 = 27

2 7 times 10 = 70

3 9 times 8 = 72

4 15 times 10 = 150

5 6 times 9 = 54

6 10 times 23 = 230

7 9 times 9 = 81

8 10 times 20 = 200

9 54 divide 9 = 6

10 42 divide 6 = 7

11 24 divide 3 = 8

12 64 divide 8 = 8

13 90 divide 10 = 9

14 56 divide 7 = 8

15 81 divide 9 = 9

16 110 divide 11 = 10

17 12 + 8 divide 212 + 4

16

18 15 - ( 4 + 3 ) times 2

15 - 7 times 2

15 - 14

1

19 18 - ( 8 - 5 ) 2

18 - ( 3 ) 2

18 - 9

9

20 6 + 7 times 3 - 5

6 + 21 - 5

27 - 5

22

21 9 + ( 2 2 + 3 ) 2 times 2

9 + ( 4 + 3 ) 2 times 2

9 + ( 7 ) 2 times 2

9 + 49 times 2

9 + 98

107

22 6 + 5 - 4 times 3 divide 2

6 + 5 - 12 divide 2

6 + 5 - 6

11 - 6

5

LESSON 21

Your Turn


will be negative


-3 ( 5 ) = -15


will be positive

ǀ -10 ǀ times ǀ -2 ǀ = 10 times 2 = 20

( -10 ) ( -2 ) = 20


0 ( -22 ) = 0


will be positive

8 ( 4 ) = 32

Guided Practice

1 -1 ( 9 ) = -9

2 14 ( -2 ) = -28

3 ( -9 ) ( -6 ) = 54

4 ( -2 ) ( 50 ) = -100

5 ( -4 ) ( 15 ) = -60

6 -18 ( 0 ) = 0

7 ( -7 ) ( -7 ) = 49

8 -15 ( 9 ) = -135

9 ( 8 ) ( -12 ) = -96

10 -3 ( -100 ) = 300

11 0 ( -153 ) = 0

12 -6 ( 32 ) = -192

13 7 ( -75 ) = -525 -$525



15 6 ( -2 ) = -12 -12degF








19 5 ( -4 ) = -20 $20 decrease





22 9 ( -6 ) = -54 -54 ( 2 ) = -108 Casey has $108

less in his savings

23 7 ( -8 ) = -56 7 ( -5 ) = -35





160 points


25 a 3 ( 3 ) ( -3 ) = 9 ( -3 ) = -27

b 3 ( -3 ) ( -3 ) = -9 ( -3 ) = 27

c -3 ( -3 ) ( -3 ) = 9 ( -3 ) = -27

d 3 ( 3 ) ( 3 ) ( -3 ) = 9 ( 3 ) ( -3 ) = 27 ( -3 ) = -81

e 3 ( 3 ) ( -3 ) ( -3 ) = 9 ( -3 ) ( -3 ) = -27 ( -3 ) = 81

f 3 ( -3 ) ( -3 ) ( -3 ) = -9 ( -3 ) ( -3 ) = 27 ( -3 ) = -81




negative



3 ( 3 ) ( -3 ) ( -3 ) = 9 ( -3 ) ( -3 ) = 81 the sign of the

product is positive


26 -1 ( 3 ) ( 1 ) 1 ( -3 ) ( 1 ) -1 ( -3 ) ( -1 )









negative

LESSON 22

Your Turn


0 divide ( -6 ) = 0


will be negative

38 divide ( -19 ) = -2


will be positive

-13 divide ( -1 ) = 13



Guided Practice

1 -14 ____ 2 = -7

2 21 divide ( -3 ) = -7

3 26 ____ -13

= -2

4 0 divide ( -4 ) = 0

5 -45 ____ -5 = 9

6 -30 divide ( 10 ) = -3

7 -11 ____ -1

= 11

8 -31 divide ( -31 ) = 1

9 0 ___ -7 = 0

10 -121 _____ -11

= 11

11 84 divide ( -7 ) = -12

12 500 ____ -25

= -20


undefined

14 -63 ____ -21

= 3

15 -40 divide ( 4 ) = -10 $10

16 -22 divide ( 11 ) = -2 2 points

17 -75 divide ( -15 ) = 5 5 targets

18 -99 divide ( -9 ) = 11 11 times





20 -24 divide ( 12 ) = -2 $2







is -200 ft _______ 10 min



= -15 ftmin







-20 divide 5 = -4 and -20 times 5 = -100

-100 lt -4



negative





incorrectly

29 a divide ( -3 ) = 8

a = -24

8 divide b = -4






integers

LESSON 23

Your Turn


3 ( -30 ) + 200 = -90 + 200

= 110

2 -6 ( 13 ) - 21 = -78 - 21

= -99

4 ( -12 ) divide 6 + 2 = -2 + 2

= 0

5 -87 divide ( -3 ) -9 = 29 - 9

= 20

6 40 divide ( -5 ) + 30 = -8 + 30

= 22

7 -39 divide 3 -15 = -13 - 15

= -28



moved further back

9 ( -10 ) divide 2 - 2 = -5 - 2 = -7

( -28 ) divide 4 + 1 = -7 + 1 = -6

10 42 divide ( -3 ) + 9 = -14 + 9 = -5

( -36 ) divide 9 - 2 = -4 - 2 = -6

Guided Practice

1 -6 ( -5 ) + 12 = 30 + 12

= 42

2 3 ( -6 ) - 3 = -18 - 3

= -21

3 -2 ( 8 ) + 7 = -16 + 7

= -9

4 4 ( -13 ) + 20 = -52 + 20

= -32

5 -4 ( 0 ) - 4 = 0 - 4

= -4

6 -3 ( -5 ) - 16 = 15 - 16

= -1

7 7 ( -5 ) + 20 = -35 + 20

= -15

15 dollars less

8 7 ( -10 ) + ( -100 ) = -70 + ( -100 )

= -170

170 fewer points

9 6 ( -4 ) + 10 = -24 + 10

= -14

Ned lost 14 points

10 4 ( -12 ) + 10 = -48 + 10

= -38

$38 less

11 -3 ( -2 ) + 3 = 6 + 3

= 9

3 ( -4 ) + 9 = -12 + 9

= -3

9 gt -3

-3 ( -2 ) + 3 gt 3 ( -4 ) + 9

12 -8 ( -2 ) -20 = 16 -20

= -4

3 ( -2 ) + 2 = - 6 + 2

= -4

-4 = -4

-8 ( -2 ) -20 = 3 ( -2 ) + 2

13 -7 ( 5 ) - 9 = -35 - 9

= -44

-3 ( 20 ) + 10 = -60 + 10

= -50

-44 gt -50

-7 ( 5 ) -9 gt -3 ( 20 ) + 10

14 -16 ( 0 ) -3 = 0 -3

= -3

-8 ( -2 ) -3 = 16 -3

= 13

-3 lt 13

-16 ( 0 ) -3 lt -8 ( -2 ) -3





16 -12 ( -3 ) + 7 = 36 + 7

= 43

17 -42 divide ( -6 ) + 5 -8 = 7 + 5 -8

= 12 -8

= 4

18 10 ( -60 ) -18 = -600 -18

= -618

19 ( -11 ) ( -7 ) + 5 - 82 = 77 + 5 - 82

= 82 - 82

= 0

20 35 divide ( -7 ) + 6 = -5 + 6

= 1

21 -13 ( -2 ) - 16 - 8 = 26 - 16 - 8

= 10 - 8

= 2

22 a 5 ( 2 ) -12 + 3 = 10 -12 + 3

= -2 + 3

= 1

b -3 ( 2 ) -1 + 6 + 7 = -6 -1 + 6 + 7

= -7 + 6 + 7

= -1 + 7

= 6


the game

23 5 ( -4 ) -8 = -20 - 8 = -28

24 -36 divide ( -4 ) + 9 = 9 + 9 = 18


25 a 4 ( -35 ) -9 = -140 -9

= -149

$149 less

b Yes $200 - $149 = $51 $51 gt $50 so Arleen

has enough money

26 a 2 ( -10 ) + 3 = -20 + 3= -17

b 7 + 2 + ( -7 ) = 2




7 of clubs





had change








MODULE 2

Ready to Go On


will be negative

( -2 ) ( 3 ) = -6


will be positive

( -5 ) ( -7 ) = 35



( 8 ) ( -11 ) = -88

4 ( -3 ) ( 2 ) ( -2 ) = ( -6 ) ( -2 ) = 12

5 5 ( -3 ) = -15 -15degC

6 -63 ____ 7 = -9

7 -15 ____ -3

= 5

8 0 ____ -15

= 0

9 96 ____ -12

= -8

10 -24 divide 6 = -4 -4 Ib

11 ( -4 ) ( 5 ) + 8 = -20 + 8

= -12

12 ( -3 ) ( -6 ) -7 = 18 -7

= 11

13 -27 ____ 9 - 11 = -3 - 11

= -14

14 -24 ____ -3

- ( -2 ) = 8 + 2

= 10




( -3 ) ( 5 ) + 10 = -15 + 10 = -5 He had $05 less

than before



Are You Ready

1 9 ___ 14

times 7 __ 6 =

3

2

9 ___ 14

times 7 __ 6 1

2

= 3 __ 4

2 3 __ 5 times 4 __

7 = 12 ___

35

3 11 ___ 8

times 10 ___ 33

= 1

4

11 ___ 8 times 10 ___

33 5

3

= 5 ___ 12

4 4 __ 9 times 3 =

3

4 __ 9 times 3 __

1 1

= 4 __ 3 or 1 1 __

3

5 1 __ 2 divide 1 __

4 = 1 __

2 times 4 __

1

=

1 1 __ 2 times 4 __

1 2

= 2 __ 1 = 2

6 3 __ 8 divide 13 ___

16 = 3 __

8 times 16 ___

13

= 1 3 __ 8 times 16 ___

13 2

= 6 ___ 13

7 2 __ 5 divide 14 ___

15 = 2 __

5 times 15 ___

14

= 1

1 2 __ 5 times 15 ___

14 3

7

= 3 __ 7

8 4 __ 9 divide 16 ___

27 = 4 __

9 times 27 ___

16

= 1

1 4 __ 9 times 27 ___

16 3

4

= 3 __ 4

9 3 __ 5 divide 5 __

6 = 3 __

5 times 6 __

5

= 18 ___ 25

10 1 __ 4 divide 23 ___

24 = 1 __

4 times 24 ___

23

= 1 1 __ 4 times 24 ___

23 6

= 6 ___ 23

11 6 divide 3 __ 5 = 6 __

1 times 5 __

3

= 2

6 __ 1 times 5 __

3 1

= 10 ___ 1 = 10

12 4 __ 5 divide 10 = 4 __

5 times 1 ___

10

= 2

4 __ 5 times 1 ___

10 5

= 2 ___ 25

13 21 - 6 divide 3

21 - 2

19

14 18 + ( 7 - 4 ) times 3

18 + 3 times 3

18 + 9

27

15 5 + ( 8 - 3 ) 2

5 + ( 5 ) 2

5 + 25

30

16 9 + 18 divide 3 + 10

9 + 6 + 10

15 + 10

25

17 60 - ( 3 - 1 ) 4 times 3

60 - ( 2 ) 4 times 3

60 - 16 times 3

60 - 48

12

18 10 - 16 divide 4 times 2 + 6

10 - 4 times 2 + 6

10 - 8 + 6

2 + 6

8

LESSON 31

Your Turn

0 _

571428

4 7 ⟌ _


_ -35

50

_ -49

10

_ -7

30

_ -28

20

_ -14

60

_ -56




-0 _

571428 or -0571428571428hellip


0 _ 3

5 3 ⟌ _


_ -3




0333hellip

045

6 20 ⟌ _

900

_ -8 0

1 00

_ -1 00

0

-045

7 -2 3 __ 4 = -thinsp 4 times 2 + 3

_________ 4 = -11 ____

4

275

4 ⟌ _

1100

_ -8

30

_ -28

20

_ -20

0

-275 terminating

8 7 1 __ 3 =

3 times 7 + 1 _________

3 = 22 ___

3

7 _ 3

3 ⟌ _


_ -21





Guided Practice

06

1 5 ⟌ _

30

_ -3 0

0

06 terminating

089

2 100 ⟌ _

8900

_ -80 0

9 00

_ -9 00

0

-089 terminating


4 ___ 12

= 4 times 1 _____ 4 times 3

= 1 __ 3

0 _ 3

3 ⟌ _


_ -3





0 _

25

4 99 ⟌ _


_ -19 8

520

_ -495




25 or


0 _ 7

5 9 ⟌ _


_ -63





036

6 25 ⟌ _

900

_ -7 5

1 50

_ -1 50

0

-036 terminating

004

7 25 ⟌ _

100

_ -1 00

0

004 terminating

01420 _

45

8 176 ⟌ _

250000000

_ -17 6

7 40

_ -7 04

360

_ -352

80

_ -0


_ -704

960

_ -880




-01420 _


0012

9 1000 ⟌ _

12000

_ -10 00

2 000

_ -2 000

0

0012 terminating


10 -11 1 __ 6 = -thinsp 6 times 11 + 1

_________ 6 = -67 ____

6

111 _ 6

6 ⟌ _

67000

_ -6

07

_ -6

1 0

_ -6


_ -36




- 67 ___ 6

-111 _ 6 or -111666hellip

11 2 9 ___ 10

= 10 times 2 + 9

__________ 10

= 29 ___ 10

29

10 ⟌ _

290

_ -20

9 0

_ -9 0

0

29 ___ 10

29

12 -8 23 ____ 100

= - 100 times 8 + 23

____________ 100

= -823 _____ 100

823

100 ⟌ _

82300

_ -800

23 0

_ -20 0

3 00

_ -3 00

0

-823 _____ 100

-823

13 7 3 ___ 15

= 15 times 7 + 3

__________ 15

= 108 ____ 15

72

15 ⟌ _

1080

_ -105

3 0

_ -3 0

0

108 ____ 15

72

14 54 3 ___ 11

= 11 times 54 + 3

__________ 11

= 597 ____ 11

54 _

27

11 ⟌ _

597000

_ -55

47

_ -44


_ -22

80

_ -77




597 ____ 11

54 _

27 or 542727hellip

15 -3 1 ___ 18

= -thinsp 18 times 3 + 1 __________

18 = -55 ____

18

30 _ 5

18 ⟌ _

55000

_ -54

1 0

_ -0


_ -90




-55 ____ 18

-30 _ 5 or -30555hellip

16 3 2 __ 3 =

3 times 3 + 2 _________

3 = 11 ___

3

3 _ 6

3 ⟌ _

1100

_ -9


_ -1 8





17 -2 7 __ 8 = -

8 times 2 + 7 _________

8 = -23 ____

8

2875

8 ⟌ _

23000

_ -16

7 0

_ -6 4

60

_ -56

40

_ -40

0

-2875 lb




3 ___ 47








= 5 ___ 11

0 _

45

11 ⟌ _


_ -4 4

60

_ -55




5 ___ 11

0 _


20 hockey players


= 6 ___ 10

06

10 ⟌ _

60

_ -6 0

0

6 ___ 10

06 terminating

21 polo players


= 4 ___ 11

036

11 ⟌ _


_ -3 3

70

_ -66




4 ___ 11

0 _


22 lacrosse players


= 10 ___ 15

= 5 times 2 _____ 5 times 3

= 2 __ 3

0 _ 6

3 ⟌ _


_ -1 8




10 ___ 15


23 football players


= 11 ___ 11

= 1

11 ___ 11

1 terminating







25 a -4 7 __ 8 = -thinsp 8 times 4 + 7

_________ 8 = - 39 ___

8

b 4875

8 ⟌ _

39000

_ -32

7 0

_ -6 4

60

_ -56

40

_ -40

0

-4875








is equal

to 85 ___ 16


is

equal to 127 ____ 24

or 52916hellip ft




















090625











0121212hellip


LESSON 32

Your Turn

2

50 1 2 3 4

3 + 1 1 __ 2 = 4 1 __

2

3

0-7 -6 -5 -4 -3 -2 -1

-25 + ( -45 ) = -7

6

0 1 2-5-6-7-8 -4 -3-2-1

-8 + 5 = -3

7

10-1

1 __ 2 + ( - 3 __

4 ) = - 1 __

4

8

3 4 5 6 7 80 1 2-3-2-1

-1 + 7 = 6

9

3 4 50 1 2-5-4 -3-2-1

2 1 __ 2 + ( -2 1 __

2 ) = 0

10

3 4 50 1 2-5-4 -3-2-1

-45 + 45 = 0

11

1-1 0

3 __ 4 + ( - 3 __

4 ) = 0


12 -15 + 35 + 2

-15 + 55

55 - 15

4

13 3 1 __ 4 + ( -2 ) + ( -2 1 __

4 )

3 1 __ 4 + ( -4 1 __

4 )

3 1 __ 4 - 4 1 __

4

-1

14 -275 + ( 325 ) + 5

-6 + 5

-1

15 15 + 8 + ( -3 )

23 + 3

20

Guided Practice

1

3 4 50 1 2-5-4 -3-2-1

-3 + ( -15 ) = -45

2

0 54321-5-4-3-2-1

15 + 35 = 5

3

0 105-1 -05

1 __ 4 + 1 __

2 = 3 __

4

4

0 54321-5-4-3-2-1

-1 1 __ 2 + ( -1 1 __

2 ) = -3

5

0 54321-5-4-3-2-1

3 + ( -5 ) = -2

6

0 54321-5-4-3-2-1

-15 + 4 = 25

7 -2150 + 2150 = 0 $0

8 -874 + 874 = 0 $0

9 275 + ( -2 ) + ( -525 )

275 + ( -725 )

- ( 725 - 275 )

-45

10 -3 + 1 1 __ 2 + 2 1 __

2 = -3 + 4 = 1

11 124 + 92 + 1

-124 + 102

- ( 124 - 102 )

-22

12 -12 + 8 +13

-12 + 21

21 - 12

9

13 45 + ( -12 ) + ( -45 )

45 + ( -45 ) + ( -12 )

0 + ( -12 )

-12

14 1 __ 4 + ( - 3 __

4 ) = - ( 3 __

4 - 1 __

4 ) = - 2 __

4 = - 1 __

2


15 -4 1 __ 2 + 2 = - ( 4 1 __

2 - 2 ) = -2 1 __

2

16 -8 + ( -1 1 __ 8 ) = -9 1 __

8


The sum is 2



19 -$225 + $1500 = $1500 - $225 = $1275

20 -3525 m + ( -85 ) = -4375 m

21 4 3 __ 4 mi + ( -3 1 __

4 mi ) = 1 2 __

4 mi = 1 1 __

2 mi


23 30 + 15 - 25 = 45 - 25 = 20 pts

24 January

Income - Expenses

$1205 - $129060

- ( $129060 - $1205 ) -$8560

February

Income - Expenses

$1183 - $134544

-($134544 - $1183)

-$16244


February

25 June

Income - Expenses

$2413 - $210623

$30677

July

Income - Expenses

$2260 - $195850

$30150

August

Income - Expenses

$2183 - $184512

$33788


$33788 in August






the end of August

Income = $1205 + $1183 + $1664 + $2413

$2260 + $2183 = $10908

Expenses = $129060 + $134544 + $1664 +$210623 + $195850 + $184512

= $1020989

Profit = $10908 - $1020989 + $250

= $94811


28 a 7 ( 10 ) + 3 ( -15 ) = 70 - 45 = 25 pts

b 2 ( 10 ) + 8 ( -15 ) = 20 - 120 = -100 pts








the positive number







LESSON 33

Your Turn

1

-9 -8 -7 -6 -5 -4

-65 - 2 = -85

2

42 30-1 1

1 1 __ 2 - 2 = - 1 __

2

3

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0

-225 - 55 = -775

6

1 2-1 0

025 - ( -150 ) = 175

7

1-1 0

- 1 __ 2 - ( - 3 __

4 ) = 1 __

4

Guided Practice

1

1312111098765 14 15

5 - ( -8 ) = 13

2

-9 -8 -7 -6 -5 -4 -3

3 1 __ 2 - 4 1 __

2 = -8


3

-15 -13 -11 -9 -5-7

-7 - 4 = -11

4

-6 -5 -4 -3 -2 -1 0 1

-05 - 35 = -4

5 -14 - 22 = -36

6 -125 - ( -48 )

-125 + 48

- ( 125 - 48 )

-77

7 1 __ 3 - ( - 2 __

3 ) = 1 __

3 + 2 __

3 = 1

8 65 - ( -14 ) = 65 + 14 = 79

9 - 2 __ 9

- ( -3 )

- 2 __ 9

+ 3

3 - 2 __ 9

2 9 __ 9 - 2 __

9

2 7 __ 9

10 24 3 __ 8

- ( -54 1 __ 8 )

24 3 __ 8

+ 54 1 __ 8

78 4 __ 8

78 1 __ 2

11 -1 m + ( 105 m ) = -15 m


12 -12 1 __ 2 + ( -5 ) = -17 1 __

2

17 1 __ 2

or 175 yards


533 ft - ( -10 ft ) = 533 ft + 10 ft = 543 ft

14 -4500 + (-3015) = -7515 $7515






16 -126degC - 75degC = -201degC

17 -2565 ft - 165 ft + 1245 ft = -297 ft


18 -9500 ft - ( -26000 ft ) = 16500 ft

19 29035 ft - ( -36198 ft ) = 65233 ft

70000 ft - ( -26000 ft ) = 96000 ft


96000 ft - ( 65233 ft ) = 30767 ft


b 78degF - 32degF


21 a -$1258 + ( -$3072 ) = -$4330

b -$4330 + ( -$25 ) = -$6830

c $6830 since -$6830 + $6830 = 0



23 a 5 ft - 72 ft + 22 ft

b 5 ft - 72 ft + 22 ft

5 ft + 22 ft - 72 ft

72 ft - 72 ft



24 a Yes

$425 + $089 + $1099

= $1613 lt $20

b $20 - $1613 = $387 left over





- 7 ___ 16

- 1 __ 4 - 5 ___

16 = ( - 7 ___

16 ) + ( - 1 __

4 ) + ( - 5 ___

16 )

( - 7 ___ 16

) + ( - 5 ___ 16

) + ( - 1 __ 4 ) by CPA

( -7 + ( -5 ) __________

16 ) + ( - 1 __

4 )

( -12 ____ 16

) + ( - 1 __ 4 )

( - 4 times 3 _____ 4 times 4

) + ( - 1 __ 4 )

( - 3 __ 4 ) + ( - 1 __

4 )

( -3 + ( -1 ) __________

4 )

( -4 ___ 4 ) = -1





and c __ d

Both fractions









LESSON 34

Your Turn

1

-8 -7 -6 -5 -2 -1 0-4 -3

2 ( -35 ) = -7

2

-2 -1 0 1 2 3 4-4 -3

-3 ( -125 ) = 375

4 ( - 3 __ 4 ) ( - 4 __

7 ) ( - 2 __

3 ) = -



= - 2 __ 7

5 ( - 2 __ 3 ) ( - 3 __

4 ) ( 4 __


__________ 13 times 41 times 5


= 2 __ 5

6 ( 2 __ 3 ) ( - 9 ___

10 ) ( 5 __

6 ) = -


____________ 13 times 210 times 63


= - 1 __ 2

Guided Practice

1

-5 -2 -1 0-4 -3

5 ( - 2 __ 3 ) = 5 __

1 times ( - 2 __

3 )

= - 5 times 2 _____ 1 times 3

= - 10 ___ 3

= -3 1 __ 3

2

-1 -05 0-2 -15

3 ( - 1 __ 4 ) = 3 __

1 times - 1 __

4

= - 3 times 1 _____ 1 times 4

= - 3 __ 4

3

0 1 2-2 -1

-3 ( - 4 __ 7 ) = 3 __

1 times 4 __

7

= 3 times 4 _____ 1 times 7

= 12 ___ 7

= 1 5 __ 7

4

-2 -1 0 1 2 3 4-4 -3

- 3 __ 4 ( -4 ) = 3 __

4 times 4 __

1

= 3 times 41

______ 14 times 1

= 3 times 1 _____ 1 times 1

= 3 __ 1

= 3

5 4 ( -3 ) = -12

6 -18 ( 5 ) = -9

7 -2 ( -34 ) = 68

8 054 ( 8 ) = 432

9 -5 ( -12 ) = 6

10 -24 ( 3 ) = -72

11 1 __ 2 times 2 __

3 times 3 __

4 = ( 1 times 21

______ 12 times 3

) ( 3 __ 4 )

= ( 1 __ 3 ) ( 3 __

4 )

= 1

1 __ 3 times 3 __

4 1

= 1 __ 4

12 - 4 __ 7 ( -thinsp 3 __

5 ) ( - 7 __

3 ) = ( - 4 times 3 _____

7 times 5 ) ( - 7 __

3 )

= 12 ___ 35

( - 7 __ 3 )

= - 4

5 12 times 7 ______ 35 times 3

1

1

= - 4 times 1 _____ 5 times 1

= - 4 __ 5

13 ( - 1 __ 8 ) times 5 times 2 __

3 = ( - 1 __

8 ) times 5 __

1 times 2 __

3


__________ 48 times 1 times 3


= - 5 ___ 12


14 ( - 2 __ 3

) ( 1 __ 2 ) ( - 6 __


__________ 13 times 21 times 7


= 2 __ 7


16 18 ( -100 ) = -1800 or a $1800 change









amount

b 200 + 6 ( -1998 )

= 200 - 11988

= 8012 $8012





which is 6

20 8 ( -3 1 __ 4 ) = -8 ( 13 ___

4 )

= - 1

8 __ 1 times 13 ___

4 1

= - 2 times 13 ______ 1 times 1

= - 26 ___ 1





(below the surface)

22 5 + ( -3 ) ( 15 )

= 5 + ( -45 )

= 05 cups left





a positive



25 Total score is

2 times ( 6 ) + 16 times ( 05 )

+ 7 times ( -05 ) + 2 times ( -15 )

= 12 + 8 - 35 - 3

= 20 - 65

= 135 pts




= 12 + 5 ( -68 )

= 12 + ( -34 )

= -22degC

27 a b c d

+ + + +

+ + - +

+ - + +

- + + +

- - - +

- - + -

- + - -

+ - - -









LESSON 35

Your Turn

3 28 ___ -4

= - 28 ___ 4 = -07

4 -664 ______ -04

= 664 ____ 04

= 166

5 - 55 ___ 05

= - 55 ___ 5 = -11

6 -4256 _______ 112

= -38


per minute

7 - 5 __

8 ___

- 6 __ 7 = - 5 __

8 divide - 6 __

7

= - 5 __ 8 times - 7 __

6

= 35 ___ 48

8 - 5 ___

12 ____

2 __ 3 = - 5 ___

12 divide 2 __

3

= - 5 ___ 12

times 3 __ 2

= - 15 ___ 24

= - 5 __ 8


9 -4__5

___1__2 =-4__5divide1__

2

=-4__5times2__1

=-8__5

=-13__5

Guided Practice

1 072_____-09=-72___

9 =-08

2 -1__5

___7__5 =-1__

15times5

1__

7=-1times1_____

1times7=-1__7

3 56___-7=-56___7=-8

4 251____4 divide(-3__

8)=251____

4 times-8__

3

=-251times82________

14times3


=-502____3

5 75____-1__5

=-75___1times5__

1=-75times5______

1times1=-375

6 -91____-13=91___

13=7

7 -3__7

___9__4 =-

13__7times4__93


=-4___21

8 - 12____003

=-1200_____

3 =-400


changeindays

=-35L______4day

=-0875 L____day

or-0875Lperday


changeindays

=-$4575________5day



numberofminutes

=-044mi________08min

=-44mi______8min

=-055mileperminute



13 5___-2__

8=-5__

1times8__

24

1=-5times4_____

1times1=-20

14 51__3divide(-11__

2)


2

=-16___3divide3__

2

=-16___3times2__

3


=-32___9

15 -120_____-6 =120____

6 =20

16 -4__5

___-2__

3=

24__5times3__

21=2times3_____

5times1=6__

5

17 103divide(-103)=-103____1 times 1____

103

=-103times1________1times103

=-103____103

=-103____103

=-01

18 -04_____80

=-04___80

=-0005

19 1divide9__5=1__

1times5__

9=5__

9

20 -1___4 ___

23___24

=-1__

14times246

___23


=-6___23

21 -1035_______-23 =1035_____

23 =45


= 21h______7days

=3 h____day


times3days=9hours




=-4times15+3___________4 times1__

9

yd___run

=-763___4 times1__

91yd

___run

=-153__

4yd______

9runs

=-153__4times1__

9

yd___run

=-7__4or-13__

4yardsperrun





_____________________________________ 4

= 414degC ______ 4

= -1035degC per day

25 a total profit


= $1750

______ 7 days

= $250 per day

b $150

_____ day


c total change


= - $490

______ 7 days

= -$70 per day


= 996 m ______ 12 s

= 83 ms





- 3 __

4 ___

4 __ 3

= - 3 __

4 times 3 __

4 = - 9 ___

16



= -629 m





-85degF divide 15 d

= - 1785 ____ 315

degF __ d

= - 17 ___ 3 degF __

d or -5 2 __

3 degF __


d


every day





definition

LESSON 36

Your Turn


3 times 2 1 __ 2 = 7 1 __

2


30 - 7 1 __ 2 = 22 1 __

2


22 1 __ 2 divide 4 = 5 5 __

8











12 3 __ 5 = 126

= 0126


750 times 0126 = 945

750 + 945 = 8445


8445 times 0126 asymp 10641

8445 + 10641 = 95091


95091 times 0126 asymp 11981

95091 + 11981 = 107072


Guided Practice











78 times 3 = 234


234 divide 4 = 585




12 - 3 1 __ 2 = 8 1 __

2

Find half the width

8 1 __ 2 divide 2 = 4 1 __

4


of the page


11 times 1 __ 3 = 3 2 __

3

10 times 3 __ 4 = 7 1 __

2

3 2 __ 3 + 7 1 __

2 = 11 1 __

6


box

11 1 __ 6 lt 12





41 3 __ 4 divide 2 = 20 7 __

8


50 - 20 7 __ 8 = 29 1 __

8




( 78 + 10 ) = 88


88 = 88 ____ 100

= 44 ___ 50


Donovan

44 - 39 = 5


Donovan







19 ___ 37


15 times ( - 1 __ 2 ) = -075







-79 9 ___ 10

divide ( -188 ) = 425


19 1 __ 8 - 1275 - 425 = 2 1 __

8


-28 9 ___ 10

- ( -79 9 ___ 10

) = 51


51 divide 2 1 __ 8 = 24


ascent was 24 ftmin

15 Sample answer



the result by 037



(276 + 159)037 = (276)(037) + (159)(037)




make errors








MODULE 3

Ready to Go On

1 4 1 __ 5 =

5 times 4 + 1 _________

5 = 21 ___

5

42

5 ⟌ _

210

_ -20

1 0

_ -1 0

0

42


2 12 14 ___ 15

= 15 times 12 + 14

___________ 15

= 194 ____ 15

129 _ 3

15 ⟌ _

194000

_ -15

44

_ -30

14 0

_ -13 5

50 first 50

_ -45

50 second 50



129 _ 3 or 12933

3 5 5 ___ 32

= 32 times 5 + 5

__________ 32

= 165 ____ 32

515625

32 ⟌ _

16500000

_ -160

5 0

_ -3 2

1 80

_ -1 60

200

_ -192

80

_ -64

160

_ -160

0

515625

4 45 + 71 = 116

5 5 1 __ 6 + ( -3 5 __

6 ) = 4

6+1 ____

6 -3 5 __

6

= 1 2 __ 6

= 1 1 __ 3

6 - 1 __ 8 -6 7 __

8 = - 1 __

8 + ( -6 7 __

8 )

= -6 8 __ 8

= -7

7 142 - ( -49 ) = 142 + 49

= 191

8 -4 ( 7 ___ 10

) = - 4 __ 1 times 7 ___

10

= - 24 times 7 _______ 1 times 105

= - 2 times 7 _____ 1 times 5

= - 14 ___ 5 or -2 4 __

5

9 -32 ( -56 ) ( 4 ) = 32 times 56 times 4

= 7168

10 - 19 ___ 2 divide 38 ___

7 = -

119 times 7 _______ 2 times 382

= - 1 times 7 _____ 2 times 2

= - 7 __ 4

11 -3201 _______ -33

= 3201 _____ 33

97

33 ⟌ _

3201

_ -297

23 1

_ -23 1

0

97


second day

$8360 + $1535 = $9895


-4 3 __ 4 = -475 or -00475




price

$9895 times -00475 asymp -$47

$9895 - $47 = $9425






prices



Are You Ready

1 3 __ 4 divide 4 __

5 = 3 __

4 times 5 __

4

= 15 ___ 16

2 5 __ 9 divide 10 ___

11 = 5 __

9 times 11 ___

10

= 1

5 __ 9 times 11 ___

10 2

= 11 ___ 18

3 3 __ 8 divide 1 __

2 = 3 __

8 times 2 __

1

= 4

3 __ 8 times 2 __

1 1

= 3 __ 4

4 16 ___ 21

divide 8 __ 9 = 16 ___

21 times 9 __

8

=thinsp 2

7 16 ___ 21

times 9 __ 8 3

1

= 6 __ 7

5 B ( -4 1 )

6 C ( 3 0 )

7 D ( 5 4 )

8 E ( -2 -2 )

9 F ( 0 0 )

10 G ( 0 -4 )

LESSON 41

Your Turn

3 1 __ 6 acre divide ( 1 __

4 hour ) = 1 __

6 times 4 __

1

= 3


2

= 1 times 2 _____ 3 times 1


4 3 cups divide ( 3 __ 4 cups ) = 3 __

1 divide 3 __

4

= 3 __ 1 times 4 __

3

= 1


1

= 1 times 4 _____ 1 times 1

= 4 cups


5 = 3 __

4 times 5 __

1 = 15 ___

4 = 3 3 __

4


6 = 2 ___

1 3 times 6

2 __

1 = 4 __

1 = 4






flavor

Guided Practice

1

Distance (mi) 8 1 __ 2 17 25 1 __

2 34 42 1 __

2

Time (h) 1 __ 2 1 1 1 __

2 2 2 1 __

2

2 3 1 __ 2 miles divide ( 1 1 __

4 hours ) = 7 __

2 divide 5 __

4 mi ___ h

= 7 times 4 _____ 2 times 5

= 1 7 times 4 _____ 2 times 5

2

= 7 times 2 _____ 1 times 5

= 14 ___ 5 mi ___

h


3 5 __ 8 page divide ( 2 __

3 minute ) = 5 __

8 times 3 __

2

= 15 ___ 16

page per minute

4 1 __ 6 foot divide ( 1 __

3 hour ) = 1 __

6 times 3 __

1

= 2 1 times 3 _____ 6 times 1

1

= 1 times 1 _____ 2 times 1


5 5 __ 8 sq ft divide ( 1 __

4 hour ) = 5 __

8 times 4 __

1

= 2 5 times 4 _____ 8 times 1

1

= 5 times 1 _____ 2 times 1

= 5 __ 2 or 2 1 __



UNIT

2



1 divide 1 __

3

= 240 ____ 1 times 3 __

1

= 720 ____ 1



1 divide 1 __

2

= 325 ____ 1 times 2 __

1

= 650 ____ 1




1 __ 4 cup divide ( 2 __

3 serving ) = 1 __

4 times 3 __

2

= 3 __ 8

cup _______

serving


1 __ 3 cup divide ( 3 __

4 serving ) = 1 __

3 times 4 __

3

= 4 __ 9

cup _______

serving




72 and 4 __

9 = 32 ___

72




the rate


1 __ 2 hour

= 1 __




$10 divide ( 35 hours ) = 10 ___ 35

$ __



$125 divide ( 1 __ 2 hours ) = 125 ____

05 $ __





multiply by 60


= 005 ____ 1

$ ____


1 h

= $3 per hour



one


8 cup






originally

c 1 __ 2 divide 1 __

8 = 1 ___

1 2 times 8

4 __

1 = 4 __

1 = 4


sunflower seeds

11 10 songs


= 5 songs ____________

1 commercials


6 mi divide ( 1 __ 2 h ) = 6 __

1 times 2 __

1

= 12 miles per hour

Jessersquos rate


4

= 2 __ 1 times 4 __

1 mi ___ h

= 8 miles per hour

b Terrance

50 mi divide ( 12 mi ___ h ) = 50 ___

1 times 1 ___

12

= 50 ___ 12

h

= 4 1 __ 6 h

= 4 10 ___ 60

h


Jesse

50 mi divide ( 8 mi ___ h ) = 50 ___

1 times 1 __

8

= 50 ___ 8 h

= 6 1 __ 4 h

= 6 15 ___ 60

h



4

= 8 __ 1 times 4 __

3

= 32 ___ 3





13 1 ___ 10

h = 6 ___ 60

h = 6 min

300 words _________ 6 min

= 50 words per min

1 ___ 12

h = 5 ___ 60

h = 5 min

300 words _________ 5 min

= 60 words per min










b For the 10-pack



For the 12-pack








2 day ) = 1 room _____

day so at the same





LESSON 42

Your Turn


was not constant




= 12 ___ 1 = 36 ___

3 = 60 ___




s or s = 12a

Guided Practice

1 45 ___ 1 = 45 90 ___

2 = 45 135 ____

3 = 45 180 ____

4 = 45


2 k = y __ x = 10 ___

2 = 5 y = 5x

3 k = y __ x = 2 __

8 = 1 __

4 y = 1 __

4 x


of proportionality


5 k = y __ x = 74 ___

4 = 1850 y = 1850x

6 $1099

_______ 05 days

= $2198 per day


($1850)

8 100 ft _____ 08 s

= 1000 _____ 8 ft __ s = 125 ft __ s

500 ft _____ 31 s

= 5000 _____ 31


1875 ft ______ 15 s

= 1875 ______ 15





9 $3125

______ 5 h


______ 8 h

= $625 per







12 y = $625 ( 3 ) = $1875

13 300 ft _____ 2 min

= 6750

_____ 45


150 ft _____ min

times 60 min ______ 1 h


14 y = 150x



hours




same factor




of corn

LESSON 43

Your Turn

1 No because 11 ___ 1 ne 16 ___





b k = 60 mi _____ 4 h

= 15 mi ___ h


distance in miles

Guided Practice

1

Time (h) 3 5 9 10

Pages 195 325 585 650


per hour

2

Time (h) 2 3 5 8

Earnings 15 2250 3750 60








5 k = 28 ft ____ 8 s

= 7 __ 2 ft __ s = 35 ft __ s y = 7 __



6 k = $2 ______

8 items = 1 __

4

$ _____

items = 025

$ _____

items so y = 1 __

4 x or


y = cost in dollars


origin



0 minutes





x or 2 __ 5 x




5 = 48




2

2

4

6

8

10

4 6 8 10Time (min)

Dis

tanc

e (m

i)

A

B

O








equation

15 a

2

8

16

24

32

40

4 6 8 10DVDs

Cost

($)

O



cost $20






18 k = 8 ft ___ 4 s










because 65 ___ 1 ne 85 ___

2





distance column

MODULE 4

Ready to Go On

1 $140

_____ 18 ft 2


2 $299

_____ 14 lb


3 $56 ______


$3205

______ 15 gal


4 $160

_____ 5 g


$315

_____ 9 g




3


6 k = $9

___ 8euro

= $27 ____

24euro = 9 __

8 $ __

euro or 1125

$ __

euro So y = 9 __

8 x or





_______ pt

or k = 25 servings

_______ pt

Therefore

y = 5 __ 2




2

2

4

6

8

10

4 6 8 10Pints

Serv

ings

Frozen Yogurt

O





constant rate



Are You Ready

1 22 = 22 ____ 100

= 022

2 75 = 75 ____ 100

= 075

3 6 = 6 ____ 100

= 006

4 189 = 100 + 89

= 100 ____ 100

+ 89 ____ 100

= 1 + 089

= 189

5 059 = 59

6 098 = 98

7 002 = 2

8 133 = 133

9 64

_ timesthinsp05

320

32

10 30

_ timesthinsp007

210

21

11 160

_ timesthinsp015

800

_ +1600

2400

24

12 62

_ timesthinsp032

124

_ +thinsp1860

1984

1984

13 4

_ timesthinsp12

8

_ +thinsp40

48

48

14 1000

_ timesthinsp006

6000

60

LESSON 51

Your Turn

2 x = ( $64 - 52 )

__________ $52

x = $12

____ $52

asymp 23

4 x = ( 18 - 12 )

________ 18

x = 6 ___ 18

asymp 33

5 x = ( 16 - 10 )

________ 16

x = 6 ___ 16

= 375

8 010 times $499 = $4990

$499 + $4990 = $54890

9 030 times $499 = $14970

$499 - $14970 = $34930

Guided Practice

1 x = ( $8 - $5 )

_________ $5

x = $3

___ $5

= 60

2 x = ( 30 - 20 )

_________ 20

x = 10 ___ 20

= 50

3 x = ( 150 - 86 )

__________ 86

x = 64 ___ 86

asymp 74

4 x = ( $389 - $349 )

______________ $349

x = $040

_____ $349

asymp 11

5 x = ( 14 - 13 )

________ 13

x = 1 ___ 13

asymp 8

6 x = ( 16 - 5 )

________ 5

x = 11 ___ 5 = 220

7 x = ( 64 - 36 )

_________ 36

x = 28 ___ 36

asymp 78

8 x = ( 80 - 64 )

_________ 80

x = 16 ___ 80

= 20

9 x = ( 95 - 68 )

_________ 95

x = 27 ___ 95

asymp 28


10 x=( 90-45)_________

90

x=45___90

=50

11 x=( 145-132)__________

145

x=13____145

asymp9

12 x=( 64-21)_________

64

x=43___64

asymp67

13 x=( 16-0)________

16

x=16___16

=100

14 x=( 3-1__

2)_______

3

x=21__

2___

3 asymp83

15 010times$900=$090 $900+$090=$990

16 025times48=12 48-12=36cookies

17 020times340=68 $340-68=272pages

18 050times28=14 28+14=42members

19 004times$29000=$1160 $29000-$1160=$27840

20 130times810=1053 810+1053=1863songs

21 030times20=6 20+6=26miles



ItemOriginal

PriceNew Price

Percent Change

Increase or





24 a 55

x=( 8-3)_______

8 =5__

8=625

x=( 12-7)________

12 =5___

12asymp417



x=( 12-3)________

3

x=9__3=300increase



b $100_____5 =$020each$100_____

4 =$025each



=25

26 Percenterror=( 136-133)___________

136 times100

=03____136

times100asymp2







LESSON 52

Your Turn

2 a 1c+01c11c

b s=11times$28=$3080

3 a 200

b 1c+2c3c

5 a

1b - 024b

1b024b

b 1b-024b=076b

6 a 1p-005p095p

b 095p=$1425




Guided Practice

1 a 035s

b 1s + 035s 135s

c 135 times $3200 = $4320

d 035 times $3200 = $1120


Price

2 Hat $18 15 $270 $2070

3 Book $2250 42 $945 $3195

4 Shirt $3375 75 $2531 $5906

5 Shoes $7499 33 $2475 $9974

6 Clock $4860 100 $4860 $9720

7 Painting $18500 125 $23125 $41625

8 $4500 - 022 ( $4500 ) = $3510

9 $8900 - 033 ( $8900 ) = $5963

10 $2399 - 044 ( $2399 ) = $1343

11 $27999 - 075 ( $27999 ) = $7000





13 a 046b

b 1b - 046b 054b

c 054 times $2900 = $1566

d 046 times $2900 = $1334


Sale Price $201

Regular Price $419

Sale Price $245

Regular Price $279

Sale Price $115

Regular Price $309

Sale Price $272

Regular Price $377

Sale Price $224


$050


$9950


$350

16 p = 127 ( $7400 ) = $9398

s = 127 ( $4800 ) = $6096

j = 127 ( $32500 ) = $41275

2 ( 9398 ) + 3 ( $6096 ) + $41275 = $78359









greater




the coat

LESSON 53

Your Turn

1 005 times $2000 = $100 $100 + $2000 = $2100

3 005 times $40000 = $2000

$2000 times 4 years = $8000

$40000 + $8000 = $48000


Total $2200 + $16875 = $236875

Guided Practice

1 005 times $3000 = $150

2 015 times $7000 = $1050

3 0004 times $10000 = $040

4 15 times $2200 = $3300

5 001 times $8000 = $080

6 20 times $500 = $1000

7 a 007 times $4399 = $308

b $4399 + $308 = $4707

8 115 times $7550 = $8683

9 007 times $2000 = $140


10 003 times $550 = $1650

$1650 times 10 years = $165

$550 + $165 = $715

11 a 090 times $20 = $18

b 1085 times $18 = $1953

12 020 times $2999 = $600 tip

00625 times $2999 = $187 tax

$2999 + $600 + $187 = $3786 total



to the price


14 $3275 + $3988 = $7263 total meal cost

014 times $7263 = $1017 tip

$7263 + $1017 = $8280 total with tip


$7865 times 020 = $1573 tip

$7865 + $1573 - $1180 = $8258 total


0075 times $29375 = $2203 tax

$29375 + $2203 = $31578 total with tax


17 $7999 times 012 = $960 discount

$7999 - $960 = $7039 price before tax





19 $4500 + 00725 = $32625 commission

$750 + $32625 = $107625 total income


$475 + $3850 = $51350 total income










nearest inch

22 a $4998 times 05 = $2499 50 discount

$2499 - $1000 = $1499 $10 discount

b $4998 - $1000 = $3998 $10 discount

$3998 times 05 = $1999 50 discount


$8550 + $1599 = $10149 total


$95 + $1439 = $10939 total



d $10149 times 008 = $812 tax

$10149 + $812 = $10961 total

24 a Store 1 $22 divide 2 = $11

Store 2 $1299 times 09 = $1169




b Store 3 $2098 times 045 = $944






to $2050 per month


____________ 137

times 100 = 05 ____ 137

asymp 36

MODULE 5

Ready to Go On

1 x = ( 63 - 36 )

_________ 36

x = 27 ___ 36

= 75 increase

2 x = ( 50 - 35 )

_________ 50

x = 15 ___ 50

= 30 decrease

3 x = ( 72 - 40 )

_________ 40

x = 32 ___ 40

= 80 increase

4 x = ( 92 - 69 )

_________ 92

x = 23 ___ 92

= 25 decrease

5 $60 times 015 = $9

$60 + $9 = $69

6 $32 times 0125 = $4

$32 + $4 = $36

7 $50 times 022 = $11

$50 - $11 = $39

8 $125 times 030 = $3750

$12500 - $3750 = $8750


$325 + $312 = $637 total income

10 $5310

______ $1735

asymp 31



$700 times 020 = $140

$700 + $140 = $840


5 less than Priya

$840 times 005 = $042

$840 - $042 = $798





$45 times 026 = $1170

$45 + $1170 = $5670






Are You Ready

1 5 + x

2 11 - n

3 -9 ___ y

4 2x - 13

5 2x + 3

= 2 ( 3 ) + 3

= 6 + 3

= 9

6 -4x + 7

= -4 ( 1 ) + 7

= -4 + 7

= 11

7 15x - 25

= 15 ( 3 ) - 25

= 45 - 25

= 2

8 04x + 61

= 04 ( -5 ) + 61

= -20 + 61

= 41

9 2 __ 3 x - 12

= 2 __ 3

( 18 ) - 12

= 2 __ 3

times ( 18 ___ 1 ) - 12

= 36 ___ 3 - 12

= 0

10 - 5 __ 8

x + 10

= - 5 __ 8 ( -8 ) + 10

= - 5 __ 8 times- 8 __

1 + 10

= - 5 ___ 1 8

times- 8 1 __

1 + 10

= - 5 __ 1 times- 1 __

1 + 10

= 5 + 10

= 15

11 1 __ 2 divide 1 __

4

= 1 times 4 _____ 2 times 1

= 1 times 4 2 ______

1 2 times 1

= 1 times 2 _____ 1 times 1

= 2

12 3 __ 8 divide 13 ___

16

= 3 __ 8 times 16 ___

13

= 3 times 16 2 _______

1 8 times 13

= 3 times 2 ______ 1 times 13

= 6 ___ 13

13 2 __ 5 divide 14 ___

15

= 2 __ 5 times 15 ___

14

= 1 2 times 15

3 ________

1 5 times 14 7

= 1 times 3 _____ 1 times 7

= 3 __ 7

14 4 __ 9 divide 16 ___

27

= 4 __ 9 times 27 ___

16

= 1 4 times 27

3 ________

1 9 times 16 4

= 1 times 3 _____ 1 times 4

= 3 __ 4

LESSON 61

Your Turn

2 ( 3x + 1 __ 2 ) + ( 7x - 4 1 __

2 )

= 3x + 7x + 1 __ 2 - 4 1 __

2

= 10x - 4

3 ( -025x - 3 ) - ( 15x + 14 ) = -025x - 3 - 15x - 14

= -175x - 44

4 02(3b - 15c) + 6c

= 06b - 3c + 6c

= 06b + 3c

5 2 __ 3 (6e + 9f - 21g) - 7f

= 4e + 6f - 14g - 7f

= 4e - f - 14g

6 5x - 3(x - 2) - x

= 5x - 3x + 6 - x

= x + 6

7 83 + 34y - 05(12y - 7)

= 83 + 34y - 6y + 35

= 118 - 26y


UNIT

3


Guided Practice


14 + 12n + 23 + 16n

14 + 23 + 12n + 16n

37 + 28n


37 + 28n

2 37 + 28n

37 + 28 ( 9 )

= 37 + 252

= 289

3 14 + 5(x + 3) - 7x = 14 + 5x + 15 - 7x

= 29 - 2x

4 3 ( t - 4 ) - 8 ( 2 - 3t ) = 3t - 12 - 16 + 24t

= 27t - 28

5 63c - 2 ( 15c + 41 ) = 63c - 3c - 82

= 33c - 82

6 9 + 1 __ 2 ( 7n - 26 ) - 8n = 9 + 35n - 13 - 8n

= -4 - 4 1 __ 2 n

7 2x + 12

2 ( x + 6 )

8 12x + 24

12 ( x + 2 )

9 7x + 35

7 ( x + 5 )







15 ( 100 + 5d ) + 20 ( 50 + 7d ) = 15 ( 100 ) + 15 ( 5d ) + 20 ( 50 ) + 20 ( 7d )

= 1500 + 75d + 1000 + 140d

= 1500 + 1000 + 75d + 140d

= 2500 + 215d


New width 60 + w


2(96 + l) + 2(60 + w)

=2(96) + 2l + 2(60) + 2w

192 + 2l + 120 + 2w

192 + 120 + 2l + 2w

312 + 2l + 2w

13 Width 3


Factors 3 and x + 2

Product 3 ( x + 2 ) = 3x + 6

14 Width 4



Product 4 ( 2x - 1 ) = 8x - 4




and 6 times 4 ) So 6 ( 9 ) = 6 ( 5 ) + 6 ( 4 )


6x = ( x + 3 ) + ( 2x + 4 ) +

6x = 3x + 7 +

-3x = _ -3x

3x = 7 +

_ -7 = _ -7

3x - 7 =



10x + 6 = 2 ( 3x - 3 ) + 2 ( )

10x + 6 = 6x - 6 + 2

_ -6x = _ -6x

4x + 6 = - 6 + 2

_ + 6 = _ + 6

4x + 12 = 2

( 4x + 12 ) divide 2 = ( 2 ) divide 2

2x + 6 =


18 a P = 2l + 2w


2(2x + 6) + 2(x)

= 4x + 12 + 2x

= 6x + 12


2(3x - 14) + 2( 1 __ 2 x + 32)

= 6x - 28 + x + 64

= 7x + 36

b (7x + 36) - (6x + 12)

= 7x + 36 - 6x - 12

= x + 24


Let x = 36

2x + 6 = 2 ( 36 ) + 6

= 72 + 6

= 78


Let x = 36

1 __ 2 x + 32 = 1 __

2 ( 36 ) + 32

= 18 + 32

= 50


Let x = 36

3x - 14 = 3 ( 36 ) - 14

= 108 - 14

= 94





( x ) ( x ) = x 2

( x ) 1 = x

( 1 ) 1 = 1


x

x

1

11

1 1

x2 x x x

x 1 1 1x 1 1 1

Area =

x 2 + x + x + x + x + x + 1 + 1 + 1 + 1 + 1 + 1

= x 2 + 5x + 6

( x + 3 ) ( x + 2 ) = x 2 + 5x + 6




1160 = 1334 So 58 ( 23 ) = 58 ( 3 ) + 58 ( 20 )


8 ( 1000 - 3 ) = 8000 - 24 = 7976


Property 8 ( 900 + 90 + 7 ) = 7200 + 720 + 56 =

7976

LESSON 62

Your Turn

1 49 + z = -9

_ -49 _ -49

z = -139

2 r - 171 = -48

_ +171 _ +171

r = 123

3 -3c = 36

-3c ____ -3

= 36 ___ -3

c = -12

5 x - 15 = 525

_ +15 _ +15

x = 675


6 x ___ 35

= -12

x ___ 35

( 35 ) = -12 ( 35 )

x = -42


7 25x = 75

25x ____ 25

= 75 ___ 25

x = 3


Guided Practice



x + ( -134 ) = -17 or x - 134 = -17

x - 134 = -17

_ +134 _ +134

x = 117


warmer



-1 1 __ 2 x = -9

( - 2 __ 3 ) ( - 3 __

2 x ) = ( - 2 __

3 ) ( -9 )

x = 18 ___ 3

x = 6


3 -2x = 34

-2x ____ -2

= 34 ___ -2

x = -17

4 y - 35 = -21

_ + 35 _ + 35

y = 14

y = 14

5 2 __ 3 z = -6

( 3 __ 2 ) 2z ___

3 = ( 3 __

2 ) ( -6 )

z = -9





x - 870737 = 203215

_ +870737 _ +870 737

x = 2902887



2825131 - x = 2320106

_ -2825131 _ -2825131

-x = - 505025

x = 505025




2825131 - x = 1119421

_ -2825131 _ -2825131

-x = -1705710

x = 1705710



1250 - 935 = 315

Use an equation


descends

( -22 1 __ 2 ) x = -315

( - 45 ___ 2 ) x = -315

( - 2 ___ 45

) ( - 45 ___ 2 ) x = -315 ( - 2 ___

45 )

x = 14



4106 - 3205 = 901




34x = 901

34x ____ 34

= 901 ____ 34

x = 265 = 26 1 __ 2




- 25 + x = -07

_ + 25 _ + 25

x = 18





181 - x = -07

_ - 181 _ -181

-x = -188

x = 188





125 + x = 181

_ -125 _ -125

x = 56



their next play

-26 1 __ 3

+ x = 10

+26 1 __ 3

______

+26 1 __ 3

______

x = 36 1 __ 3



( -2 1 __ 2 ) x = -156

( -25 ) x = -156

( -25 _____ -25

) x = -156 ______ -25

x = 624



rate and the time


x __ 5 = 455

( 5 ) x __ 5 = 455 ( 5 )

x = 2275


Sample answer


to $22750



below sea level



lower elevation

20 -4x = -48

( -4x ____ -4

) = -48 _____ -4

x = 12

- 1 __ 4 x = -48

( -4 ) ( - 1 __ 4 ) x = -48 ( -4 )

x = 192

192 ____ 12

= 16








$21085

LESSON 63

Your Turn


purchased






Equation 150 - 35x = 45





Guided Practice

1

+ + ++ ++

+++ + +

+++

2

----

+ ++ ++

- - -

























place 28 +1-tiles


bicycle





Equation 85d + 55 = 123






Equation 125r + 675 = 3175








Equation 45n + 60 = 285




means + 45





1 _ 2

bull n + 45 = 172

Equation 1 __ 2 n + 45 = 172





uniforms equipment


Equation 295u + 548 = 2023





weeks


Equation 500 - 20x = 220






Total bill $88


shirts bill















10 + 5c = 25

10 - 10 + 5c = 25 - 10

5c = 15

5c ___ 5 = 15 ___

5

c = 3

3 children



10 + 5 ( 5 ) = $35














bought

LESSON 64

Your Turn


+ ++ +

+ ++ ++ +

+ ++ ++ +

++


+ ++ +

+ ++ ++ +

+ ++ ++ +

++


++

+ ++ +

++


++ ++


+ + ++ + ++ +

+++

+++

__



+ + ++ + ++

++ +

+++

+++

__


+ + ++++ + +++


+ + +++


++++

______

______

____



++++

+

++

+

++

______

______

____


++++

____


++ __



____

________

++



________

________

++

____


________

________

We get -y = -1

____


tile to each side

++

__ ++ __


++++

__


+++

6 3n + 10 = 37


3n + 10 = 37

-10 ____

-10 ____

3n = 27

3n ___ 3 = 27 ___

3

n = 9


7 n __ 4 - 5 = 15


n __ 4 - 5 = 15

+5 ___

+5 ___

n __ 4 = 20

n __ 4 ( 4 ) = 20 ( 4 )

n = 80

The number is 80

8 -20 = 5 __ 9 ( x - 32 )


-20 = 5 __ 9 ( x - 32 )

-20 = 5 __ 9 x - 160 ____

9

+ 160 ____ 9

______

+ 160 ____ 9

______

- 20 ___ 9 = 5 __

9 x

- 20 ___ 9 divide ( 5 __

9 ) = 5 __

9 x divide ( 5 __

9 )

4 20 times 9

1 _______

9 1 times 5

1 = x

- 4 __ 1 = x

-4 = x


9 120 - 4x = 92


120 - 4x = 92

-120 _____

-120 _____

- 4x = -28

-4x ____ -4

= -28 ____ -4

x = 7



Guided Practice





++++

+ +++++++++


++++

++++++++


++ + + + +




Solve the equation

2 ( 18 ) + 2w = 58

36 + 2w = 58

36 - 36 + 2w = 58 - 36

2w = 22

2w ___ 2 = 22 ___

2

w = 11


4 1200 minus 25x = 500


1200 - 25x = 500

_ -1200 _ -1200

-25x = -700

-25x _____ -25

= -700 _____ -25

x = 28






equation


6 9s + 3 = 57

9s + 3 - 3 = 57 - 3

9s = 54

9s ___ 9 = 54 ___

9

s = 6

7 4d + 6 = 42

4d + 6 - 6 = 42 - 6

4d = 36

4d ___ 4 = 36 ___

4

d = 9

8 115 - 3y = -485

115 - 115 - 3y = -485 - 115

thinsp-3y = -60

-3y

____ -3

= -60 ____ -3

y = 20

9 k __ 2 + 9 = 30

k __ 2 + 9 - 9 = 30 - 9

k __ 2 = 21

2 sdot k __ 2 = 2 sdot 21

k = 42

10 g

__ 3 - 7 = 15

g

__ 3 - 7 + 7 = 15 + 7

g

__ 3 = 22

3 sdot g

__ 3 = 3 sdot 22

g = 66

11 z __ 5 + 3 = -35

z __ 5 + 3 - 3 = -35 - 3

z __ 5 = -38

5 sdot z __ 5 = 5 ( -38 )

z = -190

12 -9h - 15 = 93

-9h - 15 + 15 = 93 + 15

-9h = 108

-9h ____ -9 = 108 ____

-9

h = -12

13 - 1 __ 3 (n + 15) = -2

- 1 __ 3 n - 5 = -2

- 1 __ 3 n - 5 + 5 = -2 + 5

- 1 __ 3 n = 3

-3 sdot - 1 __ 3 n = -3 sdot 3

n = -9

14 -17 + b __ 8 = 13

-17 + 17 + b __ 8 = 13 + 17

b __ 8 = 30

8 sdot b __ 8 = 8 sdot 30

b = 240


15 7 ( c - 12 ) = -21

7c - 84 = -21

_ +84 _ +84

7c = 63

7c ___ 7 = 63 ___

7

c = 9

16 -35 + p

__ 7 = -52

-35 + 35 + p

__ 7 = -52 + 35

p

__ 7 = -17

7 sdot p

__ 7 = -17 sdot 7

p = -119

17 46 = -6t - 8

46 + 8 = -6t - 8 + 8

54 = -6t

54 ___ -6

= -6t ____ -6

t = -9





2 (a + $26) = $264

Solve the equation

2 ( a + 26 ) = 264

2 ( a + 26 )

_________ 2 = 264 ____

2

a + 26 = 132

a + 26 - 26 = 132 - 26

a = 106






Solve the equation

2t - 6 = 20

2t - 6 + 6 = 20 + 6

2t = 26

2t __ 2 = 26 ___

2

t = 13


20 -35 = 5 __ 9 ( x - 32 )

-35 = 5 __ 9 x - 160 ____

9

+ 160 ____ 9

______

+ 160 ____ 9

- 155 ____ 9 = 5 __

9 x

thinsp- 155 ____ 9 divide ( 5 __

9 ) = 5 __

9 x divide ( 5 __

9 )

-thinsp 31

155 times 9

1

= x

9 1

times 5

1

- 31 ___ 1 = x

-31 = x




Solve the equation

-a + 40 = 28

-a + 40 - 40 = 28 - 40

-a = -12

-a ___ -1

= -12 ____ -1

a = 12






Solve the equation

2c + 11 = 73

2c + 11 - 11 = 73 - 11

2c = 62

2c ___ 2 = 62 ___

2

c = 31




price paid


1 __ 2

middot p -6 = 88

Solve the equation

1 __ 2 p - 6 = 88

1 __ 2 p - 6 + 6 = 88 + 6

1 __ 2 p = 94

2 sdot 1 __ 2 p = 2 sdot 94

p = 188



24 115 minus 8n = 19


115 - 8n = 19

_ -115 _ -115

-8n = -96

-8n _____ -8

= -96 _____ -8

n = 12


25 -55x + 056 = -164

-55x + 056 - 056 = -164 - 056

-55x = -22

-55x ______ -22

= -22 _____ -22

x = 04

26 -42x + 315 = -651

-42x + 315 - 315 = -651 - 315

-42x = -966

-42x ______ -42

= -966 ______ -42

x = 23

27 k ___ 52

+ 819 = 472

k ___ 52

+ 819 - 819 = 472 - 819

k ___ 52

= -347

52 sdot k ___ 52

= 52 ( -347 )

k = -18044




divide 2 by 3

3x + 2 = 15

3x ___ 3 + 2 __

3 = 15 ___

3

x + 2 __ 3 = 5

- 2 __ 3

___

- 2 __ 3

___

x = 5 - 2 __ 3

x = 5 times3

___ 1

times3 - 2 __

3

x = 15 ___ 3 - 2 __

3

x = 13 ___ 3 or 4 1 __

3


31 a 2(x + 40) = 234


2x + 80 = 234

2x + 80 - 80 = 234 - 80

2x = 154

2x ___ 2 = 154 ____

2

x = 77

Trey saved $77






32 F = 18c + 32

F - 32 = 18c + 32 - 32

F - 32 = 18c

F - 32 ______ 18

= 18c ____ 18

F - 32 ______ 18

= c

33 P = 2 ( ℓ + w ) P = 2ℓ + 2w

P - 2ℓ = 2ℓ - 2ℓ + 2w

P - 2ℓ = 2w

P - 2ℓ ______ 2 = 2w ___

2

P - 2ℓ ______ 2 = w

34 ax + b = c

ax + b - b = c - b

ax = c - b

ax ___ a = c - b ______ a

x = c - b ______ a

MODULE 6

Ready to Go On




15n + 60 + 12n + 95



2 h + 97 = -97

_ -97 _ -97

h = -194

3 - 3 __ 4 + p = 1 __

2

+ 3 __ 4 + 3 __

4

p = 1 __ 2 + 3 __

4

p = 1 times2

___ 2

times2 + 3 __

4

p = 2 __ 4 + 3 __

4

p = 5 __ 4

4 -15 = -02k

-15 _____ -02

= -02k ______ -02

75 = k


5 y ___

-3 = 1 __

6

y ___

-3 ( -3 ) = 1 __

6 ( -3 )

y = 1 __ 6 times -3 ___

1

y = -3 ___ 6

y = -1 ___ 2

6 - 2 __ 3

m = -12

- 2 __

3 m _____

- 2 __ 3 = -12 ____

- 2 __ 3

m = -12 divide - 2 __ 3

m = -12 ____ 1 divide - 2 __

3

m = -12 ____ 1 times - 3 __

2

m = -36 ____ -2

m = 18

7 24 = - t ___ 45

24 ( 45 ) = - t ___ 45

( 45 )

108 = -t

-108 = t







2 middot d + 15 = 33


9 5n + 8 = 43

5n + 8 - 8 = 43 - 8

5n = 35

5n ___ 5 = 35 ___

5

n = 7

10 y __

6 - 7 = 4

y __

6 - 7 + 7 = 4 + 7

y __

6 = 11

6 sdot y __

6 = 6 sdot 11

y = 66

11 8w - 15 = 57

8w - 15 + 15 = 57 + 15

8w = 72

8w ___ 8 = 72 ___

8

w = 9

12 g

__ 3 + 11 = 25

g

__ 3 + 11 - 11 = 25 - 11

g

__ 3 = 14

3 sdot g

__ 3 = 3 sdot 14

g = 42

13 f __ 5 - 22 = -25

f __ 5 - 22 + 22 = -25 + 22

f __ 5 = -03

5 sdot f __ 5 = 5 ( -03 )

f = -15

14 - 1 __ 4 (p + 16) = 2

- 1 __ 4 p - 4 = 2

- 1 __ 4 p - 4 + 4 = 2 + 4

- 1 __ 4 p = 6

-4 sdot - 1 __ 4 p = 6 sdot -4

p = -24




situation



Are You Ready

1 9w = -54

9w ___ 9 = -54 ____

9

w = -6

2 b - 12 = 3

thinsp _ + 12 = _ + 12

b = 15

3 n __ 4

= -11

4 times n __ 4

= 4 ( -11 )

n = -44

4-7


75 4 6

8 3 - (-5)

3 + 5

8

9 -4 - 5

-9

10 6 - 10

-4

11 -5 - (-3)

-5 + 3

-2

12 8 - (-8)

8 + 8

16

13 9 - 5

4

14 -3 - 9

-12

15 0 - (-6)

0 + 6

6

LESSON 71

Your Turn


_ +5 _ +5

y ge minus2

-4-5 -3 -2-1 0 1 2 3 4 5


minus1 ge -8


2 le 16

5 21 gt 12 + x

_ -12 _ minus12

9 gt x

x lt 9

10 2 3 4 5 6 7 8 9 10


21 gt 12 + 8

21 gt 12 + 8

21 gt 20

6 -10y lt 60

-10y

_____ -10

lt 60 ____ -10

y gt -6

-10-9 -8 -7 -6 -5 -4 -3 -2-1 0 1


-10y lt 60

-10(-5) lt 60

50 lt 60

7 7 ge - t __ 6

7(-6) le - t __ 6 (-6)

-42 le t

t ge -42

-46 -45 -44 -43 -42 -41 -40-47


7 ge - t __ 6

7 ge - ( -36 ____

6 )

7 ge 6



35m le 315

35m ____ 35

le 315 ____ 35

m le 9



Guided Practice

1 -5 le -2

_ +7 _ +7

2 le 5

2 -6 lt -3

-6 ___ -3

gt -3 ___ -3

2 gt 1

3 7 gt -4

_ -7 _ -7

0 gtthinsp -11


4 -1 ge -8

-1 ( -2 ) le -8 ( -2 )

2 le 16

5 n - 5 ge -2

_ +5 _ +5

n ge 3

-5 -4 -3 -2-1 0 3 4 51 2


n - 5 ge -2

4 - 5 ge -2

-1 ge -2

6 3 + x lt 7

_ -3 _ -3

x lt 4

-2-1 0 3 4 5 6 7 81 2


3 + x lt 7

3 + 3 lt 7

6 lt 7

7 -7y le 14

-7y

____ -7 ge 14 ___ -7

y ge -2

-5-6-7 -4 -3 -2-1 0 1 2 3


-7y le 14

-7 ( -1 ) le 14

7 le 14

8 b __ 5 gt -1

b __ 5 ( 5 ) gt -1 ( 5 )

b gt -5

-5-6-7-8 -4 -3 -2-1 0 1 2


b __ 5 gt -1

0 __ 5 gt

-1

0 gt -1

9 a -4t ge -80

b -4t ge -80

-4t ____ -4

le -80 ____ -4

t le 20








number


11 x - 35 gt 15

_ + 35 _ +35

x gt 50

100 20 30 40 50 60 70 80 90100


x - 35 gt 15

51 minus 35 gt 15

16 gt 15

12 193 + y ge 201

_ -193 _ minus193

y ge 8

10 2 3 4 5 6 7 8 9 10


193 + y ge 201

193 + 9 ge 201

202 ge 201

13 - q

__ 7 ge -1

- q

__ 7 ( -7 ) le -1 ( -7 )

q le 7

8 9 105 6 70 1 2 3 4


- q

__ 7 ge -1

- -14 ____ 7 ge

-1

2 ge -1

14 -12x lt 60

-12x _____ -12

gt 60 ____ -12

x gt -5

0-10-9 -8 -7 -6 -5 -4 -3 -2-1


-12x lt 60

-12 ( -4 ) lt 60

48 lt 60

15 5 gt z -3

_ +3 _ +3

8 gt z

z lt 8

10 2 3 4 5 6 7 8 9 10


5 gt z - 3

5 gt 7 - 3

5 gt 4


16 05 le y __

8

05 ( 8 ) le y __

8 ( 8 )

4 le y

y ge 4

8 9 105 6 70 1 2 3 4


05 le y __

8

05 le 8 __

8

05 le 1



12 + x le 28

_ -12 _ -12

x le 16




w __ 7 lt 35

w __ 7 ( 7 ) lt 35 ( 7 )

w lt 245





6s le 42

6s ___ 6 le 42 ___

6

s le 7




3025 + x ge 50

_ -3025 _ -3025

x ge 1975




155w ge 1705

155w ______ 155

ge 1705 _____ 155

w ge 11




thinsp-12t lt -120

-12t _____ -12

gt -120 _____ -12

t gt 10






3s le 10

3s ___ 3 le 10 ___

3

s le 3 1 __ 3


pounds



m ___ 05

le 55

m ___ 05

( 05 ) le 55 ( 05 )

m le 275




125x le 3

125x _____ 125

le 3 ____ 125

x le 24



buy 25 pounds







not true





prism

V = lwh



( 13 ) ( 1 __ 2 ) h lt 65

65h lt 65

65h ____ 65

lt 65 ___ 65

h lt 10





LESSON 72Your Turn


raise



Target amount $6000



must raise equal to




can go on

Starting amount $40

Admission price $6




equal to




are looking for




10 is added to 3x



than 30








looking for












Guided Practice

1

- -- -

-

lt

++++++

+ + ++ + +

+

2

---

gt

+ + ++ + +

+ + ++ + +

+ + +


raise








1250 + 92a ge 7000




greater than 32







inequality






3a + 28 gt 200




cheese to has


075n + 129 le 700












120 + 32n le 720




month month


2100 + 005s ge 2400






668 + 7n gt 2000


day



buys to a month


$7 + $10 middot c le $100

7 + 10c le 100






$22 + $17 middot n le $80

22 + 17n le 80














is given by

95 + 86 + 89 + 3s

________________ 6


tests



95 + 86 + 89 + 3s

________________ 6 ge 90 or

95 + 86 + 89 + 3s ge 540 or

270 + 3s ge 540












So -m gt 0

25 n gt 1 __ n if n gt 1


n = 1 __ n if n = 1

LESSON 73

Your Turn


++

++++

+++

++++

++++

+++

gt


++

++++

+++

++++

++++

+++

gt

- -- -- --

- -- -- --


++

++++

gt


++

++++

gt



+ + +gt


+++++

----

+++++

+ +++++

ge


+++++

----

+++++

+ ++

++++

+++

++++

ge


+++++

+++++

+ +++++

++++

ge


+++++

+++++

+ +++++

++++

ge


+ + + +ge


5 - p

__ 6 le 4

5 - 5 - p

__ 6 le 4 - 5

thinsp- p

__ 6 le -1

thinsp-6 ( - p

__ 6 ) ge -6 ( -1 )

p ge 6


arrow

0 1 4 5 72 3 6 8 9 10



3v - 8 gt 22

v = 9 v = 10 v = 11

3 ( 9 ) - 8 gt 22 3 ( 10 ) - 8 gt 22 3 ( 11 ) - 8 gt 22


results

3 ( 9 ) - 8 gt 22 3 ( 10 ) - 8 gt

22 3 ( 11 ) - 8 gt

22

27 - 8 gt 22 30 - 8 gt

22 33 - 8 gt

22

19 gt 22 22 gt

22 25 gt

22


v = 11


5h + 12 le -3

h = -3 h = -4 h = -5

5 ( -3 ) + 12 le -3 5 ( -4 ) + 12 le -3 5 ( -5 ) + 12 le -3


results

5 ( -3 ) + 12 le -3 5 ( -4 ) + 12 le

-3 5 ( -5 ) + 12 le

-3

-15 + 12 le -3 -20 + 12 le

-3 -25 + 12 le

-3

-3 le -3 -8 le

-3 -13 le

-3

true true true

h = -3 h = -4 h = -5


Guided Practice




5d - 13 lt 32

5d - 13 + 13 lt 32 + 13

5d lt 45

5d ___ 5 lt 45 ___

5

d lt 9


20 6 84 10 12 14 16 18 20


-4b + 9 le -7

-4b + 9 - 9 le -7 - 9

-4b le -16

-4b ____ -4

ge -16 ____ -4

b ge 4


20 6 84 10 12 14 16 18 20


2m + 18 gt - 4

m = -12 m = -11 m = -10

2 ( -12 ) + 18 gt -4 2 ( -11 ) + 18 gt -4 2 ( -10 ) + 18 gt -4


results

2 ( -12 ) + 18 gt -4 2 ( -11 ) + 18 gt

- 4 2 ( -10 ) + 18 gt

- 4

- 24 + 18 gt -4 - 22 + 18 gt

- 4 - 20 + 18 gt

- 4

- 6 gt - 4 - 4 gt

- 4 - 2 gt

- 4


m = -10


- 6y + 3 ge 0

y = 1 y = 1 __ 2 y = 0

-6 ( 1 ) + 3 ge 0 -6 ( 1 __ 2 ) + 3 ge 0 -6 ( 0 ) + 3 ge 0


results

-6 ( 1 ) + 3 ge 0 - 6 ( 1 __

2 ) + 3 ge

0 - 6 ( 0 ) + 3 ge

0

-6 + 3 ge 0 -3 + 3 ge

0 0 + 3 ge

0

-3 ge 0 0 ge

0 3 ge

0

not true true true

y = 1 __ 2

y = 0


65 - 4t ge 15

65 - 65 - 4t ge 15 - 65

-4t ge -5

-4t ____ -4

le -5 ___ -4

t le 125


0 05 1 15 2 25



time






8 2s + 5 ge 49

2s + 5 - 5 ge 49 - 5

2s ge 44

2s ___ 2 ge 44 ___

2

s ge 22

10 14 1612 18 20 22 24 26 28 30

9 -3t + 9 ge -21

-3t + 9 - 9 ge -21 -9

-3t ge -30

-3t ____ -3

le -30 ____ -3

t le 10


10 55 gt -7v + 6

55 - 6 gt -7v + 6 - 6

49 gt - 7v

49 ___ -7 lt -7v ____ -7

v gt -7

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0

11 21 1 __ 3 gt 3m - 2 2 __

3

21 1 __ 3 + 2 2 __

3 gt 3m - 2 2 __

3 + 2 2 __

3

24 gt 3m

24 ___ 3 gt 3m ___

3

8 gt m or m lt 8

0 1 4 5 72 3 6 8 9 10

12 a ___ -8

+ 15 gt 23

a ___ -8

+ 15 - 15 gt 23 - 15

a ___ -8

gt 8

-8 ( a ___ -8

) lt -8 ( 8 )

a lt -64

-70 -68 -66 -64 -62 -60


13 f __ 2 - 22 lt 48

f __ 2 - 22 + 22 lt 48 + 22

f __ 2 lt 70

2 ( f __ 2 ) lt 2 ( 70 )

f lt 140

100 110 120 130 140 150

14 -25 + t __ 2 ge 50

-25 + 25 + t __ 2 ge 50 + 25

t __ 2 ge 75

2 ( t __ 2 ) ge 2 ( 75 )

t ge 150

130 140 150 160 170 180

15 10 + g ___

-9 gt 12

10 - 10 + g ___

-9 gt 12 - 10

g ___

-9 gt 2

-9 ( g ___

-9 ) lt -9 ( 2 )

g lt -18

-20 -18 -14 -12 -10-16

16 252 le -15y + 12

252 - 12 le -15y + 12 - 12

24 le - 15y

24 ____ -15

ge -15y

_____ -15

y le -16

-20 -18 -14 -12 -10-16

17 -36 ge -03a + 12

-36 - 12 ge -03a + 12 - 12

-48 ge -03a

-48 _____ -03

le -03a ______ -03

a ge 16

10 11 12 13 14 16 17 18 19 2015

18 80 - 2w ge 50

80 - 80 - 2w ge 50 - 80

- 2w ge -30

-2w ____ -2

le -30 ____ -2

w le 15



11 12 13 14 and 15


7n - 25 ge 65

7n - 25 + 25 ge 65 + 25

7n ge 90

7n ___ 7 ge 90 ___

7

n ge 12 6 __ 7


be a whole number





21 a

10 3 42 5 6 7 8 9 10

b

10 3 42 5 6 7 8 9 10














MODULE 7

Ready to Go On

1 n + 7 lt -3

thinsp _ -7

_ -7

n lt -10

2 5p ge -30

5p

___ 5 ge -30 ____

5

p ge -6

3 14 lt k + 11

_ -11 _ -11

3 lt k

4 d ___ -3

le minus6

( -3 ) ( d ) ge ( -3 ) ( -6 )

d ge 18


5 c - 25 le 25

_ +25 _ +25

c le 5

6 12 ge -3b

12 ___ -3

le -3b _____ -3

-4 le b




562 + n ge 650

_ -562 _ -562

n ge 88


-20 - 20t ge -100

9 2s + 3 gt 15

_ -3 _ -3

2s gt 12

2s ___ 2

gt 12 ___ 2

s gt 6

10 - d ___ 12

- 6 lt 1

_ +6 _ +6

- d ___ 12

lt 7

12 ( - d ___ 12

) lt 12 ( 7 )

-d lt 84

d gt -84

11 -6w - 18 ge 36

_ +18 _ +18

thinsp-6w ge 54

-6w _____ -6

le 54 ___ -6

w le -9

12 z __ 4 + 22 le 38

_ -22 _ -22

z __ 4 le 16

4 ( z __ 4 ) le 4 ( 16 )

z le 64

13 b __ 9 - 34 lt -36

_ +34 _ +34

b __ 9 lt -2

9 ( b __ 9 ) lt 9 ( -2 )

b lt -18

14 -2p + 12 gt 8

-12 ____

-12 ____

-2p gt -4

-2p

____ -2 lt -4 ___

-2

p lt 2






Are You Ready

1 3x + 4 = 10

3x + 4 - 4 =10 - 4

3x = 6

3x ___ 3 = 6 __

3

x = 2

2 5x - 11 = 34

5x - 11 + 11 = 34 + 11

5x = 45

5x ___ 5 = 45 ___

5

x = 9

3 -2x + 5 = -9

-2x + 5 - 5 = -9 - 5

-2x = -14

-2x ____ -2

= -14 ____ -2

x = 7

4 -11 = 8x + 13

-11 - 13 = 8x + 13 - 13

-24 = 8x

-24 ____ 8 = 8x ___

8

-3 = x

5 4x - 7 = -27

4x - 7 + 7 = -27 + 7

4x = -20

4x ___ 4 = -20 ____

4

x = -5

6 1 __ 2 x + 16 = 39

1 __ 2 x + 16 - 16 = 39 - 16

1 __ 2 x = 23

( 2 ) 1 __ 2 x = ( 2 ) 23

x = 46

7 12 = 2x - 16

12 + 16 = 2x - 16 + 16

28 = 2x

28 ___ 2 = 2x ___

2

14 = x

8 5x - 15 = -65

5x - 15 + 15 = -65 + 15

5x = -50

5x ___ 5 = -50 ____

5

x = -10

9 x __ 5 = 18 ___

30


30x = 90

30x ____ 30

= 90 ___ 30

x = 3

10 x ___ 12

= 24 ___ 36


36x = 288

36x ____ 36

= 288 ____ 36

x = 8

11 3 __ 9 = x __

3


9 = 9x

9 __ 9 = 9x ___

9

1 = x

12 14 ___ 15

= x ___ 75


1050 = 15x

1050 _____ 15

= 15x ____ 15

70 = x

13 8 __ x = 14 ___ 7


56 = 14x

56 ___ 14

= 14x ____ 14

4 = x

14 14 ___ x = 2 __ 5


70 = 2x

70 ___ 2 = 2x ___

2

35 = x

15 5 __ 6 = x ___

15


75 = 6x

75 ___ 6 = 6x ___

6

125 = x


UNIT

4


16 81 ___ 33

= x ____ 55


4455 = 33x

4455 _____ 33

= 33x ____ 33

135 = x

LESSON 81

Your Turn


= 22 ft


= 10 ft


Guided Practice

1

Blueprint

length (in)3 6 9 12 15 18

Actual

length (ft)5 10 15 20 25 30



= 15 in







= 25 m


= 15 m


4 a


scales



the drawing


6 a 2 in times 40 cm ______ 1 in

= 80 cm

15 in times 40 cm ______ 1 in

= 60 cm


b 80 cm times 60 cm = 4800 c m 2

c 80 cm times 1 in _______ 254 cm

asymp 315 in

60 cm times 1 in _______ 254 cm

asymp 236 in


315 in by 236 in



= 24 units


= 15 units


15 units




larger



r = 810 m ______ 54 ft

r = 150 m ______ 1 ft



= 648 in



b = 162 bricks



h = 30 ft times 126 cm _______ 1 ft

h = 378 cm



_________ 63 cm

n = 6 toothpicks



asymp 5 swabs






s = 10 cm times 2 ft _____ 1 cm

s = 20 ft










original size


2

LESSON 82

Guided Practice















triangle






6 cm

3 cm120˚








same angle measures








between them






LESSON 83

Guided Practice


2 rectangle

3 triangle





















volume is 480 in 3





LESSON 84

Your Turn



intersecting lines




mangFGD and mangDGC



mangBGC and mangCGD



Because lines _

BE and _




mangCGD = 55deg



3x ___ 3 = 126deg ____

3

x = 42deg





Guided Practice




so mangDGE = 30deg





value by 3














measures are equal

mangKMI = mangHMG

84 = 4x

84 ___ 4 = 4x ___

4

x = 21deg



x + 84 - 84 = 180 - 84

x = 96

mangKMH = 96deg



x + 62 - 62 = 180 - 62

x = 118

mangCBE = 118deg



x + 62 - 62 = 90 - 62

x = 28

mangABF = 28deg




x + 28 - 28 = 152

mangCBA = 152deg




2x ___ 2 = 86deg ___

2





6x ___ 6 = 180deg ____

6









_ -48deg268 _ -48deg268

mangK = 41deg3352






greater than 38deg











( 90 - ( 90 - xdeg ) ) = ( 90 - 90 + xdeg ) = xdeg

MODULE 8

Ready to Go On

1

Living


Actual


Blueprint





created




A point is another




mangFGE = 50deg




3 ( mangY ) ________ 3 = 120deg ____

3

mangY = 40deg

mangY = 40deg


rooms or gardens



Are You Ready

1 416

_ times 13

1248

_ +thinsp4160

5408

5408

2 647

_ times thinsp04

2588

2588

3 705

_ times thinsp94

2820

_ +thinsp63450

66270

6627

4 256

_ timesthinsp049

2304

_ +thinsp10240

12544

12544

5 1 __ 2 ( 14 ) ( 10 )

7 ( 10 )

70 i n 2

6 ( 35 ) ( 35 )

1225 ft 2

7 ( 8 1 __ 2 ) ( 6 )

17 ___ 1 2 sdot 6 3 __

1

51 i n 2

8 1 __ 2 ( 125 ) ( 24 )

1 __ 2 ( 24 ) ( 125 )

( 12 ) ( 125 )

15 m 2

LESSON 91

Your Turn

3 d = 11 cm

C = πd

C asymp 314 ( 11 )

C asymp 3454


6 C = πd

44 asymp 314d

44 ____ 314

asymp d

d asymp 1401 yards


rate

1401 divide 7 = 2001


Guided Practice

1 d = 9 in

C asymp 314 ( 9 )

C asymp 2826 in

2 r = 7 cm

C = 2πr

C asymp 2 ( 22 ___ 7 ) ( 7 )

C asymp 44 cm

3 d = 25 m

C = πd

C asymp 314 ( 25 )

C asymp 785 m

4 r = 48 yd

C = 2πr

C asymp 2 ( 314 ) ( 48 )

C asymp 3014 yd

5 r = 75 in

C = 2πr

C asymp 2 ( 314 ) ( 75 )

C asymp 471 in

6 Find the diameter

C = πd

66 asymp 314d

66 ____ 314

asymp 314d _____ 314

21 asymp d

Find the cost


25 times $045 = $1125



r = 05 yd

d = 1 yd


2πr = 788

2πr ___ 2π

= 788 ____ 2π

r asymp 788 _______ 2 ( 314 )

r asymp 1255 ft

d = 2r asymp 2 ( 1255 ft )

d asymp 2510 ft

9 d = 2r so r = d __ 2 asymp 34 ___

2

r asymp 17 in

C = πd asymp 314 ( 34 )

C = 1068 in





11 d = 59 ft

C = πd

C asymp 314 ( 59 )

C asymp 1853 ft

12 r = 56 cm

C = 2πr

C asymp 2 ( 22 ___ 7 ) ( 56 )

C asymp 352 cm

13 d = 35 in

C = πd

C asymp ( 22 ___ 7 ) ( 35 )

C asymp 110 in



15 r = 94 ft

d = 2r = 2 ( 94 )

d = 188 ft

C = πd

C asymp 314 ( 188 )

C asymp 590 ft

16 d = 475 in

r = d __ 2 = 475 ____

2

r = 2375 in

C = πd

C asymp 314 ( 475 )

C asymp 14915 in

17 d = 18 in

r = d __ 2 = 18 ___

2

r = 9 in

C = πd

C asymp 314 ( 18 )

C asymp 5652 in

18 r = 15 ft

C = 2πr

C asymp 2 ( 314 ) ( 15 ) = 942 ft


so ( 942 ) ( 075 ) = 7065 or about $707

19 C = πd

C asymp ( 22 ___ 7 ) ( 63 )

C asymp 198 ft




20 C = πd asymp 314 ( 2 )

C asymp 628 ft

Converting km to ft

2 km sdot ( 3280 ft _______

1 km ) = 6560 ft

6560 ft

_______ 628 ft

= 104459




1 __ 2 C = 1 __

2 πd asymp 1 __

2 sdot 314 ( 025 ) = 03925





Height 180 ft



_______ 2 ( 314 )

asymp 48 ft

Diameter d = 2r = 2 ( 48 ) = 96 ft



plus the diameter

1 __ 2 C = 1 __

2 πd asymp 1 __

2 sdot 314 ( 30 ) = 471



per linear foot

( 771 ft ) ( $925 _____

ft ) = $71318



C = πd asymp 314 ( 18 ) = 5652 ft


inches to feet

( 54 in ) ( 1 ft _____ 12 in

) = 45 ft



5652 ft _______ 45 ft

= 1256


must buy 13 strands


C inner

= πd asymp 314 ( 150 ) = 471 ft


C outer

= πd asymp 314 ( 154 ) = 48356 ft








smaller gear





314 ( 75 ) - 314 ( 732 ) = 314 ( 018 ) asymp 057

057 m asymp 187 ft

LESSON 92

Your Turn

4 A = π r 2 A = π ( 10 ) 2

A asymp 314 ( 10 ) 2


A asymp 314 f t 2

Guided Practice

1 r = d __ 2 = 14 ___

2 = 7 m

A = π r 2 A = π ( 7 ) 2

A asymp 314 ( 7 ) 2

A asymp 314 sdot 49

A asymp 1539 m 2

2 A = π r 2 A = π ( 12 ) 2

A asymp 314 ( 12 ) 2


A asymp 4522 m m 2

3 r = d __ 2 = 20 ___

2 = 10 yd

A = π r 2 A = π ( 10 ) 2

A asymp 314 ( 10 ) 2


A asymp 314 y d 2

4 A = π r 2 A = π ( 8 ) 2

A asymp 314 ( 8 ) 2

A asymp 314 sdot 64

A asymp 20096 i n 2

5 r = d __ 2 = 12 ___

2 = 6 cm

A = π r 2 A = π ( 6 ) 2

A asymp 314 ( 6 ) 2

A asymp 314 sdot 36

A asymp 11304 c m 2

6 r = d __ 2 = 13 ___

2 = 65 in

A = π r 2 A = π ( 65 ) 2

A asymp 314 ( 65 ) 2


A asymp 13267 i n 2

7 C = 4π = 2πr

4π ___ 2π

= 2πr ___ 2π

r = 2

A = π r 2 A = π ( 2 ) 2


8 C = 12π = 2πr

12π ____ 2π

= 2πr ___ 2π

r = 6

A = π r 2 A = π ( 6 ) 2


9 C = π __ 2 = 2πr

π __ 2 divide 2π = 2πr ___

2π

π __ 2 sdot 1 ___

2π = r

1 __ 4 = r

A = π r 2

A = π ( 1 __ 4 ) 2 = π ( 1 ___

16 )

A = π ___ 16

square units

10 A = π r 2 = 64π

π r 2 ___ π = 64π ____ π

r 2 = 64

r = 8

C = 2πr

= 2π ( 8 )

=16π yd

11 A = π r 2


12 r = d __ 2 = 10 ___

2 = 5 in

A = π r 2 A = π ( 5 ) 2

A asymp 314 ( 5 ) 2

A asymp 314 sdot 25

A asymp 785 i n 2

13 A = π r 2 A = π ( 16 ) 2

A asymp 314 ( 16 ) 2


A asymp 80384 c m 2


diameter 36 in

r = d __ 2 = 36 ___

2 = 18 in

A semicircle

= 1 __ 2 π r 2

A semicircle

= 1 __ 2 π ( 18 ) 2

A semicircle

asymp 1 __ 2 ( 314 ) ( 18 ) 2

A semicircle


A asymp 50868 i n 2




A = π r 2 A = π ( 3 ) 2

A asymp 314 ( 3 ) 2



A r = 75 mi

- A r = 50 mi

π ( 75 ) 2 - π ( 50 ) 2



greater







s 2 minus π r 2 = 1 2 2 minus π ( 6 ) 2

= 144 minus π ( 36 )

asymp 144 minus 11304 = 3096










16π in 2





about $20

_____ π ( 9 ) 2



_____ π ( 6 ) 2

asymp $009






A = π r 2 = π ( 8 ) 2

= π ( 64 )

asymp 20096


201 mi 2




A new

minus A old

= π ( 10 ) 2 - π ( 8 ) 2

= π ( 1 0 2 - 8 2 ) = π ( 100 - 64 )

= π ( 36 ) asymp 11304


more area









A


A whole target

=

π ( 15 ) 2 ______

π ( 75 ) 2

= ( 15 ) 2

_____ ( 75 ) 2

= 225 _____ 5625

= 004


LESSON 93

Your Turn


two right triangles





A = ℓw = 11 sdot 4 = 44 f t 2


A = 1 __ 2 bh = 1 __



A = 1 __ 2 bh = 1 __

2 sdot 3 sdot 3 = 45 f t 2


44 + 3 + 45 = 515 f t 2


semicircle



or 10 ___ 2 = 5 m


A = s 2 = 1 0 2 = 100 m 2


A = 1 __ 2 π r 2

A asymp 1 __ 2 sdot 314 sdot ( 5 ) 2


A asymp 3925 m 2


100 + 3925 = 13925 m 2







4 __ 2 = 2 ft


A = ℓw = 5 sdot 4 = 20 f t 2


A = π r 2 A asymp 314 sdot ( 2 ) 2



two areas

20 + 1256 = 3256 f t 2



( 3256 f t 2 ) ( $28 ____

f t 2 ) = $91168


Guided Practice


a parallelogram



2 ( 4 ) ( 2 ) = 4




2 parallelogram

15 cm 2


4 + 15 + 15 = 34 cm 2


2 Method 1

A 1 = ℓw A

2 = ℓw

= 12 sdot 9 = 20 sdot 9 = 108 = 180


Method 2

A 1 = ℓw A

2 = ℓw

= 9 sdot 8 = 12 sdot 8 = 72 = 216






1 + b

2 )

A = 1 __ 2 ( 5 ) ( 7 + 4 )

A = 1 __ 2 ( 5 ) ( 11 ) = 275 f t 2



275 + 16 = 435 ft 2


find the cost

( 435 f t 2 ) ( $225 _____

f t 2 ) = $9788


simpler figures




A asymp 1 __ 2 sdot 314 sdot ( 13 ) 2


A asymp 26533 i n 2


676 + 26533 = 94133 in 2






A = 1 __ 2 sdot 6 sdot 7

A = 1 __ 2 sdot 42

A = 21 f t 2


40 + 21 = 61 f t 2


square foot

( 61 f t 2 ) ( $250 _____

f t 2 ) = $15250

7

O 42-2-4

2

-4

y

A (-2 4) B (0 4)

C (2 1)D (5 1)

E (5 -2)F (-2 -2)










Area of trapezoid

A = 1 __ 2 h ( b

1 + b

2 )

A = 1 __ 2 ( 3 ) ( 4 + 2 )

A = 1 __ 2 ( 3 ) ( 6 ) = 9 square units











A = 1 __ 2 sdot 8 sdot 8

A = 1 __ 2 sdot 64

A = 32 m 2


A asymp 1 __ 4 sdot 314 sdot ( 8 ) 2


A asymp 5024 f t 2


64 + 32 + 5024 = 14624 m 2









48 + 1256 = 6056 cm 2






A = 1 __ 2 sdot 1 sdot 1

A = 1 __ 2 sdot 1

A = 05 f t 2


3 + 05 = 35 ft 2





( 42 f t 2 ) ( $125 _____

f t 2 ) = $5250


area of triangle

325 ft 2 - 75 ft 2 = 25 ft 2



square is 5 ft






20 ( 15 ) or 300 carrots








triangle



A = 1 __ 2 sdot 12 sdot 8

A = 1 __ 2 sdot 96

A = 48 i n 2


144 + 48 = 192 in 2










420 - 176625 = 243375 in 2 or 243 3 __

8 i n 2










A asymp 1 __ 2 sdot 314 sdot ( 20 ) 2


A asymp 628 i n 2


1600 + 628 = 2228 in 2






40 + 2 sdot 4 = 48 in




total of 40 + 4 = 44 in






A asymp 1 __ 2 sdot 314 sdot ( 24 ) 2


A asymp 90432 i n 2


the sum

2112 + 90432 asymp 3016 in 2

LESSON 94

Your Turn


B = l times w

= 9 times 2

= 18 square inches


P = 2 ( 9 ) + 2 ( 2 )

= 18 + 4 = 22 inches


S = Ph + 2B

S = 22 ( 1 1 __ 2 ) + 2 ( 18 )

= 33 + 36

= 69



B = times w

= 12 times 12

= 144 square inches


P = 4 ( 12 )

= 48 inches


S = Ph + 2B

S = 48 ( 12 ) + 2 ( 144 )

= 576 + 288

= 864 square inches


B = l times w

= 8 times 8

= 64 square inches


P = 4 ( 8 )

= 32 inches


S = Ph + 2B

S = 32 ( 8 ) + 2 ( 64 )

= 256 + 128

= 384 square inches








Guided Practice



Height = 7 ft

Base area = 1 __ 2 ( 3 ) ( 8 ) = 12 ft 2

Surface area

S = ( 18 ft ) ( 7 ft ) + 2 ( 12 ft 2 ) = 150 ft 2


B = l times w

= 25 times 25

= 625 m 2


P = 4 ( 25 )

= 10 m


S = Ph + 2B

S = 10 ( 25 ) + 2 ( 625 )

= 25 + 125

= 375


S = 375 m 2


B = l times w

= 11 times 9

= 99 m 2


prism

P = 2 ( 11 ) + 2 ( 9 )

= 22 + 18

= 40 m


S = Ph + 2B

S = 40 ( 7 ) + 2 ( 99 )

= 280 + 198

= 478


S = 478 m 2


A = ( 25 ) ( 25 ) = 625



= 375 + 478 -2 ( 625 ) = 503 m 2




surface




B = l times w

= 10 times 3

= 30 in 2


P = 2 ( 10 ) + 2 ( 3 )

= 20 + 6

= 26 in


S = Ph + 2B

S = 26 ( 4 ) + 2 ( 30 )

=104 + 60

= 164 in 2



B = l times w

= 20 times 15

= 300 cm 2


P = 2 ( 20 ) + 2 ( 15 )

= 40 + 30

= 70 cm


S = Ph + 2B

S = 70 ( 9 ) + 2 ( 300 )

= 630 + 600

= 1230 cm 2


1230 - 300 = 930 cm 2



Convert cm 2 to mm

2


2 ________

1 cm 2 = 93000 mm

2


93000 divide 25 = 3720




= 2 + 3 = 5 in 2


Perimeter = 3 + 3 + 1 + 2 + 2 + 1

= 12 in


S = Ph + 2B

S = 12 ( 3 ) + 2 ( 5 )

= 36 + 10

= 46 in 2



Perimeter = 25 + 25 + 3 = 8 ft

Base area = 1 __ 2 ( 2 ) ( 3 ) = 3 ft 2


= 8 ( 4 ) + 2 ( 3 )

= 32 + 6 = 38 ft 2


Perimeter = 2 ( 3 ) + 2 ( 4 ) = 14 ft



= 14 ( 2 ) + 2 ( 12 )

= 28 + 24 = 52 ft 2



Surface area = 38 + 52 - 12 - 12 = 66 ft 2







1 + b

2 ) h

1 __ 2 ( 16 + 48 ) 12 = 384 in

2


P = 48 + 20 + 16 + 20 = 104 in


S = Ph + 2B

S = 104 ( 24 ) + 2 ( 384 )

= 2496 + 768

= 3264 in 2



B = l times w

= 7 times l

= 7 ft 2


P = 2 ( 7 ) + 2 ( 1 )

= 14 + 2

= 16 ft


S = Ph + 2B

S = 16 ( 2 ) + 2 ( 7 )

= 32 + 14

= 46 f t 2


B = l times w

= 1 times 1

= 1 ft 2


P = 2 ( 1 ) + 2 ( 1 )

= 2 + 2 = 4 ft


S = Ph + 2B

S = 4 ( 3 ) + 2 ( 1 )

= 12 + 2

= 14 ft 2



Surface area = 46 + 14 - 1 - 1 = 58 ft 2



58 divide 25 = 232


needed


3 times 679 = 2037




B = l times w

= 27 times 24

= 648 cm 2


P = 2 ( 27 ) + 2 ( 24 )

= 54 + 48

= 102 cm


S = Ph + 2B

S = 102 ( 10 ) + 2 ( 648 )

= 1020 + 1296

= 2316 cm 2






2 ( 2l + 2w ) = 2P


New S = 2Ph + 2 ( 4B )


doubles



B = l times w

= 25 times 25

= 625 ft 2


P = 4 ( 25 )

= 10 ft


S = Ph + 2B

S = 10 ( 35 ) + 2 ( 625 )

= 35 + 135

= 485 ft 2



485 - 625 = 4225 ft 2



4225 _____ 485

times 100 asymp 87




15


r = 2 in

9 in


A = πr 2

asymp 31 4 ( 2 ) 2 = 1256 in 2


C = πd

asymp 314 ( 4 ) = 1256 in 2




S = Ch + 2B

asymp 1256 ( 9 ) + 2 ( 1256 ) = 13816 in 2





1500 times 1382 = 207300 in 2



( 207300 in 2 ) 1 ft 2 _______

144 in 2 asymp 1440 ft 2






show

LESSON 95

Your Turn


B = 1 __ 2 bh

= 1 __ 2 ( 24 ) 7

= 84 m 2


V = Bh

= ( 84 ) ( 22 )

= 1848 m 3



B = 1 __ 2 ( b 1 + b 2 ) h

= 1 __ 2 ( 8 + 12 ) 10

= 1 __ 2 ( 20 ) 10 = 100 cm

2


V = Bh

= ( 100 ) ( 22 )

= 2200 cm 3




B = bh

= ( 13 ) 13

= 169 in 2


V = Bh

= ( 169 ) ( 30 )

= 5070 in 3



B = 1 __ 2 bh

= 1 __ 2 ( 9 ) 13

= 585 in 2


V = Bh

= ( 585 ) ( 30 )

= 1755 in 3


5070 + 1755 = 6825 in 3


Guided Practice

1 B = 1 __ 2 bh = 1 __

2 ( 8 ) ( 3 ) = 12 ft 2

V = Bh = ( 12 times 7 ) ft 3 = 84 ft 3

2 B = 1 __ 2 ( b 1 + b 2 ) h = 1 __

2 ( 15 + 5 ) 3 = 30 m

2

V = Bh = ( 30 times 11 ) m 3 = 330 m 3


B = bh

= ( 4 ) 6 = 24 ft 2


V = Bh

= ( 24 ) ( 12 ) = 288 ft 3



B = 1 __ 2 bh

= 1 __ 2 ( 6 ) 4 = 12 ft 2


V = Bh

= ( 12 ) ( 6 ) = 72 ft 3



288 + 72 = 360 ft 3



B = bh

= ( 40 ) ( 50 ) = 2000 ft 2


V = Bh

= ( 2000 ) ( 15 ) = 30000 ft 3


B = 1 __ 2 bh

= 1 __ 2 ( 40 ) ( 10 ) = 200 ft 2


V = Bh

= ( 200 ) ( 50 ) = 10000 ft 3


30000 + 10000 = 40000 ft 3



B = 1 __ 2 ( b 1 + b 2 ) h

= 1 __ 2 ( 10 + 12 ) 5

= 1 __ 2 ( 22 ) 5 = 55 cm

2


V = Bh

= ( 55 ) ( 7 ) = 385 cm 3







V = Bh

= ( 35 ) ( 5 ) = 175 in 3




B = 1 __ 2 bh

= 1 __ 2 ( 7 ) ( 6 ) = 21 in

2


V = Bh

= ( 75 ) ( 7 ) = 525 in 3



B = 1 __ 2 bh

= 1 __ 2 ( 8 ) ( 4 ) = 16 ft 2


V = Bh

= ( 16 ) ( 24 ) = 384 ft 3



B = 1 __ 2 ( b 1 + b 2 ) h

= 1 __ 2 ( 7 + 5 ) 4

= 1 __ 2 ( 12 ) 4 = 24 in

2


V = Bh

= ( 24 ) ( 8 ) = 192 in 3



V = Bh

= ( 20 ) ( 15 ) = 300 in 3


300 cubic inches


given B = 234 in 3


V = Bh

= ( 234 ) ( 3 ) = 702 in 3



B = bh

= ( 3 ) ( 3 ) = 9 in 2


V = Bh

= ( 9 ) ( 3 ) = 27 in 3


702 + 27 = 972 in 3



B = bh

= ( 75 ) 375 = 28125 m 2


V = Bh

= ( 28125 ) ( 75 ) asymp 21094 cm 3


prism


15 - 75 = 75


B = bh

= ( 75 ) 375 = 28125 m 2


V = Bh

= ( 28125 ) ( 375 ) asymp 10547 cm 3


21094 + 10547 = 31641 m 3




V = Bh

= ( 21 ) ( 8 ) = 168 cm 3



260 - 168 = 92 cm 3


V = Bh

= ( 7 ) ( 14 ) = 98 cm 3



260 - 168 = 92 cm 3


a height of 14 cm

V = Bh

92 = B ( 14 )

92 ___ 14

= B ( 14 ) _____ 14

6 8 ___ 14

= B asymp 657





V = Bh

= ( 36 ) ( 5 ) = 180 in 3



prism V = Bh

= ( 32 ) ( 6 ) = 192 in 3





V = Bh

286 = B ( 8 )

286 ____ 8 = B ( 8 )

3575 = B


trapezoidal prism

1 __ 2 ( 2 + b 2 ) 13 = 3575

1 __ 2 ( 2 + b 2 ) ( 13 ___

13 ) = 3575 _____

13

( 2 ) 1 __ 2 ( 2 + b 2 ) = ( 2 ) 275

2 + b 2 = 55

_ -2 _ -2

b 2 = 35 ft



B = 1 __ 2 bh

= 1 __ 2 ( 10 ) 6 = 30 cm

2


V = Bh

= ( 30 ) ( 25 ) = 75 cm 3



_____ cm

3 )

asymp ( 75 cm 3 ) ( 86 g

_____ cm

3 ) = 645 g


about 645 g







of 120 cm 3

V = Bh

V = [ 1 __ 2 ( b 1 + b 2 ) h 1 ] h 2

120 ≟ [ 1 __ 2 ( 2 + 6 ) 4 ] 75

= [ 1 __ 2 ( 8 ) 4 ] 75

= [ 16 ] ( 75 ) = 120


V = Bh

V = [ 1 __ 2 ( b 1 + b 2 ) h 1 ] h 2

120 ≟ [ 1 __ 2 ( 1 + 7 ) 25 ] 12

= [ 1 __ 2 ( 8 ) 25 ] 12

= [ 10 ] 12 = 120






MODULE 9

Ready to Go On




2 d = 12 cm d = 6 cm so r = 12 ___ 2 = 6 ft



A asymp 11304 ft 2





A asymp 1 __ 2 sdot 314 sdot ( 8 ) 2


A asymp 10048 m 2


A = 1 __ 2 sdot 16 sdot 10

A = 1 __ 2 sdot 160

A = 80 m 2


80 + 10048 = 18048 m 2





A = 20 sdot 45

A = 90 c m 2

Area of rectangle

A = ℓw = 20 sdot 55 = 110 c m 2


90 + 110 = 200 cm 2



1 __ 2 ( 4 ) 3 = 6 cm 2


P = 3 + 4 + 5 = 12 cm


S = Ph + 2B

S = 12 ( 10 ) + 2 ( 6 )

thinsp=120 + 12

thinsp= 132 cm 2


V = Bh

= ( 6 ) 10

= 60 cm 3




1 __ 2 ( 4 ) 15 = 3 yd 2


( 4 ) 2 = 8 yd 2



P = 4 + 2 + 25 + 25 + 2 = 13 yd


S = Ph + 2B

S = 13 ( 25 ) + 2 ( 11 )

thinsp= 325 + 22

thinsp= 545 yd 2


is given

B = 234 yd 3


V = Bh

= ( 11 ) 25

= 275 yd 3






unit


Are You Ready

1 x ___16

=45___40

40x=720

40x ____40

=720____40

   x=18

2 x __5=1__

4

4x=5

4x ___4

=5__4

  x=5__4=125

3 25___10

=x ___10

125=10x

125____10

=10x ____10

125=x

4 x __6

=2__9

9x= 12

9x ___9

=12___9

   x=12___9=4__

3

5 4748495152575960range=60-47=13

6 4566689121213range=13-4=9

7 95979799100106108115range=115-95=20

8 121319273539476671range=71-12=59

9 mean=3+5+7+3+6+4+8+6+9+5_________________________________10

=56

10 mean=81+94+113+67+62+75____________________________6

=82

LESSON 101

Your Turn




Guided Practice




Jimmy 80

Darnell 90

Ping 75

Zach 85

Jamar 80

BSampleanswer

75+80+90+75+85+80___________________________6

=485____6

asymp81

Meanasymp81



Stan 80 Marcus 90

Alejandro 90 Tio 85

BSampleanswer

85+80+90+85+90+85____________________________6

=515____6 =86

Mean=size86




















b 35___60

= x ____100

xasymp58


=58



LESSON 102

Your Turn


______________________sizeofsample



6___50

= x_____3500

6sdot70______50sdot70

= x _____3500

420_____3500

= x_____3500


Guided Practice

1

6 7 8 9 10 11 12 13 14 1550 1 2 3 4


6 7 7 107 114 4 54

Leastvalue

4

Lower quartile

4

Median

65

Upper quartile

7

Greatestvalue11

Drawaboxplot

10 1550





______________________sizeofsample



4___60

= x_____4200

4sdot70______60sdot70

= x_____4200

280_____4200

= x_____4200






8___50

= x_____4500

8sdot90______50sdot90

= x_____4500

720_____4500

= x_____4500



divide060

divide060







_______________________________________ size of sample

=



4 ___ 50

= x ____ 600

4 sdot 12 ______ 50 sdot 12

= x ____ 600

48 ____ 600

= x ____ 600

x = 48



_______________________________________________ size of sample

=



2 ___ 20

= x ____ 130

2 sdot 65 _______ 20 sdot 65

= x ____ 130

13 ____ 130

= x ____ 130

x = 13



________________ size of sample



12 ___ 60

= x _____ 1200

12 sdot 20 ______ 60 sdot 20

= x _____ 1200

240 _____ 1200

= x _____ 1200

x = 240


shelters


__________________________ size of sample



12 ___ 72

= x ______ 10800

12 sdot 150 _______ 72 sdot 150

= x ______ 10800

1800

______ 10800

= x ______ 10800

x = 1800



_______ 2 = 25


14 Order the data

11 12 12 12 13 13 13 14 14 14 15 17 18 18

19 22



12 ___ 16

= x ____ 100

12 sdot 625 ________ 16 sdot 625

= x ____ 100

75 ____ 100

= x ____ 100

x = 75



15

6 7 8 9 1050 1 2 3 4


fewer siblings




















9 a 56 + 43 + 62 + 63 + 33 + 34 + 38 + 51 + 59 + 59

___________________________________________ 10

= 498


b 498 sdot 64 = 31872



10 55 + 57 + 57 + 58 + 59 + 59 + 59 + 59 + 59 + 61 + 62 + 62 + 63 + 64 + 66

_________________________________________________________________ 15

= 60






accurately

LESSON 103

Guided Practice

1 (1 600) 20

2 50 51 600








5 Shop A 10 ___ 50

times 500 = 100

Shop B 23 ____ 100

times 500 = 115

Shop C 7 ___ 25

times 500 = 140








fewest bagels










count of 75


MODULE 10

Ready to Go On




service


__________________________________________ size of sample


18 ____ 270

= x ______ 30330

18 sdot 337 ____

3 ________

270 sdot 337 ____ 3

= x ______ 30330

2022

______ 30330

= x ______ 30330

x = 2022


languages





= defective players

______________ shipment

2 ___ 10

= x _____ 5000

2 middot 500 _______ 10 middot 500

= x _____ 5000

1000

_____ 5000

= x _____ 5000

x = 1000


defective


the shipment





Are You Ready

0875

1 8 ⟌ _

7000

_ -6 400

600

_ -560

40

_ -40

0

0875 875

08

2 5 ⟌ _

40

_ -4 0

0

08 80

025

3 4 ⟌ _

100

_ -80

20

_ -20

0

025 25

03

4 10 ⟌ _

30

_ -3 0

0

03 30

5 4 6 7 7 9 11 15 17

7 + 9

_____ 2 = 8

Median = 8

Mode = 7

6 36 37 40 43 44 49 50 51 56

Median = 44

Mode none

7 9 + 16 + 13 + 14 + 10 + 16 + 17 + 9

________________________________ 8

= 13

Mean = 13

8 108 + 95 + 104 + 96 + 97 + 106 + 94

________________________________ 7 = 100

Mean = 100

LESSON 111

Your Turn








in order

1 4 4 4 5 5 5 6 6 6 6 7 7 8 11


range 10 h



range for exercise

Guided Practice




one area




no data


4 Class A

4 4 4 4 4 5 5 5 6 6 12 13 13 13 13 14 14

median 6

Class B

3 4 4 4 5 5 5 5 6 6 7 7 7 7 7 8 8 9

median 6








at 8 letters




3 + 4 + 4 + 5 + 5 + 6 + 7 + 7 + 8 + 8 + 8 + 9

________________________________________ 12

74 ___ 12

asymp 617

Mean asymp 617

3 3 4 5 5 6 7 7 8 8 8 9


average

6 + 7

_____ 2 = 13 ___

2 = 65

Median 65

Range 9 - 3 = 6


the left


interval













LESSON 112

Your Turn



Guided Practice


2 Median79

3 Range88-72=16 IQR85-75=10






























does not




LESSON 113

Your Turn

1 Team 1

Mean

44 + 47 + 67 + 89 + 55 + 76 +85 + 80 + 87 + 69 + 47 + 58 = 804

804 divide 12 = 67


ǀ 44 - 67 ǀ = 23 ǀ 47 - 67 ǀ = 20

ǀ 67 - 67 ǀ = 0 ǀ 89 - 67 ǀ = 22

ǀ 55 - 67 ǀ = 12 ǀ 76 - 67 ǀ = 9

ǀ 85 - 67 ǀ = 18 ǀ 80 - 67 ǀ = 13

ǀ 87 - 67 ǀ = 20 ǀ 69 - 67 ǀ = 2

ǀ 47 - 67 ǀ = 20 ǀ 58 - 67 ǀ = 11


23 + 20 + 0 + 22 + 12 + 9 +18 + 13 + 20 + 2 + 20 + 11 = 170


Team 2

Mean

40 + 32 + 52 + 75 + 65 + 70 +72 + 61 + 54 + 43 + 29 + 32 = 625



ǀ 40 - 521 ǀ = 121 ǀ 32 - 521 ǀ = 201

ǀ 52 - 521 ǀ = 01 ǀ 75 - 521 ǀ = 229

ǀ 65 - 521 ǀ = 129 ǀ 70 - 521 ǀ = 179

ǀ 72 - 521 ǀ = 199 ǀ 61 - 521 ǀ = 89

ǀ 54 - 521 ǀ = 19 ǀ 43 - 521 ǀ = 91

ǀ 29 - 521 ǀ = 231 ǀ 32 - 521 ǀ = 201


121 + 201 + 01 + 229 +129 + 179 + 199 + 89 +19 + 91 + 231 + 201 = 169


Difference in means

67 - 521 = 149



MAD


distributions

Guided Practice

1 Class 1 mean

12 + 1 + 6 + 10 + 1 + 2 + 3 +10 + 3 + 8 + 3 + 9 + 8 + 6 + 8 = 90

90 divide 15 = 6

Class 2 mean

11 + 14 + 11 + 13 + 6 + 7 + 8 + 6 +8 + 13 + 8 + 15 + 13 + 17 + 15 = 165

165 divide 15 = 11


ǀ 12 - 6 ǀ = 6 ǀ 1 - 6 ǀ = 5 ǀ 6 - 6 ǀ = 0

ǀ 10 - 6 ǀ = 4 ǀ 1 - 6 ǀ = 5 ǀ 2 minus 6 ǀ = 4

ǀ 3 - 6 ǀ = 3 ǀ 10 - 6 ǀ = 4 ǀ 3 - 6 ǀ = 3

ǀ 8 - 6 ǀ = 2 ǀ 3 - 6 ǀ = 3 ǀ 9 - 6 ǀ = 3

ǀ 8 - 6 ǀ = 2 ǀ 6 - 6 ǀ = 0 ǀ 8 - 6 ǀ = 2

6 + 5 + 0 + 4 + 5 + 4 + 3 + 4 +3 + 2 + 3 + 3 + 2 + 0 + 2 = 46



ǀ 11 - 11 ǀ = 0 ǀ 14 - 11 ǀ = 3 ǀ 11 - 11 ǀ = 0

ǀ 13 - 11 ǀ = 2 ǀ 6 - 11 ǀ = 5 ǀ 7 - 11 ǀ = 4

ǀ 8 - 11 ǀ = 3 ǀ 6 - 11 ǀ = 5 ǀ 8 - 11 ǀ = 3

ǀ 13 - 11 ǀ = 2 ǀ 8 - 11 ǀ = 3 ǀ 15 - 11 ǀ = 4

ǀ 13 - 11 ǀ = 2 ǀ 17 - 11 ǀ = 6 ǀ 15 - 11 ǀ = 2

0 + 3 + 0 + 2 + 5 + 4 + 3 + 5 +3 + 2 + 3 + 4 + 2 + 6 + 2 = 44



11 minus 6 = 5




comparison


different samples


5 23 + 38 + 39 + 48 + 55 + 56 + 71 +86 + 57 + 53 + 43 + 31 = 600

600 divide 12 = 50

ǀ 23 - 50 ǀ = 27 ǀ 38 - 50 ǀ = 12

ǀ 39 - 50 ǀ = 11 ǀ 48 - 50 ǀ = 2

ǀ 55 - 50 ǀ = 5 ǀ 56 - 50 ǀ = 6

ǀ 71 - 50 ǀ = 21 ǀ 86 - 50 ǀ = 36

ǀ 57 - 50 ǀ = 7 ǀ 53 - 50 ǀ = 3

ǀ 43 - 50 ǀ = 7 ǀ 31 - 50 ǀ = 19

27 + 12 + 11 + 2 + 5 + 6 + 21 +36 + 7 + 3 + 7 + 19 = 156

156 divide 12 = 13



6 ǀ 23 - 8 ǀ = 15 ǀ 38 - 23 ǀ = 15

ǀ 39 - 24 ǀ = 15 ǀ 48 - 33 ǀ = 15

ǀ 55 - 40 ǀ = 15 ǀ 56 - 41 ǀ = 15

ǀ 71 - 56 ǀ = 15 ǀ 86 - 71 ǀ = 15

ǀ 57 - 42 ǀ = 15 ǀ 53 - 38 ǀ = 15

ǀ 43 - 28 ǀ = 15 ǀ 31 - 16 ǀ = 15




7 50 - 15 = 35




8 50 - 35 = 15




9

0 4 8 12 16 20 24 28 32 36 40 44

Medians

School B

School A

0 4 8 12 16 20 24 28 32 36 40 44

Means

School B

School A




10 State A 48 - 38 = 10


State B 50 - 42 = 8

8 divide 4 = 2





well


Median 665


Median 77

77 - 665 = 105

105 divide 6 = 175


ranges













not very similar

MODULE 11

Ready to Go On


5 + 6 + 6 + 7 + 7 + 7 + 7 + 8 + 8 + 8 + 8 + 9 + 9 + 10

________________________________________________ 14

= 105 ____ 14

= 75 mi


6 + 6 + 7 + 7 + 8 + 8 + 8 + 8 + 9 + 9 + 9 + 10 + 10 + 10

__________________________________________________ 14

= 115 ___ 14

asymp 82 mi




5 6 6 7 7 7 7 8 8 8 8 9 9 10


average

7 + 8

_____ 2 = 15 ___

2 = 75

Median 75


6 6 7 7 8 8 8 8 9 9 9 10 10 10




Median 8













7 + 11 + 11 + 12 + 9 + 12 + 8 + 10

______________________________ 8

= 10


21 + 24 + 19 + 19 + 22 + 23 + 24 + 24

__________________________________ 8 = 22




12 ___ 5

= 24




groups



Are You Ready

1 6 ___ 10

= 6 divide 2 ______ 10 divide 2

= 3 __ 5

2 9 ___ 15

= 9 divide 3 ______ 15 divide 3

= 3 __ 5

3 16 ___ 24

= 16 divide 8 ______ 24 divide 8

= 2 __ 3

4 9 ___ 36

= 9 divide 9 ______ 36 divide 9

= 1 __ 4

5 45 ___ 54

= 45 divide 9 ______ 54 divide 9

= 5 __ 6

6 30 ___ 42

= 30 divide 6 ______ 42 divide 6

= 5 __ 7

7 36 ___ 60

= 36 divide 12 _______ 60 divide 12

= 3 __ 5

8 14 ___ 42

= 14 divide 14 _______ 42 divide 14

= 1 __ 3

075

9 4 ⟌ _

300

_ -2 80

20

_ -20

0

075

0875

10 8 ⟌ _

7000

_ -6400

600

_ -560

40

_ -40

0

0875

015

11 20 ⟌ _

300

_ -2 00

100

_ -100

0

015

038

12 50 ⟌ _

1900

_ -15 00

4 00

_ -4 00

0

038

13 67 = 67 ____ 100

= 067

14 31 = 31 ____ 100

= 031

15 7 = 7 ____ 100

= 007

16 146 = 100 + 46

= 100 ____ 100

+ 46 ____ 100

= 1 + 046

= 146

17 013 = 13

18 055 = 55

19 008 = 8

20 116 = 116

LESSON 121

Your Turn







is 10 ___ 20

or 1 __ 2





3


UNIT

6



P(5) + P(not 5) = 1

1 __ 8 + P(not 5) = 1

P(not 5) = 7 __ 8




1 __ 2 + P(odd) = 1

P(odd) = 1 __ 2


Guided Practice













impossible 0
















= 1 __ 4


P(5) + P(not 5) = 1

1 __ 6 + P(not 5) = 1

P(not 5) = 5 __ 6




1 __ 3 + P(not blue) = 1




P(4) + P(not 4) = 1

1 __ 5 + P(not 4) = 1

P(not 4) = 4 __ 5




4 ___ 52

+ P(not queen) = 1

P(not blue) = 48 ___ 52

= 12 ___ 13









selecting


or 2 ___ 13



9 ___ 12



or 1 __ 4



or 1 __ 4













or 5 __ 7



have red hair




or 4 __ 7





coin is 9 ___ 16














landing on blue

LESSON 122

Your Turn


Red 10 ___ 30

= 1 __ 3

Yellow 14 ___ 30

= 7 ___ 15

Blue 6 ___ 30

= 1 __ 5






Guided Practice


A 14 ___ 40

= 7 ___ 20

= 035 = 35

B 7 ___ 40

= 0175 = 175

C 11 ___ 40

= 0275 = 275

D 8 ___ 40

= 1 __ 5 = 020 = 20







4 6 ___ 10








= 8 ___ 48

= 1 __ 6





chosen is 19 ___ 20


1 ___ 20

+ P(not Ryan) = 1

P(not Ryan) = 19 ___ 20


patterns




times



get a hit next time


is 4 ___ 10





or about 417


7 ___ 12



or 417











pocket


LESSON 123

Your Turn



= 60 ____ 400

= 3 ___ 20

= 15



= 12 ___ 75

or 4 ___ 25

Guided Practice




= 50 ____ 400

or 1 __ 8











number of trials








= 33 ____ 330

= 1 ___ 10



= 60 ____ 400

= 3 ___ 20


= 55 + 60 + 23

____________ 400

= 138 ____ 400

= 69 ____ 200


and 4 color choices


P(7th grade + 100 pages) = 85 ____ 250

= 17 ___ 50




7th grade




likely





12 P(male + open toe) = 11 ____ 300











heads and 3 or 4

LESSON 124

Your Turn








Guided Practice








too high

5 98 ____ 100

= x ___ 40

= 39 ___ 40

or 39 times




6 18 ____ 100

= x _____ 5000

= 900 _____ 5000



accepted

times04

times04

times50

times50





events


8 4 ____ 100

= x ____ 200

= 8 ____ 200



9 Yes 6th grade 2 ____ 100

= x ____ 250

= 5 ____ 250

or 5 students

7th grade 4 ____ 100

= x ____ 200

= 8 ____ 200

or 8 students

8th grade 8 ____ 100

= x ____ 150

= 12 ____ 150

or 12 students



10 6 ____ 100

= x ____ 300

= 18 ____ 300










1 ___ 30

= x ____ 180




normal gas pump







4 ____ 100

= x _____ 2400

= 96 _____ 2400



MODULE 12

Ready to Go On

1 H1 H2 T1 T2

2 6 ___ 10

= 3 __ 5

3 13 ___ 20




because 3 ___ 10

= x ___ 80

= 24 ___ 80

or 24 times




times15

times15

times24

times24

times2

times2

times3

times3

times2

times2

times25

times25

times8

times8



Simulations

Are You Ready

075

1 4 ⟌ _

300

_ -2 80

20

_ -20

0

075 = 75

04

2 5 ⟌ _

20

_ -2 0

0

04 = 40

09

3 10 ⟌ _

90

_ -9 0

0

09 = 90

035

4 20 ⟌ _

700

_ -6 00

1 00

_ -1 00

0

035 = 35

0875

5 8 ⟌ _

7000

_ thinsp-6 400

600

_ -560

40

_ -40

0

0875 = 875

005

6 20 ⟌ _

100

_ -1 00

0

005 = 5

076

7 25 ⟌ _

1900

_ -17 50

1 50

_ -1 50

0

076 = 76

046

8 50 ⟌ _

2300

_ -20 50

3 00

_ -3 00

0

046 = 46

9 1 - 1 __ 5 = 5 __

5 - 1 __

5

= 4 __ 5

10 1 - 2 __ 9 = 9 __

9 - 2 __

9

= 7 __ 9

11 1 - 8 ___ 13

= 13 ___ 13

- 8 ___ 13

= 5 ___ 13

12 1 - 3 ___ 20

= 20 ___ 20

- 3 ___ 20

= 17 ___ 20

13 8 ___ 15

times 5 __ 8 =

18 ___ 315

times 5 1 ___

8 1

= 1 __ 3

14 2 __ 9 times 3 __

4 =

12 __ 39

times 3 1 ___

4 2

= 1 __ 6

15 9 ___ 16

times 12 ___ 13

= 9 ___ 416

times 12 3 _____

13

= 27 ___ 52

16 7 ___ 10

times 5 ___ 28

= 17 ___

210 times 5

1 ____

28 4

= 1 __ 8

LESSON 131

Your Turn






= 2 __ 6 = 1 __

3



probability


Guided Practice

1

Basket A Basket B


= 16

7 + 4 + 9

= 20


P(win) =

Number of red balls


3 ___

16 4 ___

20 = 1 __

5


16 use


1 __ 5 = 16 ___

80

3 ___ 16

= 15 ___ 80

Therefore 16 ___ 80

gt 15 ___ 80

so 1 __ 5 gt 3 ___

16


winning




= 6 ___ 11




= 5 ___ 11




= 2 __ 6 = 1 __

3


close


by 20




= 2 __ 6

= 1 __ 3 033 or 33



= 8 ___ 12

= 2 __ 3 067 or 67



= 4 ___ 14

= 2 __ 7 029 or 29


= 26 ___ 52

= 1 __ 2 050 or 50


= 12 - 5 ______ 12

= 7 ___ 12

058 or 58



7 adventure)

P(not a comedy)


= 5 + 7 _________

5 + 7 + 8 = 12 ___

20

= 3 __ 5 060 or 60






= 2 __ 6

= 1 __ 3 033 or 33







= 6 ___ 16

or 3 __ 8







5 ______ 5 + 15

= 5 ___ 20

= 1 __ 4

times16

times16

times5

times5




P(seventh grader) =



= 20 ___ 35

= 4 __ 7


P(eighth grader) =



= 15 ___ 35

= 3 __ 7



more likely










= 8 ___ 20


14 ___ 40

or 7 ___ 20



marble is 8 ___ 20

- 7 ___ 20

= 1 ___ 20



= 10 ___ 20


= 8 ___ 20



marble is 10 ___ 20

- 8 ___ 20

= 2 ___ 20

= 1 ___ 10




= 2 ___ 20


= 5 ___ 20



marble is 5 ___ 20

- 2 ___ 20

= 3 ___ 20



LESSON 132

Your Turn

3 P(ham sandwich) =



= 4 ___ 12

= 1 __ 3




= 6 ___ 12

= 1 __ 2




0 0 0 0

0 0 0 1

0 0 1 0

0 0 1 1


second digit

0 1 0 0

0 1 0 1

0 1 1 0

0 1 1 1


second digit

1 0 0 0

1 0 0 1

1 0 1 0

1 0 1 1


second digit

1 1 0 0

1 1 0 1

1 1 1 0

1 1 1 1



0 0 1 1

0 1 0 1

0 1 1 0

1 0 0 1

1 0 1 0

1 1 0 0





= 6 ___ 16

= 3 __ 8


Guided Practice

1

1 2 3 4 5 6

11 sdot 1

= 1

1 sdot 2

= 2

1 sdot 3

= 3

1 sdot 4

= 4

1 sdot 5

= 5

1 sdot 6

= 6

22 sdot 1

= 2

2 sdot 2

= 4

2 sdot 3

= 6

2 sdot 4

= 8

2 sdot 5

= 10

2 sdot 6

= 12

33 sdot 1

= 3

3 sdot 2

= 6

3 sdot 3

= 9

3 sdot 4

= 12

3 sdot 5

= 15

3 sdot 6

= 18

44 sdot 1

= 4

4 sdot 2

= 8

4 sdot 3

= 12

4 sdot 4

= 16

4 sdot 5

= 20

4 sdot 6

= 24

55 sdot 1

= 5

5 sdot 2

= 10

5 sdot 3

= 15

5 sdot 4

= 20

5 sdot 5

= 25

5 sdot 6

= 30

66 sdot 1

= 6

6 sdot 2

= 12

6 sdot 3

= 18

6 sdot 4

= 24

6 sdot 5

= 30

6 sdot 6

= 36





= 15 ___ 36




= 23 ___ 36

4 H

HHH HHT

H

H

Coin 1

List

Coin 2

Coin 3 T

T

HTH HTT

H T

T

H

H T

THH THT

T

H T

TTH TTT

Coin 1

List

Coin 2

Coin 3




= 1 __ 8


HHT HTH THH



= 3 __ 8




10

Checkered

Red

Checkered

Red

Blue

Black

Checkered

Red

Checkered

Red

Blue

Black

Checkered

Red

Checkered

Red

Blue

Black

Shirt Pants Shoes

Yellow

Red

Green




= 6 ___ 12

= 1 __ 2


Shirt Pants Shoes






= 4 ___ 12

= 1 __ 3



Rhee Pamela

Rhee A

Rhee B

Rhee C

Pamela A

Pamela B

Pamela C

A B

A C

B C



P(Rhee and Pamela)


= 1 ___ 10




1 2 3 4 5 6

11 + 1

= 2

1 + 2

= 3

1 + 3

= 4

1 + 4

= 5

1 + 5

= 6

1 + 6

= 7

22 + 1

= 3

2 + 2

= 4

2 + 3

= 5

2 + 4

= 6

2 + 5

= 7

2 + 6

= 8

33 + 1

= 4

3 + 2

= 5

3 + 3

= 6

3 + 4

= 7

3 + 5

= 8

3 + 6

= 9

44 + 1

= 5

4 + 2

= 6

4 + 3

= 7

4 + 4

= 8

4 + 5

= 9

4 + 6

= 10

55 + 1

= 6

5 + 2

= 7

5 + 3

= 8

5 + 4

= 9

5 + 5

= 10

5 + 6

= 11

66 + 1

= 7

6 + 2

= 8

6 + 3

= 9

6 + 4

= 10

6 + 5

= 11

6 + 6

= 12


are 10 less than 6



= 10 ___ 36

= 5 ___ 18


diagram

Khakis

Shorts

Shirt Pants Shoes

Collared Jeans

Sneakers

Flip-flops

Sandals

Sneakers

Flip-flops

Sandals

Sneakers

Flip-flops

Sandals

Khakis

Shorts

T-shirt Jeans

Sneakers

Flip-flops

Sandals

Sneakers

Flip-flops

Sandals

Sneakers

Flip-flops

Sandals







= 4 ___ 18

= 2 __ 9






outcomes



Therefore




= 7 ___ 30






diagram

Carrots

Sweet potato

Pasta

Peas

Asparagus





Carrots

Sweet potato

Peas

Asparagus





Carrots

Sweet potato

Peas

Asparagus





Carrots

Sweet potato

Peas

Asparagus





Salmon

Beef

Pork



salmon Therefore


= 1 __ 4





Carrots

Sweet potato

PastaPeas

Asparagus

Carrots

Sweet potato

Peas

Asparagus

Carrots

Sweet potato

Peas

Asparagus

Carrots

Sweet potato

Peas

Asparagus

Salmon

Beef

Pork


salmon Therefore


= 1 __ 4















codes













12453 12534 12543 13245 13254 13425

13452 13524 13542 14235 14253 14325

14352 14523 14532 15234 15243 15324













114 115 221 223 224 225 331 332 334 335

441 442 443 445 551 552 553 554 There























LESSON 133

Your Turn




3






heads is 1 __ 2

1 __ 2 = x ___

18

1 __ 2 = x ___

18

x = 9

about 9 times


P(red) = 8 ___ 17

P(not red) = 1 - 8 ___ 17

= 9 ___ 17




Therefore




Guided Practice






3 House 1 __

3



1 __ 3 = x ___

18

1 __ 3 = x ___

18

x = 6














P(hazel) = 9 ___ 28

P(brown) = 10 ___ 28

P(blue) = 7 ___ 28

P(green) = 2 ___ 28






unknown quantity




P(white or gray) = 3 __ 9 = 1 __

3


prediction is then








Y GRR

R R

RR





card is 12 ___ 52


52 use the least


52 Given

that 12 ___ 52

lt 26 ___ 52





P(ace) = 4 ___ 52

= 1 ___ 13


prediction is then


times 39 = 3



P(red card) = 26 ___ 52

= 1 __ 2








times6

times6

times9

times9


1 2 3 4 5 6

1 2 3 4 5 6 7

2 3 4 5 6 7 8

3 4 5 6 7 8 9

4 5 6 7 8 9 10

5 6 7 8 9 10 11

6 7 8 9 10 11 12




P(sum of 8) = 5 ___ 36

P(sum of 11) = 2 ___ 36



gt 2 ___ 36




= 1 __ 4




1 __ 4 times 180 = 45





so P(sum of 3) = 3 ___ 36

= 1 ___ 12


prediction is then


middot 36 = 3





time









that is not green



green is 3 + 9 _________

3 + 8 + 9 = 12 ___



20 = 12 ___

40






6 = 1 ___

12



P(5 or heads) = 1 __ 6 + 1 __

2 - 1 __

6 times 1 __

2 = 7 ___

12





LESSON 134

Your Turn



1 0 0 1 No

2 0 1 No

3 1 No

4 0 1 No

5 1 No

6 0 0 0 1 Yes

7 0 0 1 No

8 0 1 No

9 1 No

10 0 0 0 0 1 Yes




or 20



1 1 0 1 1 0 3

2 0 1 0 0 1 2

3 0 0 0 0 1 1

4 0 0 1 1 0 2

5 1 1 1 1 1 5

6 1 0 0 0 0 1

7 1 0 1 1 0 3

8 1 0 1 0 0 2

9 0 1 1 1 1 4

10 0 0 0 0 0 0



= 70


Guided Practice







numbers each time

2


1 10 3 5 1 2

2 10 4 6 5 0

3 3 2 10 3 3

4 2 10 4 4 1

5 7 3 6 3 2

6 8 4 8 5 0

7 6 2 2 8 2

8 6 5 2 4 1

9 2 2 3 2 4

10 6 3 1 5 2




8 ___ 10

= 80









= 10




= 20














1 3 1

2 4 2 2

3 2 1

4 1 1

5 2 1

6 4 5 3 2

7 4 2 2

8 4 5 2 1

9 4 4 3 3

10 5 1 2


1 + 2 + 1 + 1 + 1 + 2 + 2 + 1 + 3 + 2

_________________________________ 10

= 16 ___ 10

= 1 3 __ 5

















MODULE 13

Ready to Go On


= 12 ___________________ 12 + 12 + 15 + 9 + 12

= 12 ___ 60

= 1 __ 5 020 or 20




= 13 + 13

_______ 52

= 26 ___ 52

= 1 __ 2 050 or 50








or

40






18 a

-4

-6

-8

-2

0

2

-5 + (-3)-3 + (-5)

b No -5 + ( -3 ) is -8 and -3 + ( -5 ) is also -8


score is -11


21 -14 + ( -5 ) + ( -12 ) + ( -23 ) = -54 The total


22 a -10 + ( -8 ) = -18

b -6 + ( -2 ) = -8


23 -100 + ( -75 ) + ( -85 ) = -260


24 a -25 + ( -45 ) + ( -75 ) = -145 Jan withdrew

$145

b -35 + ( -55 ) + ( -65 ) = -155 Julie withdrew

$155








six pairs is 8

LESSON 12

Your Turn

7 -51 + 23

ǀ -51 ǀ - ǀ 23 ǀ = 28

-51 + 23 = -28

8 10 + ( -18 )

ǀ -18 ǀ - ǀ 10 ǀ = 8

10 + ( -18 ) = -8

9 13 + ( -13 )

ǀ 13 ǀ - ǀ -13 ǀ = 0

10 25 + ( -26 )

ǀ -26 ǀ - ǀ 25 ǀ = 1

25 + ( -26 ) = -1

Guided Practice

1 9 + ( -3 ) = 6

2 3 4 5 8 9 106 7 2 -2 + 7 = 5

-3-2-1 0 3 4 51 2 3 -15 + 4 = -11

-18 -16 -12 -10-14 4 1 + ( -4 ) = -3

-5-4-3-2 1 2 3-1 0 5 -4 + 5 = 1

6 -6 + 6 = 0

7 2 + ( -5 ) = -3

8 -3 + 7 = 4

9 -8 + 14 = 6

10 7 + ( -5 ) = 2

11 5 + ( -21 ) = -16

12 14 + ( -14 ) = 0

13 0 + ( -5 ) = -5

14 32 + ( -8 ) = 24





16 -15 + 71 = 56

17 -53 + 45 = -8

18 -79 + 79 = 0

19 -25 + 50 = 25

20 18 + ( -32 ) = -14

21 5 + ( -100 ) = -95

22 -12 + 8 + 7 = 3

23 -8 + ( -2 ) + 3 = -7


24 15 + ( -15 ) + 200 = 200

25 -500 + ( -600 ) + 1200 = 100
















is 8 feet deep








LESSON 13

Your Turn

4 -7 - 2 = -7 + ( -2 )

-7 + ( -2 ) = -9

5 -1 - ( -3 ) = -1 + 3

-1 + 3 = 2

6 3 - 5 = 3 + ( -5 )

3 + ( -5 ) = -2

7 -8 - ( -4 ) = -8 + 4

-8 + 4 = -4

Guided Practice







3 -4 - 5 = -4 + ( -5 ) = -9

0-1-2-3-4-5-6-7-8-9 4 1 - 4 = 1 + -4 = -3

0 1 2 3 4-1-2-3-4 5 8 - 11 = 8 + ( -11 ) = -3

6 -3 - ( -5 ) = -3 + 5 = 2

7 15 - 21 = 15 + ( -21 ) = -6

8 -17 - 1 = -17 + ( -1 ) = -18

9 0 - ( -5 ) = 0 + 5 = 5

10 1 - ( -18 ) = 1 + 18 = 19

11 15 - 1 = 14

12 -3 - ( -45 ) = -3 + 45 = 42

13 19 - ( -19 ) = 19 + 19 = 38

14 -87 - ( -87 ) = -87 + 87 = 0


example 6 - 8 = 6 + ( -8 ) = -2




25 - ( -4 ) = 25 + 4 = 29





-127 - ( -225 ) = -127 + 225 = 98



temperature 90degF

90 - ( -2 ) = 92






-425 - ( -275 ) = -425 + 275 = -150



in temperature

Gas A -8 - ( -21 ) = -8 + 21 = 13

13degC increase

Gas B 12 - ( -12 ) = 12 + 12 = 24

24degC increase

Gas C -15 - ( -19 ) = -15 + 19 = 4

4degC increase













-11 + 4 = -7




LESSON 14

Your Turn




Guided Practice


2 -23+5-7=-18-7  =-25-25degF

3 50-40+87-30=10+87-30  =97-30  =6767points

4 -6+15+15=-6+30  =24

5 9- 4- 17= 9- 21  =-12

6 50-42+10=8+10  =18

7 6+13+7-5=19+2  =21

8 65+43-11=108-11  =97

9 -35-14+45+31=-49+76  =27

10 -12+6-4=-6-4  =-10-34-3+39=-37+39  = 2  -10lt2( -12+6-4)lt( -34-3+39)

11 21-3+8=18+8  =26-14+ 31- 6= 17- 6  =11 26gt11( 21-3+8)gt( -14+31-6)



13 a 5-1+6-1=9






b 45gt-55Barry

17 a 300to400


18 100-18+22-53=51$51

19 45-17-22+18=24$24






MODULE 1

Ready to Go On

1 -8+( -6)=-14

2 -4+( -7)=-11

3 -9+( -12)=-21





4 5 + ( -2 )

ǀ 5 ǀ - ǀ -2 ǀ = 3

5 + ( -2 ) = 3

5 -8 + 4

ǀ -8 ǀ - ǀ 4 ǀ = 4

-8 + 4 = -4

6 15 + ( -8 )

ǀ 15 ǀ - ǀ -8 ǀ = 7

15 + ( -8 ) = 7

7 2 - 9 = 2 + ( -9 )

2 + ( -9 ) = -7

8 -3 - ( -4 ) = -3 + 4-3 + 4 = 1

9 11 - ( -12 ) = 11 + 12

11 + 12 = 23

10 -15 + 9 - 4 = -6 - 4

= -10


11 24 + 8 - 12 - 9 = 24 + 8 - ( 12 + 9 ) = 32 - 21

= 11




after she pays them

-10 + ( -5 ) = -15 $15 decrease



Are You Ready

1 9 times 3 = 27

2 7 times 10 = 70

3 9 times 8 = 72

4 15 times 10 = 150

5 6 times 9 = 54

6 10 times 23 = 230

7 9 times 9 = 81

8 10 times 20 = 200

9 54 divide 9 = 6

10 42 divide 6 = 7

11 24 divide 3 = 8

12 64 divide 8 = 8

13 90 divide 10 = 9

14 56 divide 7 = 8

15 81 divide 9 = 9

16 110 divide 11 = 10

17 12 + 8 divide 212 + 4

16

18 15 - ( 4 + 3 ) times 2

15 - 7 times 2

15 - 14

1

19 18 - ( 8 - 5 ) 2

18 - ( 3 ) 2

18 - 9

9

20 6 + 7 times 3 - 5

6 + 21 - 5

27 - 5

22

21 9 + ( 2 2 + 3 ) 2 times 2

9 + ( 4 + 3 ) 2 times 2

9 + ( 7 ) 2 times 2

9 + 49 times 2

9 + 98

107

22 6 + 5 - 4 times 3 divide 2

6 + 5 - 12 divide 2

6 + 5 - 6

11 - 6

5

LESSON 21

Your Turn


will be negative


-3 ( 5 ) = -15


will be positive

ǀ -10 ǀ times ǀ -2 ǀ = 10 times 2 = 20

( -10 ) ( -2 ) = 20


0 ( -22 ) = 0


will be positive

8 ( 4 ) = 32

Guided Practice

1 -1 ( 9 ) = -9

2 14 ( -2 ) = -28

3 ( -9 ) ( -6 ) = 54

4 ( -2 ) ( 50 ) = -100

5 ( -4 ) ( 15 ) = -60

6 -18 ( 0 ) = 0

7 ( -7 ) ( -7 ) = 49

8 -15 ( 9 ) = -135

9 ( 8 ) ( -12 ) = -96

10 -3 ( -100 ) = 300

11 0 ( -153 ) = 0

12 -6 ( 32 ) = -192

13 7 ( -75 ) = -525 -$525



15 6 ( -2 ) = -12 -12degF








19 5 ( -4 ) = -20 $20 decrease





22 9 ( -6 ) = -54 -54 ( 2 ) = -108 Casey has $108

less in his savings

23 7 ( -8 ) = -56 7 ( -5 ) = -35





160 points


25 a 3 ( 3 ) ( -3 ) = 9 ( -3 ) = -27

b 3 ( -3 ) ( -3 ) = -9 ( -3 ) = 27

c -3 ( -3 ) ( -3 ) = 9 ( -3 ) = -27

d 3 ( 3 ) ( 3 ) ( -3 ) = 9 ( 3 ) ( -3 ) = 27 ( -3 ) = -81

e 3 ( 3 ) ( -3 ) ( -3 ) = 9 ( -3 ) ( -3 ) = -27 ( -3 ) = 81

f 3 ( -3 ) ( -3 ) ( -3 ) = -9 ( -3 ) ( -3 ) = 27 ( -3 ) = -81




negative



3 ( 3 ) ( -3 ) ( -3 ) = 9 ( -3 ) ( -3 ) = 81 the sign of the

product is positive


26 -1 ( 3 ) ( 1 ) 1 ( -3 ) ( 1 ) -1 ( -3 ) ( -1 )









negative

LESSON 22

Your Turn


0 divide ( -6 ) = 0


will be negative

38 divide ( -19 ) = -2


will be positive

-13 divide ( -1 ) = 13



Guided Practice

1 -14 ____ 2 = -7

2 21 divide ( -3 ) = -7

3 26 ____ -13

= -2

4 0 divide ( -4 ) = 0

5 -45 ____ -5 = 9

6 -30 divide ( 10 ) = -3

7 -11 ____ -1

= 11

8 -31 divide ( -31 ) = 1

9 0 ___ -7 = 0

10 -121 _____ -11

= 11

11 84 divide ( -7 ) = -12

12 500 ____ -25

= -20


undefined

14 -63 ____ -21

= 3

15 -40 divide ( 4 ) = -10 $10

16 -22 divide ( 11 ) = -2 2 points

17 -75 divide ( -15 ) = 5 5 targets

18 -99 divide ( -9 ) = 11 11 times





20 -24 divide ( 12 ) = -2 $2







is -200 ft _______ 10 min



= -15 ftmin







-20 divide 5 = -4 and -20 times 5 = -100

-100 lt -4



negative





incorrectly

29 a divide ( -3 ) = 8

a = -24

8 divide b = -4






integers

LESSON 23

Your Turn


3 ( -30 ) + 200 = -90 + 200

= 110

2 -6 ( 13 ) - 21 = -78 - 21

= -99

4 ( -12 ) divide 6 + 2 = -2 + 2

= 0

5 -87 divide ( -3 ) -9 = 29 - 9

= 20

6 40 divide ( -5 ) + 30 = -8 + 30

= 22

7 -39 divide 3 -15 = -13 - 15

= -28



moved further back

9 ( -10 ) divide 2 - 2 = -5 - 2 = -7

( -28 ) divide 4 + 1 = -7 + 1 = -6

10 42 divide ( -3 ) + 9 = -14 + 9 = -5

( -36 ) divide 9 - 2 = -4 - 2 = -6

Guided Practice

1 -6 ( -5 ) + 12 = 30 + 12

= 42

2 3 ( -6 ) - 3 = -18 - 3

= -21

3 -2 ( 8 ) + 7 = -16 + 7

= -9

4 4 ( -13 ) + 20 = -52 + 20

= -32

5 -4 ( 0 ) - 4 = 0 - 4

= -4

6 -3 ( -5 ) - 16 = 15 - 16

= -1

7 7 ( -5 ) + 20 = -35 + 20

= -15

15 dollars less

8 7 ( -10 ) + ( -100 ) = -70 + ( -100 )

= -170

170 fewer points

9 6 ( -4 ) + 10 = -24 + 10

= -14

Ned lost 14 points

10 4 ( -12 ) + 10 = -48 + 10

= -38

$38 less

11 -3 ( -2 ) + 3 = 6 + 3

= 9

3 ( -4 ) + 9 = -12 + 9

= -3

9 gt -3

-3 ( -2 ) + 3 gt 3 ( -4 ) + 9

12 -8 ( -2 ) -20 = 16 -20

= -4

3 ( -2 ) + 2 = - 6 + 2

= -4

-4 = -4

-8 ( -2 ) -20 = 3 ( -2 ) + 2

13 -7 ( 5 ) - 9 = -35 - 9

= -44

-3 ( 20 ) + 10 = -60 + 10

= -50

-44 gt -50

-7 ( 5 ) -9 gt -3 ( 20 ) + 10

14 -16 ( 0 ) -3 = 0 -3

= -3

-8 ( -2 ) -3 = 16 -3

= 13

-3 lt 13

-16 ( 0 ) -3 lt -8 ( -2 ) -3





16 -12 ( -3 ) + 7 = 36 + 7

= 43

17 -42 divide ( -6 ) + 5 -8 = 7 + 5 -8

= 12 -8

= 4

18 10 ( -60 ) -18 = -600 -18

= -618

19 ( -11 ) ( -7 ) + 5 - 82 = 77 + 5 - 82

= 82 - 82

= 0

20 35 divide ( -7 ) + 6 = -5 + 6

= 1

21 -13 ( -2 ) - 16 - 8 = 26 - 16 - 8

= 10 - 8

= 2

22 a 5 ( 2 ) -12 + 3 = 10 -12 + 3

= -2 + 3

= 1

b -3 ( 2 ) -1 + 6 + 7 = -6 -1 + 6 + 7

= -7 + 6 + 7

= -1 + 7

= 6


the game

23 5 ( -4 ) -8 = -20 - 8 = -28

24 -36 divide ( -4 ) + 9 = 9 + 9 = 18


25 a 4 ( -35 ) -9 = -140 -9

= -149

$149 less

b Yes $200 - $149 = $51 $51 gt $50 so Arleen

has enough money

26 a 2 ( -10 ) + 3 = -20 + 3= -17

b 7 + 2 + ( -7 ) = 2




7 of clubs





had change








MODULE 2

Ready to Go On


will be negative

( -2 ) ( 3 ) = -6


will be positive

( -5 ) ( -7 ) = 35



( 8 ) ( -11 ) = -88

4 ( -3 ) ( 2 ) ( -2 ) = ( -6 ) ( -2 ) = 12

5 5 ( -3 ) = -15 -15degC

6 -63 ____ 7 = -9

7 -15 ____ -3

= 5

8 0 ____ -15

= 0

9 96 ____ -12

= -8

10 -24 divide 6 = -4 -4 Ib

11 ( -4 ) ( 5 ) + 8 = -20 + 8

= -12

12 ( -3 ) ( -6 ) -7 = 18 -7

= 11

13 -27 ____ 9 - 11 = -3 - 11

= -14

14 -24 ____ -3

- ( -2 ) = 8 + 2

= 10




( -3 ) ( 5 ) + 10 = -15 + 10 = -5 He had $05 less

than before



Are You Ready

1 9 ___ 14

times 7 __ 6 =

3

2

9 ___ 14

times 7 __ 6 1

2

= 3 __ 4

2 3 __ 5 times 4 __

7 = 12 ___

35

3 11 ___ 8

times 10 ___ 33

= 1

4

11 ___ 8 times 10 ___

33 5

3

= 5 ___ 12

4 4 __ 9 times 3 =

3

4 __ 9 times 3 __

1 1

= 4 __ 3 or 1 1 __

3

5 1 __ 2 divide 1 __

4 = 1 __

2 times 4 __

1

=

1 1 __ 2 times 4 __

1 2

= 2 __ 1 = 2

6 3 __ 8 divide 13 ___

16 = 3 __

8 times 16 ___

13

= 1 3 __ 8 times 16 ___

13 2

= 6 ___ 13

7 2 __ 5 divide 14 ___

15 = 2 __

5 times 15 ___

14

= 1

1 2 __ 5 times 15 ___

14 3

7

= 3 __ 7

8 4 __ 9 divide 16 ___

27 = 4 __

9 times 27 ___

16

= 1

1 4 __ 9 times 27 ___

16 3

4

= 3 __ 4

9 3 __ 5 divide 5 __

6 = 3 __

5 times 6 __

5

= 18 ___ 25

10 1 __ 4 divide 23 ___

24 = 1 __

4 times 24 ___

23

= 1 1 __ 4 times 24 ___

23 6

= 6 ___ 23

11 6 divide 3 __ 5 = 6 __

1 times 5 __

3

= 2

6 __ 1 times 5 __

3 1

= 10 ___ 1 = 10

12 4 __ 5 divide 10 = 4 __

5 times 1 ___

10

= 2

4 __ 5 times 1 ___

10 5

= 2 ___ 25

13 21 - 6 divide 3

21 - 2

19

14 18 + ( 7 - 4 ) times 3

18 + 3 times 3

18 + 9

27

15 5 + ( 8 - 3 ) 2

5 + ( 5 ) 2

5 + 25

30

16 9 + 18 divide 3 + 10

9 + 6 + 10

15 + 10

25

17 60 - ( 3 - 1 ) 4 times 3

60 - ( 2 ) 4 times 3

60 - 16 times 3

60 - 48

12

18 10 - 16 divide 4 times 2 + 6

10 - 4 times 2 + 6

10 - 8 + 6

2 + 6

8

LESSON 31

Your Turn

0 _

571428

4 7 ⟌ _


_ -35

50

_ -49

10

_ -7

30

_ -28

20

_ -14

60

_ -56




-0 _

571428 or -0571428571428hellip


0 _ 3

5 3 ⟌ _


_ -3




0333hellip

045

6 20 ⟌ _

900

_ -8 0

1 00

_ -1 00

0

-045

7 -2 3 __ 4 = -thinsp 4 times 2 + 3

_________ 4 = -11 ____

4

275

4 ⟌ _

1100

_ -8

30

_ -28

20

_ -20

0

-275 terminating

8 7 1 __ 3 =

3 times 7 + 1 _________

3 = 22 ___

3

7 _ 3

3 ⟌ _


_ -21





Guided Practice

06

1 5 ⟌ _

30

_ -3 0

0

06 terminating

089

2 100 ⟌ _

8900

_ -80 0

9 00

_ -9 00

0

-089 terminating


4 ___ 12

= 4 times 1 _____ 4 times 3

= 1 __ 3

0 _ 3

3 ⟌ _


_ -3





0 _

25

4 99 ⟌ _


_ -19 8

520

_ -495




25 or


0 _ 7

5 9 ⟌ _


_ -63





036

6 25 ⟌ _

900

_ -7 5

1 50

_ -1 50

0

-036 terminating

004

7 25 ⟌ _

100

_ -1 00

0

004 terminating

01420 _

45

8 176 ⟌ _

250000000

_ -17 6

7 40

_ -7 04

360

_ -352

80

_ -0


_ -704

960

_ -880




-01420 _


0012

9 1000 ⟌ _

12000

_ -10 00

2 000

_ -2 000

0

0012 terminating


10 -11 1 __ 6 = -thinsp 6 times 11 + 1

_________ 6 = -67 ____

6

111 _ 6

6 ⟌ _

67000

_ -6

07

_ -6

1 0

_ -6


_ -36




- 67 ___ 6

-111 _ 6 or -111666hellip

11 2 9 ___ 10

= 10 times 2 + 9

__________ 10

= 29 ___ 10

29

10 ⟌ _

290

_ -20

9 0

_ -9 0

0

29 ___ 10

29

12 -8 23 ____ 100

= - 100 times 8 + 23

____________ 100

= -823 _____ 100

823

100 ⟌ _

82300

_ -800

23 0

_ -20 0

3 00

_ -3 00

0

-823 _____ 100

-823

13 7 3 ___ 15

= 15 times 7 + 3

__________ 15

= 108 ____ 15

72

15 ⟌ _

1080

_ -105

3 0

_ -3 0

0

108 ____ 15

72

14 54 3 ___ 11

= 11 times 54 + 3

__________ 11

= 597 ____ 11

54 _

27

11 ⟌ _

597000

_ -55

47

_ -44


_ -22

80

_ -77




597 ____ 11

54 _

27 or 542727hellip

15 -3 1 ___ 18

= -thinsp 18 times 3 + 1 __________

18 = -55 ____

18

30 _ 5

18 ⟌ _

55000

_ -54

1 0

_ -0


_ -90




-55 ____ 18

-30 _ 5 or -30555hellip

16 3 2 __ 3 =

3 times 3 + 2 _________

3 = 11 ___

3

3 _ 6

3 ⟌ _

1100

_ -9


_ -1 8





17 -2 7 __ 8 = -

8 times 2 + 7 _________

8 = -23 ____

8

2875

8 ⟌ _

23000

_ -16

7 0

_ -6 4

60

_ -56

40

_ -40

0

-2875 lb




3 ___ 47








= 5 ___ 11

0 _

45

11 ⟌ _


_ -4 4

60

_ -55




5 ___ 11

0 _


20 hockey players


= 6 ___ 10

06

10 ⟌ _

60

_ -6 0

0

6 ___ 10

06 terminating

21 polo players


= 4 ___ 11

036

11 ⟌ _


_ -3 3

70

_ -66




4 ___ 11

0 _


22 lacrosse players


= 10 ___ 15

= 5 times 2 _____ 5 times 3

= 2 __ 3

0 _ 6

3 ⟌ _


_ -1 8




10 ___ 15


23 football players


= 11 ___ 11

= 1

11 ___ 11

1 terminating







25 a -4 7 __ 8 = -thinsp 8 times 4 + 7

_________ 8 = - 39 ___

8

b 4875

8 ⟌ _

39000

_ -32

7 0

_ -6 4

60

_ -56

40

_ -40

0

-4875








is equal

to 85 ___ 16


is

equal to 127 ____ 24

or 52916hellip ft




















090625











0121212hellip


LESSON 32

Your Turn

2

50 1 2 3 4

3 + 1 1 __ 2 = 4 1 __

2

3

0-7 -6 -5 -4 -3 -2 -1

-25 + ( -45 ) = -7

6

0 1 2-5-6-7-8 -4 -3-2-1

-8 + 5 = -3

7

10-1

1 __ 2 + ( - 3 __

4 ) = - 1 __

4

8

3 4 5 6 7 80 1 2-3-2-1

-1 + 7 = 6

9

3 4 50 1 2-5-4 -3-2-1

2 1 __ 2 + ( -2 1 __

2 ) = 0

10

3 4 50 1 2-5-4 -3-2-1

-45 + 45 = 0

11

1-1 0

3 __ 4 + ( - 3 __

4 ) = 0


12 -15 + 35 + 2

-15 + 55

55 - 15

4

13 3 1 __ 4 + ( -2 ) + ( -2 1 __

4 )

3 1 __ 4 + ( -4 1 __

4 )

3 1 __ 4 - 4 1 __

4

-1

14 -275 + ( 325 ) + 5

-6 + 5

-1

15 15 + 8 + ( -3 )

23 + 3

20

Guided Practice

1

3 4 50 1 2-5-4 -3-2-1

-3 + ( -15 ) = -45

2

0 54321-5-4-3-2-1

15 + 35 = 5

3

0 105-1 -05

1 __ 4 + 1 __

2 = 3 __

4

4

0 54321-5-4-3-2-1

-1 1 __ 2 + ( -1 1 __

2 ) = -3

5

0 54321-5-4-3-2-1

3 + ( -5 ) = -2

6

0 54321-5-4-3-2-1

-15 + 4 = 25

7 -2150 + 2150 = 0 $0

8 -874 + 874 = 0 $0

9 275 + ( -2 ) + ( -525 )

275 + ( -725 )

- ( 725 - 275 )

-45

10 -3 + 1 1 __ 2 + 2 1 __

2 = -3 + 4 = 1

11 124 + 92 + 1

-124 + 102

- ( 124 - 102 )

-22

12 -12 + 8 +13

-12 + 21

21 - 12

9

13 45 + ( -12 ) + ( -45 )

45 + ( -45 ) + ( -12 )

0 + ( -12 )

-12

14 1 __ 4 + ( - 3 __

4 ) = - ( 3 __

4 - 1 __

4 ) = - 2 __

4 = - 1 __

2


15 -4 1 __ 2 + 2 = - ( 4 1 __

2 - 2 ) = -2 1 __

2

16 -8 + ( -1 1 __ 8 ) = -9 1 __

8


The sum is 2



19 -$225 + $1500 = $1500 - $225 = $1275

20 -3525 m + ( -85 ) = -4375 m

21 4 3 __ 4 mi + ( -3 1 __

4 mi ) = 1 2 __

4 mi = 1 1 __

2 mi


23 30 + 15 - 25 = 45 - 25 = 20 pts

24 January

Income - Expenses

$1205 - $129060

- ( $129060 - $1205 ) -$8560

February

Income - Expenses

$1183 - $134544

-($134544 - $1183)

-$16244


February

25 June

Income - Expenses

$2413 - $210623

$30677

July

Income - Expenses

$2260 - $195850

$30150

August

Income - Expenses

$2183 - $184512

$33788


$33788 in August






the end of August

Income = $1205 + $1183 + $1664 + $2413

$2260 + $2183 = $10908

Expenses = $129060 + $134544 + $1664 +$210623 + $195850 + $184512

= $1020989

Profit = $10908 - $1020989 + $250

= $94811


28 a 7 ( 10 ) + 3 ( -15 ) = 70 - 45 = 25 pts

b 2 ( 10 ) + 8 ( -15 ) = 20 - 120 = -100 pts








the positive number







LESSON 33

Your Turn

1

-9 -8 -7 -6 -5 -4

-65 - 2 = -85

2

42 30-1 1

1 1 __ 2 - 2 = - 1 __

2

3

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0

-225 - 55 = -775

6

1 2-1 0

025 - ( -150 ) = 175

7

1-1 0

- 1 __ 2 - ( - 3 __

4 ) = 1 __

4

Guided Practice

1

1312111098765 14 15

5 - ( -8 ) = 13

2

-9 -8 -7 -6 -5 -4 -3

3 1 __ 2 - 4 1 __

2 = -8


3

-15 -13 -11 -9 -5-7

-7 - 4 = -11

4

-6 -5 -4 -3 -2 -1 0 1

-05 - 35 = -4

5 -14 - 22 = -36

6 -125 - ( -48 )

-125 + 48

- ( 125 - 48 )

-77

7 1 __ 3 - ( - 2 __

3 ) = 1 __

3 + 2 __

3 = 1

8 65 - ( -14 ) = 65 + 14 = 79

9 - 2 __ 9

- ( -3 )

- 2 __ 9

+ 3

3 - 2 __ 9

2 9 __ 9 - 2 __

9

2 7 __ 9

10 24 3 __ 8

- ( -54 1 __ 8 )

24 3 __ 8

+ 54 1 __ 8

78 4 __ 8

78 1 __ 2

11 -1 m + ( 105 m ) = -15 m


12 -12 1 __ 2 + ( -5 ) = -17 1 __

2

17 1 __ 2

or 175 yards


533 ft - ( -10 ft ) = 533 ft + 10 ft = 543 ft

14 -4500 + (-3015) = -7515 $7515






16 -126degC - 75degC = -201degC

17 -2565 ft - 165 ft + 1245 ft = -297 ft


18 -9500 ft - ( -26000 ft ) = 16500 ft

19 29035 ft - ( -36198 ft ) = 65233 ft

70000 ft - ( -26000 ft ) = 96000 ft


96000 ft - ( 65233 ft ) = 30767 ft


b 78degF - 32degF


21 a -$1258 + ( -$3072 ) = -$4330

b -$4330 + ( -$25 ) = -$6830

c $6830 since -$6830 + $6830 = 0



23 a 5 ft - 72 ft + 22 ft

b 5 ft - 72 ft + 22 ft

5 ft + 22 ft - 72 ft

72 ft - 72 ft



24 a Yes

$425 + $089 + $1099

= $1613 lt $20

b $20 - $1613 = $387 left over





- 7 ___ 16

- 1 __ 4 - 5 ___

16 = ( - 7 ___

16 ) + ( - 1 __

4 ) + ( - 5 ___

16 )

( - 7 ___ 16

) + ( - 5 ___ 16

) + ( - 1 __ 4 ) by CPA

( -7 + ( -5 ) __________

16 ) + ( - 1 __

4 )

( -12 ____ 16

) + ( - 1 __ 4 )

( - 4 times 3 _____ 4 times 4

) + ( - 1 __ 4 )

( - 3 __ 4 ) + ( - 1 __

4 )

( -3 + ( -1 ) __________

4 )

( -4 ___ 4 ) = -1





and c __ d

Both fractions









LESSON 34

Your Turn

1

-8 -7 -6 -5 -2 -1 0-4 -3

2 ( -35 ) = -7

2

-2 -1 0 1 2 3 4-4 -3

-3 ( -125 ) = 375

4 ( - 3 __ 4 ) ( - 4 __

7 ) ( - 2 __

3 ) = -



= - 2 __ 7

5 ( - 2 __ 3 ) ( - 3 __

4 ) ( 4 __


__________ 13 times 41 times 5


= 2 __ 5

6 ( 2 __ 3 ) ( - 9 ___

10 ) ( 5 __

6 ) = -


____________ 13 times 210 times 63


= - 1 __ 2

Guided Practice

1

-5 -2 -1 0-4 -3

5 ( - 2 __ 3 ) = 5 __

1 times ( - 2 __

3 )

= - 5 times 2 _____ 1 times 3

= - 10 ___ 3

= -3 1 __ 3

2

-1 -05 0-2 -15

3 ( - 1 __ 4 ) = 3 __

1 times - 1 __

4

= - 3 times 1 _____ 1 times 4

= - 3 __ 4

3

0 1 2-2 -1

-3 ( - 4 __ 7 ) = 3 __

1 times 4 __

7

= 3 times 4 _____ 1 times 7

= 12 ___ 7

= 1 5 __ 7

4

-2 -1 0 1 2 3 4-4 -3

- 3 __ 4 ( -4 ) = 3 __

4 times 4 __

1

= 3 times 41

______ 14 times 1

= 3 times 1 _____ 1 times 1

= 3 __ 1

= 3

5 4 ( -3 ) = -12

6 -18 ( 5 ) = -9

7 -2 ( -34 ) = 68

8 054 ( 8 ) = 432

9 -5 ( -12 ) = 6

10 -24 ( 3 ) = -72

11 1 __ 2 times 2 __

3 times 3 __

4 = ( 1 times 21

______ 12 times 3

) ( 3 __ 4 )

= ( 1 __ 3 ) ( 3 __

4 )

= 1

1 __ 3 times 3 __

4 1

= 1 __ 4

12 - 4 __ 7 ( -thinsp 3 __

5 ) ( - 7 __

3 ) = ( - 4 times 3 _____

7 times 5 ) ( - 7 __

3 )

= 12 ___ 35

( - 7 __ 3 )

= - 4

5 12 times 7 ______ 35 times 3

1

1

= - 4 times 1 _____ 5 times 1

= - 4 __ 5

13 ( - 1 __ 8 ) times 5 times 2 __

3 = ( - 1 __

8 ) times 5 __

1 times 2 __

3


__________ 48 times 1 times 3


= - 5 ___ 12


14 ( - 2 __ 3

) ( 1 __ 2 ) ( - 6 __


__________ 13 times 21 times 7


= 2 __ 7


16 18 ( -100 ) = -1800 or a $1800 change









amount

b 200 + 6 ( -1998 )

= 200 - 11988

= 8012 $8012





which is 6

20 8 ( -3 1 __ 4 ) = -8 ( 13 ___

4 )

= - 1

8 __ 1 times 13 ___

4 1

= - 2 times 13 ______ 1 times 1

= - 26 ___ 1





(below the surface)

22 5 + ( -3 ) ( 15 )

= 5 + ( -45 )

= 05 cups left





a positive



25 Total score is

2 times ( 6 ) + 16 times ( 05 )

+ 7 times ( -05 ) + 2 times ( -15 )

= 12 + 8 - 35 - 3

= 20 - 65

= 135 pts




= 12 + 5 ( -68 )

= 12 + ( -34 )

= -22degC

27 a b c d

+ + + +

+ + - +

+ - + +

- + + +

- - - +

- - + -

- + - -

+ - - -









LESSON 35

Your Turn

3 28 ___ -4

= - 28 ___ 4 = -07

4 -664 ______ -04

= 664 ____ 04

= 166

5 - 55 ___ 05

= - 55 ___ 5 = -11

6 -4256 _______ 112

= -38


per minute

7 - 5 __

8 ___

- 6 __ 7 = - 5 __

8 divide - 6 __

7

= - 5 __ 8 times - 7 __

6

= 35 ___ 48

8 - 5 ___

12 ____

2 __ 3 = - 5 ___

12 divide 2 __

3

= - 5 ___ 12

times 3 __ 2

= - 15 ___ 24

= - 5 __ 8


9 -4__5

___1__2 =-4__5divide1__

2

=-4__5times2__1

=-8__5

=-13__5

Guided Practice

1 072_____-09=-72___

9 =-08

2 -1__5

___7__5 =-1__

15times5

1__

7=-1times1_____

1times7=-1__7

3 56___-7=-56___7=-8

4 251____4 divide(-3__

8)=251____

4 times-8__

3

=-251times82________

14times3


=-502____3

5 75____-1__5

=-75___1times5__

1=-75times5______

1times1=-375

6 -91____-13=91___

13=7

7 -3__7

___9__4 =-

13__7times4__93


=-4___21

8 - 12____003

=-1200_____

3 =-400


changeindays

=-35L______4day

=-0875 L____day

or-0875Lperday


changeindays

=-$4575________5day



numberofminutes

=-044mi________08min

=-44mi______8min

=-055mileperminute



13 5___-2__

8=-5__

1times8__

24

1=-5times4_____

1times1=-20

14 51__3divide(-11__

2)


2

=-16___3divide3__

2

=-16___3times2__

3


=-32___9

15 -120_____-6 =120____

6 =20

16 -4__5

___-2__

3=

24__5times3__

21=2times3_____

5times1=6__

5

17 103divide(-103)=-103____1 times 1____

103

=-103times1________1times103

=-103____103

=-103____103

=-01

18 -04_____80

=-04___80

=-0005

19 1divide9__5=1__

1times5__

9=5__

9

20 -1___4 ___

23___24

=-1__

14times246

___23


=-6___23

21 -1035_______-23 =1035_____

23 =45


= 21h______7days

=3 h____day


times3days=9hours




=-4times15+3___________4 times1__

9

yd___run

=-763___4 times1__

91yd

___run

=-153__

4yd______

9runs

=-153__4times1__

9

yd___run

=-7__4or-13__

4yardsperrun





_____________________________________ 4

= 414degC ______ 4

= -1035degC per day

25 a total profit


= $1750

______ 7 days

= $250 per day

b $150

_____ day


c total change


= - $490

______ 7 days

= -$70 per day


= 996 m ______ 12 s

= 83 ms





- 3 __

4 ___

4 __ 3

= - 3 __

4 times 3 __

4 = - 9 ___

16



= -629 m





-85degF divide 15 d

= - 1785 ____ 315

degF __ d

= - 17 ___ 3 degF __

d or -5 2 __

3 degF __


d


every day





definition

LESSON 36

Your Turn


3 times 2 1 __ 2 = 7 1 __

2


30 - 7 1 __ 2 = 22 1 __

2


22 1 __ 2 divide 4 = 5 5 __

8











12 3 __ 5 = 126

= 0126


750 times 0126 = 945

750 + 945 = 8445


8445 times 0126 asymp 10641

8445 + 10641 = 95091


95091 times 0126 asymp 11981

95091 + 11981 = 107072


Guided Practice











78 times 3 = 234


234 divide 4 = 585




12 - 3 1 __ 2 = 8 1 __

2

Find half the width

8 1 __ 2 divide 2 = 4 1 __

4


of the page


11 times 1 __ 3 = 3 2 __

3

10 times 3 __ 4 = 7 1 __

2

3 2 __ 3 + 7 1 __

2 = 11 1 __

6


box

11 1 __ 6 lt 12





41 3 __ 4 divide 2 = 20 7 __

8


50 - 20 7 __ 8 = 29 1 __

8




( 78 + 10 ) = 88


88 = 88 ____ 100

= 44 ___ 50


Donovan

44 - 39 = 5


Donovan







19 ___ 37


15 times ( - 1 __ 2 ) = -075







-79 9 ___ 10

divide ( -188 ) = 425


19 1 __ 8 - 1275 - 425 = 2 1 __

8


-28 9 ___ 10

- ( -79 9 ___ 10

) = 51


51 divide 2 1 __ 8 = 24


ascent was 24 ftmin

15 Sample answer



the result by 037



(276 + 159)037 = (276)(037) + (159)(037)




make errors








MODULE 3

Ready to Go On

1 4 1 __ 5 =

5 times 4 + 1 _________

5 = 21 ___

5

42

5 ⟌ _

210

_ -20

1 0

_ -1 0

0

42


2 12 14 ___ 15

= 15 times 12 + 14

___________ 15

= 194 ____ 15

129 _ 3

15 ⟌ _

194000

_ -15

44

_ -30

14 0

_ -13 5

50 first 50

_ -45

50 second 50



129 _ 3 or 12933

3 5 5 ___ 32

= 32 times 5 + 5

__________ 32

= 165 ____ 32

515625

32 ⟌ _

16500000

_ -160

5 0

_ -3 2

1 80

_ -1 60

200

_ -192

80

_ -64

160

_ -160

0

515625

4 45 + 71 = 116

5 5 1 __ 6 + ( -3 5 __

6 ) = 4

6+1 ____

6 -3 5 __

6

= 1 2 __ 6

= 1 1 __ 3

6 - 1 __ 8 -6 7 __

8 = - 1 __

8 + ( -6 7 __

8 )

= -6 8 __ 8

= -7

7 142 - ( -49 ) = 142 + 49

= 191

8 -4 ( 7 ___ 10

) = - 4 __ 1 times 7 ___

10

= - 24 times 7 _______ 1 times 105

= - 2 times 7 _____ 1 times 5

= - 14 ___ 5 or -2 4 __

5

9 -32 ( -56 ) ( 4 ) = 32 times 56 times 4

= 7168

10 - 19 ___ 2 divide 38 ___

7 = -

119 times 7 _______ 2 times 382

= - 1 times 7 _____ 2 times 2

= - 7 __ 4

11 -3201 _______ -33

= 3201 _____ 33

97

33 ⟌ _

3201

_ -297

23 1

_ -23 1

0

97


second day

$8360 + $1535 = $9895


-4 3 __ 4 = -475 or -00475




price

$9895 times -00475 asymp -$47

$9895 - $47 = $9425






prices



Are You Ready

1 3 __ 4 divide 4 __

5 = 3 __

4 times 5 __

4

= 15 ___ 16

2 5 __ 9 divide 10 ___

11 = 5 __

9 times 11 ___

10

= 1

5 __ 9 times 11 ___

10 2

= 11 ___ 18

3 3 __ 8 divide 1 __

2 = 3 __

8 times 2 __

1

= 4

3 __ 8 times 2 __

1 1

= 3 __ 4

4 16 ___ 21

divide 8 __ 9 = 16 ___

21 times 9 __

8

=thinsp 2

7 16 ___ 21

times 9 __ 8 3

1

= 6 __ 7

5 B ( -4 1 )

6 C ( 3 0 )

7 D ( 5 4 )

8 E ( -2 -2 )

9 F ( 0 0 )

10 G ( 0 -4 )

LESSON 41

Your Turn

3 1 __ 6 acre divide ( 1 __

4 hour ) = 1 __

6 times 4 __

1

= 3


2

= 1 times 2 _____ 3 times 1


4 3 cups divide ( 3 __ 4 cups ) = 3 __

1 divide 3 __

4

= 3 __ 1 times 4 __

3

= 1


1

= 1 times 4 _____ 1 times 1

= 4 cups


5 = 3 __

4 times 5 __

1 = 15 ___

4 = 3 3 __

4


6 = 2 ___

1 3 times 6

2 __

1 = 4 __

1 = 4






flavor

Guided Practice

1

Distance (mi) 8 1 __ 2 17 25 1 __

2 34 42 1 __

2

Time (h) 1 __ 2 1 1 1 __

2 2 2 1 __

2

2 3 1 __ 2 miles divide ( 1 1 __

4 hours ) = 7 __

2 divide 5 __

4 mi ___ h

= 7 times 4 _____ 2 times 5

= 1 7 times 4 _____ 2 times 5

2

= 7 times 2 _____ 1 times 5

= 14 ___ 5 mi ___

h


3 5 __ 8 page divide ( 2 __

3 minute ) = 5 __

8 times 3 __

2

= 15 ___ 16

page per minute

4 1 __ 6 foot divide ( 1 __

3 hour ) = 1 __

6 times 3 __

1

= 2 1 times 3 _____ 6 times 1

1

= 1 times 1 _____ 2 times 1


5 5 __ 8 sq ft divide ( 1 __

4 hour ) = 5 __

8 times 4 __

1

= 2 5 times 4 _____ 8 times 1

1

= 5 times 1 _____ 2 times 1

= 5 __ 2 or 2 1 __



UNIT

2



1 divide 1 __

3

= 240 ____ 1 times 3 __

1

= 720 ____ 1



1 divide 1 __

2

= 325 ____ 1 times 2 __

1

= 650 ____ 1




1 __ 4 cup divide ( 2 __

3 serving ) = 1 __

4 times 3 __

2

= 3 __ 8

cup _______

serving


1 __ 3 cup divide ( 3 __

4 serving ) = 1 __

3 times 4 __

3

= 4 __ 9

cup _______

serving




72 and 4 __

9 = 32 ___

72




the rate


1 __ 2 hour

= 1 __




$10 divide ( 35 hours ) = 10 ___ 35

$ __



$125 divide ( 1 __ 2 hours ) = 125 ____

05 $ __





multiply by 60


= 005 ____ 1

$ ____


1 h

= $3 per hour



one


8 cup






originally

c 1 __ 2 divide 1 __

8 = 1 ___

1 2 times 8

4 __

1 = 4 __

1 = 4


sunflower seeds

11 10 songs


= 5 songs ____________

1 commercials


6 mi divide ( 1 __ 2 h ) = 6 __

1 times 2 __

1

= 12 miles per hour

Jessersquos rate


4

= 2 __ 1 times 4 __

1 mi ___ h

= 8 miles per hour

b Terrance

50 mi divide ( 12 mi ___ h ) = 50 ___

1 times 1 ___

12

= 50 ___ 12

h

= 4 1 __ 6 h

= 4 10 ___ 60

h


Jesse

50 mi divide ( 8 mi ___ h ) = 50 ___

1 times 1 __

8

= 50 ___ 8 h

= 6 1 __ 4 h

= 6 15 ___ 60

h



4

= 8 __ 1 times 4 __

3

= 32 ___ 3





13 1 ___ 10

h = 6 ___ 60

h = 6 min

300 words _________ 6 min

= 50 words per min

1 ___ 12

h = 5 ___ 60

h = 5 min

300 words _________ 5 min

= 60 words per min










b For the 10-pack



For the 12-pack








2 day ) = 1 room _____

day so at the same





LESSON 42

Your Turn


was not constant




= 12 ___ 1 = 36 ___

3 = 60 ___




s or s = 12a

Guided Practice

1 45 ___ 1 = 45 90 ___

2 = 45 135 ____

3 = 45 180 ____

4 = 45


2 k = y __ x = 10 ___

2 = 5 y = 5x

3 k = y __ x = 2 __

8 = 1 __

4 y = 1 __

4 x


of proportionality


5 k = y __ x = 74 ___

4 = 1850 y = 1850x

6 $1099

_______ 05 days

= $2198 per day


($1850)

8 100 ft _____ 08 s

= 1000 _____ 8 ft __ s = 125 ft __ s

500 ft _____ 31 s

= 5000 _____ 31


1875 ft ______ 15 s

= 1875 ______ 15





9 $3125

______ 5 h


______ 8 h

= $625 per







12 y = $625 ( 3 ) = $1875

13 300 ft _____ 2 min

= 6750

_____ 45


150 ft _____ min

times 60 min ______ 1 h


14 y = 150x



hours




same factor




of corn

LESSON 43

Your Turn

1 No because 11 ___ 1 ne 16 ___





b k = 60 mi _____ 4 h

= 15 mi ___ h


distance in miles

Guided Practice

1

Time (h) 3 5 9 10

Pages 195 325 585 650


per hour

2

Time (h) 2 3 5 8

Earnings 15 2250 3750 60








5 k = 28 ft ____ 8 s

= 7 __ 2 ft __ s = 35 ft __ s y = 7 __



6 k = $2 ______

8 items = 1 __

4

$ _____

items = 025

$ _____

items so y = 1 __

4 x or


y = cost in dollars


origin



0 minutes





x or 2 __ 5 x




5 = 48




2

2

4

6

8

10

4 6 8 10Time (min)

Dis

tanc

e (m

i)

A

B

O








equation

15 a

2

8

16

24

32

40

4 6 8 10DVDs

Cost

($)

O



cost $20






18 k = 8 ft ___ 4 s










because 65 ___ 1 ne 85 ___

2





distance column

MODULE 4

Ready to Go On

1 $140

_____ 18 ft 2


2 $299

_____ 14 lb


3 $56 ______


$3205

______ 15 gal


4 $160

_____ 5 g


$315

_____ 9 g




3


6 k = $9

___ 8euro

= $27 ____

24euro = 9 __

8 $ __

euro or 1125

$ __

euro So y = 9 __

8 x or





_______ pt

or k = 25 servings

_______ pt

Therefore

y = 5 __ 2




2

2

4

6

8

10

4 6 8 10Pints

Serv

ings

Frozen Yogurt

O





constant rate



Are You Ready

1 22 = 22 ____ 100

= 022

2 75 = 75 ____ 100

= 075

3 6 = 6 ____ 100

= 006

4 189 = 100 + 89

= 100 ____ 100

+ 89 ____ 100

= 1 + 089

= 189

5 059 = 59

6 098 = 98

7 002 = 2

8 133 = 133

9 64

_ timesthinsp05

320

32

10 30

_ timesthinsp007

210

21

11 160

_ timesthinsp015

800

_ +1600

2400

24

12 62

_ timesthinsp032

124

_ +thinsp1860

1984

1984

13 4

_ timesthinsp12

8

_ +thinsp40

48

48

14 1000

_ timesthinsp006

6000

60

LESSON 51

Your Turn

2 x = ( $64 - 52 )

__________ $52

x = $12

____ $52

asymp 23

4 x = ( 18 - 12 )

________ 18

x = 6 ___ 18

asymp 33

5 x = ( 16 - 10 )

________ 16

x = 6 ___ 16

= 375

8 010 times $499 = $4990

$499 + $4990 = $54890

9 030 times $499 = $14970

$499 - $14970 = $34930

Guided Practice

1 x = ( $8 - $5 )

_________ $5

x = $3

___ $5

= 60

2 x = ( 30 - 20 )

_________ 20

x = 10 ___ 20

= 50

3 x = ( 150 - 86 )

__________ 86

x = 64 ___ 86

asymp 74

4 x = ( $389 - $349 )

______________ $349

x = $040

_____ $349

asymp 11

5 x = ( 14 - 13 )

________ 13

x = 1 ___ 13

asymp 8

6 x = ( 16 - 5 )

________ 5

x = 11 ___ 5 = 220

7 x = ( 64 - 36 )

_________ 36

x = 28 ___ 36

asymp 78

8 x = ( 80 - 64 )

_________ 80

x = 16 ___ 80

= 20

9 x = ( 95 - 68 )

_________ 95

x = 27 ___ 95

asymp 28


10 x=( 90-45)_________

90

x=45___90

=50

11 x=( 145-132)__________

145

x=13____145

asymp9

12 x=( 64-21)_________

64

x=43___64

asymp67

13 x=( 16-0)________

16

x=16___16

=100

14 x=( 3-1__

2)_______

3

x=21__

2___

3 asymp83

15 010times$900=$090 $900+$090=$990

16 025times48=12 48-12=36cookies

17 020times340=68 $340-68=272pages

18 050times28=14 28+14=42members

19 004times$29000=$1160 $29000-$1160=$27840

20 130times810=1053 810+1053=1863songs

21 030times20=6 20+6=26miles



ItemOriginal

PriceNew Price

Percent Change

Increase or





24 a 55

x=( 8-3)_______

8 =5__

8=625

x=( 12-7)________

12 =5___

12asymp417



x=( 12-3)________

3

x=9__3=300increase



b $100_____5 =$020each$100_____

4 =$025each



=25

26 Percenterror=( 136-133)___________

136 times100

=03____136

times100asymp2







LESSON 52

Your Turn

2 a 1c+01c11c

b s=11times$28=$3080

3 a 200

b 1c+2c3c

5 a

1b - 024b

1b024b

b 1b-024b=076b

6 a 1p-005p095p

b 095p=$1425




Guided Practice

1 a 035s

b 1s + 035s 135s

c 135 times $3200 = $4320

d 035 times $3200 = $1120


Price

2 Hat $18 15 $270 $2070

3 Book $2250 42 $945 $3195

4 Shirt $3375 75 $2531 $5906

5 Shoes $7499 33 $2475 $9974

6 Clock $4860 100 $4860 $9720

7 Painting $18500 125 $23125 $41625

8 $4500 - 022 ( $4500 ) = $3510

9 $8900 - 033 ( $8900 ) = $5963

10 $2399 - 044 ( $2399 ) = $1343

11 $27999 - 075 ( $27999 ) = $7000





13 a 046b

b 1b - 046b 054b

c 054 times $2900 = $1566

d 046 times $2900 = $1334


Sale Price $201

Regular Price $419

Sale Price $245

Regular Price $279

Sale Price $115

Regular Price $309

Sale Price $272

Regular Price $377

Sale Price $224


$050


$9950


$350

16 p = 127 ( $7400 ) = $9398

s = 127 ( $4800 ) = $6096

j = 127 ( $32500 ) = $41275

2 ( 9398 ) + 3 ( $6096 ) + $41275 = $78359









greater




the coat

LESSON 53

Your Turn

1 005 times $2000 = $100 $100 + $2000 = $2100

3 005 times $40000 = $2000

$2000 times 4 years = $8000

$40000 + $8000 = $48000


Total $2200 + $16875 = $236875

Guided Practice

1 005 times $3000 = $150

2 015 times $7000 = $1050

3 0004 times $10000 = $040

4 15 times $2200 = $3300

5 001 times $8000 = $080

6 20 times $500 = $1000

7 a 007 times $4399 = $308

b $4399 + $308 = $4707

8 115 times $7550 = $8683

9 007 times $2000 = $140


10 003 times $550 = $1650

$1650 times 10 years = $165

$550 + $165 = $715

11 a 090 times $20 = $18

b 1085 times $18 = $1953

12 020 times $2999 = $600 tip

00625 times $2999 = $187 tax

$2999 + $600 + $187 = $3786 total



to the price


14 $3275 + $3988 = $7263 total meal cost

014 times $7263 = $1017 tip

$7263 + $1017 = $8280 total with tip


$7865 times 020 = $1573 tip

$7865 + $1573 - $1180 = $8258 total


0075 times $29375 = $2203 tax

$29375 + $2203 = $31578 total with tax


17 $7999 times 012 = $960 discount

$7999 - $960 = $7039 price before tax





19 $4500 + 00725 = $32625 commission

$750 + $32625 = $107625 total income


$475 + $3850 = $51350 total income










nearest inch

22 a $4998 times 05 = $2499 50 discount

$2499 - $1000 = $1499 $10 discount

b $4998 - $1000 = $3998 $10 discount

$3998 times 05 = $1999 50 discount


$8550 + $1599 = $10149 total


$95 + $1439 = $10939 total



d $10149 times 008 = $812 tax

$10149 + $812 = $10961 total

24 a Store 1 $22 divide 2 = $11

Store 2 $1299 times 09 = $1169




b Store 3 $2098 times 045 = $944






to $2050 per month


____________ 137

times 100 = 05 ____ 137

asymp 36

MODULE 5

Ready to Go On

1 x = ( 63 - 36 )

_________ 36

x = 27 ___ 36

= 75 increase

2 x = ( 50 - 35 )

_________ 50

x = 15 ___ 50

= 30 decrease

3 x = ( 72 - 40 )

_________ 40

x = 32 ___ 40

= 80 increase

4 x = ( 92 - 69 )

_________ 92

x = 23 ___ 92

= 25 decrease

5 $60 times 015 = $9

$60 + $9 = $69

6 $32 times 0125 = $4

$32 + $4 = $36

7 $50 times 022 = $11

$50 - $11 = $39

8 $125 times 030 = $3750

$12500 - $3750 = $8750


$325 + $312 = $637 total income

10 $5310

______ $1735

asymp 31



$700 times 020 = $140

$700 + $140 = $840


5 less than Priya

$840 times 005 = $042

$840 - $042 = $798





$45 times 026 = $1170

$45 + $1170 = $5670






Are You Ready

1 5 + x

2 11 - n

3 -9 ___ y

4 2x - 13

5 2x + 3

= 2 ( 3 ) + 3

= 6 + 3

= 9

6 -4x + 7

= -4 ( 1 ) + 7

= -4 + 7

= 11

7 15x - 25

= 15 ( 3 ) - 25

= 45 - 25

= 2

8 04x + 61

= 04 ( -5 ) + 61

= -20 + 61

= 41

9 2 __ 3 x - 12

= 2 __ 3

( 18 ) - 12

= 2 __ 3

times ( 18 ___ 1 ) - 12

= 36 ___ 3 - 12

= 0

10 - 5 __ 8

x + 10

= - 5 __ 8 ( -8 ) + 10

= - 5 __ 8 times- 8 __

1 + 10

= - 5 ___ 1 8

times- 8 1 __

1 + 10

= - 5 __ 1 times- 1 __

1 + 10

= 5 + 10

= 15

11 1 __ 2 divide 1 __

4

= 1 times 4 _____ 2 times 1

= 1 times 4 2 ______

1 2 times 1

= 1 times 2 _____ 1 times 1

= 2

12 3 __ 8 divide 13 ___

16

= 3 __ 8 times 16 ___

13

= 3 times 16 2 _______

1 8 times 13

= 3 times 2 ______ 1 times 13

= 6 ___ 13

13 2 __ 5 divide 14 ___

15

= 2 __ 5 times 15 ___

14

= 1 2 times 15

3 ________

1 5 times 14 7

= 1 times 3 _____ 1 times 7

= 3 __ 7

14 4 __ 9 divide 16 ___

27

= 4 __ 9 times 27 ___

16

= 1 4 times 27

3 ________

1 9 times 16 4

= 1 times 3 _____ 1 times 4

= 3 __ 4

LESSON 61

Your Turn

2 ( 3x + 1 __ 2 ) + ( 7x - 4 1 __

2 )

= 3x + 7x + 1 __ 2 - 4 1 __

2

= 10x - 4

3 ( -025x - 3 ) - ( 15x + 14 ) = -025x - 3 - 15x - 14

= -175x - 44

4 02(3b - 15c) + 6c

= 06b - 3c + 6c

= 06b + 3c

5 2 __ 3 (6e + 9f - 21g) - 7f

= 4e + 6f - 14g - 7f

= 4e - f - 14g

6 5x - 3(x - 2) - x

= 5x - 3x + 6 - x

= x + 6

7 83 + 34y - 05(12y - 7)

= 83 + 34y - 6y + 35

= 118 - 26y


UNIT

3


Guided Practice


14 + 12n + 23 + 16n

14 + 23 + 12n + 16n

37 + 28n


37 + 28n

2 37 + 28n

37 + 28 ( 9 )

= 37 + 252

= 289

3 14 + 5(x + 3) - 7x = 14 + 5x + 15 - 7x

= 29 - 2x

4 3 ( t - 4 ) - 8 ( 2 - 3t ) = 3t - 12 - 16 + 24t

= 27t - 28

5 63c - 2 ( 15c + 41 ) = 63c - 3c - 82

= 33c - 82

6 9 + 1 __ 2 ( 7n - 26 ) - 8n = 9 + 35n - 13 - 8n

= -4 - 4 1 __ 2 n

7 2x + 12

2 ( x + 6 )

8 12x + 24

12 ( x + 2 )

9 7x + 35

7 ( x + 5 )







15 ( 100 + 5d ) + 20 ( 50 + 7d ) = 15 ( 100 ) + 15 ( 5d ) + 20 ( 50 ) + 20 ( 7d )

= 1500 + 75d + 1000 + 140d

= 1500 + 1000 + 75d + 140d

= 2500 + 215d


New width 60 + w


2(96 + l) + 2(60 + w)

=2(96) + 2l + 2(60) + 2w

192 + 2l + 120 + 2w

192 + 120 + 2l + 2w

312 + 2l + 2w

13 Width 3


Factors 3 and x + 2

Product 3 ( x + 2 ) = 3x + 6

14 Width 4



Product 4 ( 2x - 1 ) = 8x - 4




and 6 times 4 ) So 6 ( 9 ) = 6 ( 5 ) + 6 ( 4 )


6x = ( x + 3 ) + ( 2x + 4 ) +

6x = 3x + 7 +

-3x = _ -3x

3x = 7 +

_ -7 = _ -7

3x - 7 =



10x + 6 = 2 ( 3x - 3 ) + 2 ( )

10x + 6 = 6x - 6 + 2

_ -6x = _ -6x

4x + 6 = - 6 + 2

_ + 6 = _ + 6

4x + 12 = 2

( 4x + 12 ) divide 2 = ( 2 ) divide 2

2x + 6 =


18 a P = 2l + 2w


2(2x + 6) + 2(x)

= 4x + 12 + 2x

= 6x + 12


2(3x - 14) + 2( 1 __ 2 x + 32)

= 6x - 28 + x + 64

= 7x + 36

b (7x + 36) - (6x + 12)

= 7x + 36 - 6x - 12

= x + 24


Let x = 36

2x + 6 = 2 ( 36 ) + 6

= 72 + 6

= 78


Let x = 36

1 __ 2 x + 32 = 1 __

2 ( 36 ) + 32

= 18 + 32

= 50


Let x = 36

3x - 14 = 3 ( 36 ) - 14

= 108 - 14

= 94





( x ) ( x ) = x 2

( x ) 1 = x

( 1 ) 1 = 1


x

x

1

11

1 1

x2 x x x

x 1 1 1x 1 1 1

Area =

x 2 + x + x + x + x + x + 1 + 1 + 1 + 1 + 1 + 1

= x 2 + 5x + 6

( x + 3 ) ( x + 2 ) = x 2 + 5x + 6




1160 = 1334 So 58 ( 23 ) = 58 ( 3 ) + 58 ( 20 )


8 ( 1000 - 3 ) = 8000 - 24 = 7976


Property 8 ( 900 + 90 + 7 ) = 7200 + 720 + 56 =

7976

LESSON 62

Your Turn

1 49 + z = -9

_ -49 _ -49

z = -139

2 r - 171 = -48

_ +171 _ +171

r = 123

3 -3c = 36

-3c ____ -3

= 36 ___ -3

c = -12

5 x - 15 = 525

_ +15 _ +15

x = 675


6 x ___ 35

= -12

x ___ 35

( 35 ) = -12 ( 35 )

x = -42


7 25x = 75

25x ____ 25

= 75 ___ 25

x = 3


Guided Practice



x + ( -134 ) = -17 or x - 134 = -17

x - 134 = -17

_ +134 _ +134

x = 117


warmer



-1 1 __ 2 x = -9

( - 2 __ 3 ) ( - 3 __

2 x ) = ( - 2 __

3 ) ( -9 )

x = 18 ___ 3

x = 6


3 -2x = 34

-2x ____ -2

= 34 ___ -2

x = -17

4 y - 35 = -21

_ + 35 _ + 35

y = 14

y = 14

5 2 __ 3 z = -6

( 3 __ 2 ) 2z ___

3 = ( 3 __

2 ) ( -6 )

z = -9





x - 870737 = 203215

_ +870737 _ +870 737

x = 2902887



2825131 - x = 2320106

_ -2825131 _ -2825131

-x = - 505025

x = 505025




2825131 - x = 1119421

_ -2825131 _ -2825131

-x = -1705710

x = 1705710



1250 - 935 = 315

Use an equation


descends

( -22 1 __ 2 ) x = -315

( - 45 ___ 2 ) x = -315

( - 2 ___ 45

) ( - 45 ___ 2 ) x = -315 ( - 2 ___

45 )

x = 14



4106 - 3205 = 901




34x = 901

34x ____ 34

= 901 ____ 34

x = 265 = 26 1 __ 2




- 25 + x = -07

_ + 25 _ + 25

x = 18





181 - x = -07

_ - 181 _ -181

-x = -188

x = 188





125 + x = 181

_ -125 _ -125

x = 56



their next play

-26 1 __ 3

+ x = 10

+26 1 __ 3

______

+26 1 __ 3

______

x = 36 1 __ 3



( -2 1 __ 2 ) x = -156

( -25 ) x = -156

( -25 _____ -25

) x = -156 ______ -25

x = 624



rate and the time


x __ 5 = 455

( 5 ) x __ 5 = 455 ( 5 )

x = 2275


Sample answer


to $22750



below sea level



lower elevation

20 -4x = -48

( -4x ____ -4

) = -48 _____ -4

x = 12

- 1 __ 4 x = -48

( -4 ) ( - 1 __ 4 ) x = -48 ( -4 )

x = 192

192 ____ 12

= 16








$21085

LESSON 63

Your Turn


purchased






Equation 150 - 35x = 45





Guided Practice

1

+ + ++ ++

+++ + +

+++

2

----

+ ++ ++

- - -

























place 28 +1-tiles


bicycle





Equation 85d + 55 = 123






Equation 125r + 675 = 3175








Equation 45n + 60 = 285




means + 45





1 _ 2

bull n + 45 = 172

Equation 1 __ 2 n + 45 = 172





uniforms equipment


Equation 295u + 548 = 2023





weeks


Equation 500 - 20x = 220






Total bill $88


shirts bill















10 + 5c = 25

10 - 10 + 5c = 25 - 10

5c = 15

5c ___ 5 = 15 ___

5

c = 3

3 children



10 + 5 ( 5 ) = $35














bought

LESSON 64

Your Turn


+ ++ +

+ ++ ++ +

+ ++ ++ +

++


+ ++ +

+ ++ ++ +

+ ++ ++ +

++


++

+ ++ +

++


++ ++


+ + ++ + ++ +

+++

+++

__



+ + ++ + ++

++ +

+++

+++

__


+ + ++++ + +++


+ + +++


++++

______

______

____



++++

+

++

+

++

______

______

____


++++

____


++ __



____

________

++



________

________

++

____


________

________

We get -y = -1

____


tile to each side

++

__ ++ __


++++

__


+++

6 3n + 10 = 37


3n + 10 = 37

-10 ____

-10 ____

3n = 27

3n ___ 3 = 27 ___

3

n = 9


7 n __ 4 - 5 = 15


n __ 4 - 5 = 15

+5 ___

+5 ___

n __ 4 = 20

n __ 4 ( 4 ) = 20 ( 4 )

n = 80

The number is 80

8 -20 = 5 __ 9 ( x - 32 )


-20 = 5 __ 9 ( x - 32 )

-20 = 5 __ 9 x - 160 ____

9

+ 160 ____ 9

______

+ 160 ____ 9

______

- 20 ___ 9 = 5 __

9 x

- 20 ___ 9 divide ( 5 __

9 ) = 5 __

9 x divide ( 5 __

9 )

4 20 times 9

1 _______

9 1 times 5

1 = x

- 4 __ 1 = x

-4 = x


9 120 - 4x = 92


120 - 4x = 92

-120 _____

-120 _____

- 4x = -28

-4x ____ -4

= -28 ____ -4

x = 7



Guided Practice





++++

+ +++++++++


++++

++++++++


++ + + + +




Solve the equation

2 ( 18 ) + 2w = 58

36 + 2w = 58

36 - 36 + 2w = 58 - 36

2w = 22

2w ___ 2 = 22 ___

2

w = 11


4 1200 minus 25x = 500


1200 - 25x = 500

_ -1200 _ -1200

-25x = -700

-25x _____ -25

= -700 _____ -25

x = 28






equation


6 9s + 3 = 57

9s + 3 - 3 = 57 - 3

9s = 54

9s ___ 9 = 54 ___

9

s = 6

7 4d + 6 = 42

4d + 6 - 6 = 42 - 6

4d = 36

4d ___ 4 = 36 ___

4

d = 9

8 115 - 3y = -485

115 - 115 - 3y = -485 - 115

thinsp-3y = -60

-3y

____ -3

= -60 ____ -3

y = 20

9 k __ 2 + 9 = 30

k __ 2 + 9 - 9 = 30 - 9

k __ 2 = 21

2 sdot k __ 2 = 2 sdot 21

k = 42

10 g

__ 3 - 7 = 15

g

__ 3 - 7 + 7 = 15 + 7

g

__ 3 = 22

3 sdot g

__ 3 = 3 sdot 22

g = 66

11 z __ 5 + 3 = -35

z __ 5 + 3 - 3 = -35 - 3

z __ 5 = -38

5 sdot z __ 5 = 5 ( -38 )

z = -190

12 -9h - 15 = 93

-9h - 15 + 15 = 93 + 15

-9h = 108

-9h ____ -9 = 108 ____

-9

h = -12

13 - 1 __ 3 (n + 15) = -2

- 1 __ 3 n - 5 = -2

- 1 __ 3 n - 5 + 5 = -2 + 5

- 1 __ 3 n = 3

-3 sdot - 1 __ 3 n = -3 sdot 3

n = -9

14 -17 + b __ 8 = 13

-17 + 17 + b __ 8 = 13 + 17

b __ 8 = 30

8 sdot b __ 8 = 8 sdot 30

b = 240


15 7 ( c - 12 ) = -21

7c - 84 = -21

_ +84 _ +84

7c = 63

7c ___ 7 = 63 ___

7

c = 9

16 -35 + p

__ 7 = -52

-35 + 35 + p

__ 7 = -52 + 35

p

__ 7 = -17

7 sdot p

__ 7 = -17 sdot 7

p = -119

17 46 = -6t - 8

46 + 8 = -6t - 8 + 8

54 = -6t

54 ___ -6

= -6t ____ -6

t = -9





2 (a + $26) = $264

Solve the equation

2 ( a + 26 ) = 264

2 ( a + 26 )

_________ 2 = 264 ____

2

a + 26 = 132

a + 26 - 26 = 132 - 26

a = 106






Solve the equation

2t - 6 = 20

2t - 6 + 6 = 20 + 6

2t = 26

2t __ 2 = 26 ___

2

t = 13


20 -35 = 5 __ 9 ( x - 32 )

-35 = 5 __ 9 x - 160 ____

9

+ 160 ____ 9

______

+ 160 ____ 9

- 155 ____ 9 = 5 __

9 x

thinsp- 155 ____ 9 divide ( 5 __

9 ) = 5 __

9 x divide ( 5 __

9 )

-thinsp 31

155 times 9

1

= x

9 1

times 5

1

- 31 ___ 1 = x

-31 = x




Solve the equation

-a + 40 = 28

-a + 40 - 40 = 28 - 40

-a = -12

-a ___ -1

= -12 ____ -1

a = 12






Solve the equation

2c + 11 = 73

2c + 11 - 11 = 73 - 11

2c = 62

2c ___ 2 = 62 ___

2

c = 31




price paid


1 __ 2

middot p -6 = 88

Solve the equation

1 __ 2 p - 6 = 88

1 __ 2 p - 6 + 6 = 88 + 6

1 __ 2 p = 94

2 sdot 1 __ 2 p = 2 sdot 94

p = 188



24 115 minus 8n = 19


115 - 8n = 19

_ -115 _ -115

-8n = -96

-8n _____ -8

= -96 _____ -8

n = 12


25 -55x + 056 = -164

-55x + 056 - 056 = -164 - 056

-55x = -22

-55x ______ -22

= -22 _____ -22

x = 04

26 -42x + 315 = -651

-42x + 315 - 315 = -651 - 315

-42x = -966

-42x ______ -42

= -966 ______ -42

x = 23

27 k ___ 52

+ 819 = 472

k ___ 52

+ 819 - 819 = 472 - 819

k ___ 52

= -347

52 sdot k ___ 52

= 52 ( -347 )

k = -18044




divide 2 by 3

3x + 2 = 15

3x ___ 3 + 2 __

3 = 15 ___

3

x + 2 __ 3 = 5

- 2 __ 3

___

- 2 __ 3

___

x = 5 - 2 __ 3

x = 5 times3

___ 1

times3 - 2 __

3

x = 15 ___ 3 - 2 __

3

x = 13 ___ 3 or 4 1 __

3


31 a 2(x + 40) = 234


2x + 80 = 234

2x + 80 - 80 = 234 - 80

2x = 154

2x ___ 2 = 154 ____

2

x = 77

Trey saved $77






32 F = 18c + 32

F - 32 = 18c + 32 - 32

F - 32 = 18c

F - 32 ______ 18

= 18c ____ 18

F - 32 ______ 18

= c

33 P = 2 ( ℓ + w ) P = 2ℓ + 2w

P - 2ℓ = 2ℓ - 2ℓ + 2w

P - 2ℓ = 2w

P - 2ℓ ______ 2 = 2w ___

2

P - 2ℓ ______ 2 = w

34 ax + b = c

ax + b - b = c - b

ax = c - b

ax ___ a = c - b ______ a

x = c - b ______ a

MODULE 6

Ready to Go On




15n + 60 + 12n + 95



2 h + 97 = -97

_ -97 _ -97

h = -194

3 - 3 __ 4 + p = 1 __

2

+ 3 __ 4 + 3 __

4

p = 1 __ 2 + 3 __

4

p = 1 times2

___ 2

times2 + 3 __

4

p = 2 __ 4 + 3 __

4

p = 5 __ 4

4 -15 = -02k

-15 _____ -02

= -02k ______ -02

75 = k


5 y ___

-3 = 1 __

6

y ___

-3 ( -3 ) = 1 __

6 ( -3 )

y = 1 __ 6 times -3 ___

1

y = -3 ___ 6

y = -1 ___ 2

6 - 2 __ 3

m = -12

- 2 __

3 m _____

- 2 __ 3 = -12 ____

- 2 __ 3

m = -12 divide - 2 __ 3

m = -12 ____ 1 divide - 2 __

3

m = -12 ____ 1 times - 3 __

2

m = -36 ____ -2

m = 18

7 24 = - t ___ 45

24 ( 45 ) = - t ___ 45

( 45 )

108 = -t

-108 = t







2 middot d + 15 = 33


9 5n + 8 = 43

5n + 8 - 8 = 43 - 8

5n = 35

5n ___ 5 = 35 ___

5

n = 7

10 y __

6 - 7 = 4

y __

6 - 7 + 7 = 4 + 7

y __

6 = 11

6 sdot y __

6 = 6 sdot 11

y = 66

11 8w - 15 = 57

8w - 15 + 15 = 57 + 15

8w = 72

8w ___ 8 = 72 ___

8

w = 9

12 g

__ 3 + 11 = 25

g

__ 3 + 11 - 11 = 25 - 11

g

__ 3 = 14

3 sdot g

__ 3 = 3 sdot 14

g = 42

13 f __ 5 - 22 = -25

f __ 5 - 22 + 22 = -25 + 22

f __ 5 = -03

5 sdot f __ 5 = 5 ( -03 )

f = -15

14 - 1 __ 4 (p + 16) = 2

- 1 __ 4 p - 4 = 2

- 1 __ 4 p - 4 + 4 = 2 + 4

- 1 __ 4 p = 6

-4 sdot - 1 __ 4 p = 6 sdot -4

p = -24




situation



Are You Ready

1 9w = -54

9w ___ 9 = -54 ____

9

w = -6

2 b - 12 = 3

thinsp _ + 12 = _ + 12

b = 15

3 n __ 4

= -11

4 times n __ 4

= 4 ( -11 )

n = -44

4-7


75 4 6

8 3 - (-5)

3 + 5

8

9 -4 - 5

-9

10 6 - 10

-4

11 -5 - (-3)

-5 + 3

-2

12 8 - (-8)

8 + 8

16

13 9 - 5

4

14 -3 - 9

-12

15 0 - (-6)

0 + 6

6

LESSON 71

Your Turn


_ +5 _ +5

y ge minus2

-4-5 -3 -2-1 0 1 2 3 4 5


minus1 ge -8


2 le 16

5 21 gt 12 + x

_ -12 _ minus12

9 gt x

x lt 9

10 2 3 4 5 6 7 8 9 10


21 gt 12 + 8

21 gt 12 + 8

21 gt 20

6 -10y lt 60

-10y

_____ -10

lt 60 ____ -10

y gt -6

-10-9 -8 -7 -6 -5 -4 -3 -2-1 0 1


-10y lt 60

-10(-5) lt 60

50 lt 60

7 7 ge - t __ 6

7(-6) le - t __ 6 (-6)

-42 le t

t ge -42

-46 -45 -44 -43 -42 -41 -40-47


7 ge - t __ 6

7 ge - ( -36 ____

6 )

7 ge 6



35m le 315

35m ____ 35

le 315 ____ 35

m le 9



Guided Practice

1 -5 le -2

_ +7 _ +7

2 le 5

2 -6 lt -3

-6 ___ -3

gt -3 ___ -3

2 gt 1

3 7 gt -4

_ -7 _ -7

0 gtthinsp -11


4 -1 ge -8

-1 ( -2 ) le -8 ( -2 )

2 le 16

5 n - 5 ge -2

_ +5 _ +5

n ge 3

-5 -4 -3 -2-1 0 3 4 51 2


n - 5 ge -2

4 - 5 ge -2

-1 ge -2

6 3 + x lt 7

_ -3 _ -3

x lt 4

-2-1 0 3 4 5 6 7 81 2


3 + x lt 7

3 + 3 lt 7

6 lt 7

7 -7y le 14

-7y

____ -7 ge 14 ___ -7

y ge -2

-5-6-7 -4 -3 -2-1 0 1 2 3


-7y le 14

-7 ( -1 ) le 14

7 le 14

8 b __ 5 gt -1

b __ 5 ( 5 ) gt -1 ( 5 )

b gt -5

-5-6-7-8 -4 -3 -2-1 0 1 2


b __ 5 gt -1

0 __ 5 gt

-1

0 gt -1

9 a -4t ge -80

b -4t ge -80

-4t ____ -4

le -80 ____ -4

t le 20








number


11 x - 35 gt 15

_ + 35 _ +35

x gt 50

100 20 30 40 50 60 70 80 90100


x - 35 gt 15

51 minus 35 gt 15

16 gt 15

12 193 + y ge 201

_ -193 _ minus193

y ge 8

10 2 3 4 5 6 7 8 9 10


193 + y ge 201

193 + 9 ge 201

202 ge 201

13 - q

__ 7 ge -1

- q

__ 7 ( -7 ) le -1 ( -7 )

q le 7

8 9 105 6 70 1 2 3 4


- q

__ 7 ge -1

- -14 ____ 7 ge

-1

2 ge -1

14 -12x lt 60

-12x _____ -12

gt 60 ____ -12

x gt -5

0-10-9 -8 -7 -6 -5 -4 -3 -2-1


-12x lt 60

-12 ( -4 ) lt 60

48 lt 60

15 5 gt z -3

_ +3 _ +3

8 gt z

z lt 8

10 2 3 4 5 6 7 8 9 10


5 gt z - 3

5 gt 7 - 3

5 gt 4


16 05 le y __

8

05 ( 8 ) le y __

8 ( 8 )

4 le y

y ge 4

8 9 105 6 70 1 2 3 4


05 le y __

8

05 le 8 __

8

05 le 1



12 + x le 28

_ -12 _ -12

x le 16




w __ 7 lt 35

w __ 7 ( 7 ) lt 35 ( 7 )

w lt 245





6s le 42

6s ___ 6 le 42 ___

6

s le 7




3025 + x ge 50

_ -3025 _ -3025

x ge 1975




155w ge 1705

155w ______ 155

ge 1705 _____ 155

w ge 11




thinsp-12t lt -120

-12t _____ -12

gt -120 _____ -12

t gt 10






3s le 10

3s ___ 3 le 10 ___

3

s le 3 1 __ 3


pounds



m ___ 05

le 55

m ___ 05

( 05 ) le 55 ( 05 )

m le 275




125x le 3

125x _____ 125

le 3 ____ 125

x le 24



buy 25 pounds







not true





prism

V = lwh



( 13 ) ( 1 __ 2 ) h lt 65

65h lt 65

65h ____ 65

lt 65 ___ 65

h lt 10





LESSON 72Your Turn


raise



Target amount $6000



must raise equal to




can go on

Starting amount $40

Admission price $6




equal to




are looking for




10 is added to 3x



than 30








looking for












Guided Practice

1

- -- -

-

lt

++++++

+ + ++ + +

+

2

---

gt

+ + ++ + +

+ + ++ + +

+ + +


raise








1250 + 92a ge 7000




greater than 32







inequality






3a + 28 gt 200




cheese to has


075n + 129 le 700












120 + 32n le 720




month month


2100 + 005s ge 2400






668 + 7n gt 2000


day



buys to a month


$7 + $10 middot c le $100

7 + 10c le 100






$22 + $17 middot n le $80

22 + 17n le 80














is given by

95 + 86 + 89 + 3s

________________ 6


tests



95 + 86 + 89 + 3s

________________ 6 ge 90 or

95 + 86 + 89 + 3s ge 540 or

270 + 3s ge 540












So -m gt 0

25 n gt 1 __ n if n gt 1


n = 1 __ n if n = 1

LESSON 73

Your Turn


++

++++

+++

++++

++++

+++

gt


++

++++

+++

++++

++++

+++

gt

- -- -- --

- -- -- --


++

++++

gt


++

++++

gt



+ + +gt


+++++

----

+++++

+ +++++

ge


+++++

----

+++++

+ ++

++++

+++

++++

ge


+++++

+++++

+ +++++

++++

ge


+++++

+++++

+ +++++

++++

ge


+ + + +ge


5 - p

__ 6 le 4

5 - 5 - p

__ 6 le 4 - 5

thinsp- p

__ 6 le -1

thinsp-6 ( - p

__ 6 ) ge -6 ( -1 )

p ge 6


arrow

0 1 4 5 72 3 6 8 9 10



3v - 8 gt 22

v = 9 v = 10 v = 11

3 ( 9 ) - 8 gt 22 3 ( 10 ) - 8 gt 22 3 ( 11 ) - 8 gt 22


results

3 ( 9 ) - 8 gt 22 3 ( 10 ) - 8 gt

22 3 ( 11 ) - 8 gt

22

27 - 8 gt 22 30 - 8 gt

22 33 - 8 gt

22

19 gt 22 22 gt

22 25 gt

22


v = 11


5h + 12 le -3

h = -3 h = -4 h = -5

5 ( -3 ) + 12 le -3 5 ( -4 ) + 12 le -3 5 ( -5 ) + 12 le -3


results

5 ( -3 ) + 12 le -3 5 ( -4 ) + 12 le

-3 5 ( -5 ) + 12 le

-3

-15 + 12 le -3 -20 + 12 le

-3 -25 + 12 le

-3

-3 le -3 -8 le

-3 -13 le

-3

true true true

h = -3 h = -4 h = -5


Guided Practice




5d - 13 lt 32

5d - 13 + 13 lt 32 + 13

5d lt 45

5d ___ 5 lt 45 ___

5

d lt 9


20 6 84 10 12 14 16 18 20


-4b + 9 le -7

-4b + 9 - 9 le -7 - 9

-4b le -16

-4b ____ -4

ge -16 ____ -4

b ge 4


20 6 84 10 12 14 16 18 20


2m + 18 gt - 4

m = -12 m = -11 m = -10

2 ( -12 ) + 18 gt -4 2 ( -11 ) + 18 gt -4 2 ( -10 ) + 18 gt -4


results

2 ( -12 ) + 18 gt -4 2 ( -11 ) + 18 gt

- 4 2 ( -10 ) + 18 gt

- 4

- 24 + 18 gt -4 - 22 + 18 gt

- 4 - 20 + 18 gt

- 4

- 6 gt - 4 - 4 gt

- 4 - 2 gt

- 4


m = -10


- 6y + 3 ge 0

y = 1 y = 1 __ 2 y = 0

-6 ( 1 ) + 3 ge 0 -6 ( 1 __ 2 ) + 3 ge 0 -6 ( 0 ) + 3 ge 0


results

-6 ( 1 ) + 3 ge 0 - 6 ( 1 __

2 ) + 3 ge

0 - 6 ( 0 ) + 3 ge

0

-6 + 3 ge 0 -3 + 3 ge

0 0 + 3 ge

0

-3 ge 0 0 ge

0 3 ge

0

not true true true

y = 1 __ 2

y = 0


65 - 4t ge 15

65 - 65 - 4t ge 15 - 65

-4t ge -5

-4t ____ -4

le -5 ___ -4

t le 125


0 05 1 15 2 25



time






8 2s + 5 ge 49

2s + 5 - 5 ge 49 - 5

2s ge 44

2s ___ 2 ge 44 ___

2

s ge 22

10 14 1612 18 20 22 24 26 28 30

9 -3t + 9 ge -21

-3t + 9 - 9 ge -21 -9

-3t ge -30

-3t ____ -3

le -30 ____ -3

t le 10


10 55 gt -7v + 6

55 - 6 gt -7v + 6 - 6

49 gt - 7v

49 ___ -7 lt -7v ____ -7

v gt -7

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0

11 21 1 __ 3 gt 3m - 2 2 __

3

21 1 __ 3 + 2 2 __

3 gt 3m - 2 2 __

3 + 2 2 __

3

24 gt 3m

24 ___ 3 gt 3m ___

3

8 gt m or m lt 8

0 1 4 5 72 3 6 8 9 10

12 a ___ -8

+ 15 gt 23

a ___ -8

+ 15 - 15 gt 23 - 15

a ___ -8

gt 8

-8 ( a ___ -8

) lt -8 ( 8 )

a lt -64

-70 -68 -66 -64 -62 -60


13 f __ 2 - 22 lt 48

f __ 2 - 22 + 22 lt 48 + 22

f __ 2 lt 70

2 ( f __ 2 ) lt 2 ( 70 )

f lt 140

100 110 120 130 140 150

14 -25 + t __ 2 ge 50

-25 + 25 + t __ 2 ge 50 + 25

t __ 2 ge 75

2 ( t __ 2 ) ge 2 ( 75 )

t ge 150

130 140 150 160 170 180

15 10 + g ___

-9 gt 12

10 - 10 + g ___

-9 gt 12 - 10

g ___

-9 gt 2

-9 ( g ___

-9 ) lt -9 ( 2 )

g lt -18

-20 -18 -14 -12 -10-16

16 252 le -15y + 12

252 - 12 le -15y + 12 - 12

24 le - 15y

24 ____ -15

ge -15y

_____ -15

y le -16

-20 -18 -14 -12 -10-16

17 -36 ge -03a + 12

-36 - 12 ge -03a + 12 - 12

-48 ge -03a

-48 _____ -03

le -03a ______ -03

a ge 16

10 11 12 13 14 16 17 18 19 2015

18 80 - 2w ge 50

80 - 80 - 2w ge 50 - 80

- 2w ge -30

-2w ____ -2

le -30 ____ -2

w le 15



11 12 13 14 and 15


7n - 25 ge 65

7n - 25 + 25 ge 65 + 25

7n ge 90

7n ___ 7 ge 90 ___

7

n ge 12 6 __ 7


be a whole number





21 a

10 3 42 5 6 7 8 9 10

b

10 3 42 5 6 7 8 9 10














MODULE 7

Ready to Go On

1 n + 7 lt -3

thinsp _ -7

_ -7

n lt -10

2 5p ge -30

5p

___ 5 ge -30 ____

5

p ge -6

3 14 lt k + 11

_ -11 _ -11

3 lt k

4 d ___ -3

le minus6

( -3 ) ( d ) ge ( -3 ) ( -6 )

d ge 18


5 c - 25 le 25

_ +25 _ +25

c le 5

6 12 ge -3b

12 ___ -3

le -3b _____ -3

-4 le b




562 + n ge 650

_ -562 _ -562

n ge 88


-20 - 20t ge -100

9 2s + 3 gt 15

_ -3 _ -3

2s gt 12

2s ___ 2

gt 12 ___ 2

s gt 6

10 - d ___ 12

- 6 lt 1

_ +6 _ +6

- d ___ 12

lt 7

12 ( - d ___ 12

) lt 12 ( 7 )

-d lt 84

d gt -84

11 -6w - 18 ge 36

_ +18 _ +18

thinsp-6w ge 54

-6w _____ -6

le 54 ___ -6

w le -9

12 z __ 4 + 22 le 38

_ -22 _ -22

z __ 4 le 16

4 ( z __ 4 ) le 4 ( 16 )

z le 64

13 b __ 9 - 34 lt -36

_ +34 _ +34

b __ 9 lt -2

9 ( b __ 9 ) lt 9 ( -2 )

b lt -18

14 -2p + 12 gt 8

-12 ____

-12 ____

-2p gt -4

-2p

____ -2 lt -4 ___

-2

p lt 2






Are You Ready

1 3x + 4 = 10

3x + 4 - 4 =10 - 4

3x = 6

3x ___ 3 = 6 __

3

x = 2

2 5x - 11 = 34

5x - 11 + 11 = 34 + 11

5x = 45

5x ___ 5 = 45 ___

5

x = 9

3 -2x + 5 = -9

-2x + 5 - 5 = -9 - 5

-2x = -14

-2x ____ -2

= -14 ____ -2

x = 7

4 -11 = 8x + 13

-11 - 13 = 8x + 13 - 13

-24 = 8x

-24 ____ 8 = 8x ___

8

-3 = x

5 4x - 7 = -27

4x - 7 + 7 = -27 + 7

4x = -20

4x ___ 4 = -20 ____

4

x = -5

6 1 __ 2 x + 16 = 39

1 __ 2 x + 16 - 16 = 39 - 16

1 __ 2 x = 23

( 2 ) 1 __ 2 x = ( 2 ) 23

x = 46

7 12 = 2x - 16

12 + 16 = 2x - 16 + 16

28 = 2x

28 ___ 2 = 2x ___

2

14 = x

8 5x - 15 = -65

5x - 15 + 15 = -65 + 15

5x = -50

5x ___ 5 = -50 ____

5

x = -10

9 x __ 5 = 18 ___

30


30x = 90

30x ____ 30

= 90 ___ 30

x = 3

10 x ___ 12

= 24 ___ 36


36x = 288

36x ____ 36

= 288 ____ 36

x = 8

11 3 __ 9 = x __

3


9 = 9x

9 __ 9 = 9x ___

9

1 = x

12 14 ___ 15

= x ___ 75


1050 = 15x

1050 _____ 15

= 15x ____ 15

70 = x

13 8 __ x = 14 ___ 7


56 = 14x

56 ___ 14

= 14x ____ 14

4 = x

14 14 ___ x = 2 __ 5


70 = 2x

70 ___ 2 = 2x ___

2

35 = x

15 5 __ 6 = x ___

15


75 = 6x

75 ___ 6 = 6x ___

6

125 = x


UNIT

4


16 81 ___ 33

= x ____ 55


4455 = 33x

4455 _____ 33

= 33x ____ 33

135 = x

LESSON 81

Your Turn


= 22 ft


= 10 ft


Guided Practice

1

Blueprint

length (in)3 6 9 12 15 18

Actual

length (ft)5 10 15 20 25 30



= 15 in







= 25 m


= 15 m


4 a


scales



the drawing


6 a 2 in times 40 cm ______ 1 in

= 80 cm

15 in times 40 cm ______ 1 in

= 60 cm


b 80 cm times 60 cm = 4800 c m 2

c 80 cm times 1 in _______ 254 cm

asymp 315 in

60 cm times 1 in _______ 254 cm

asymp 236 in


315 in by 236 in



= 24 units


= 15 units


15 units




larger



r = 810 m ______ 54 ft

r = 150 m ______ 1 ft



= 648 in



b = 162 bricks



h = 30 ft times 126 cm _______ 1 ft

h = 378 cm



_________ 63 cm

n = 6 toothpicks



asymp 5 swabs






s = 10 cm times 2 ft _____ 1 cm

s = 20 ft










original size


2

LESSON 82

Guided Practice















triangle






6 cm

3 cm120˚








same angle measures








between them






LESSON 83

Guided Practice


2 rectangle

3 triangle





















volume is 480 in 3





LESSON 84

Your Turn



intersecting lines




mangFGD and mangDGC



mangBGC and mangCGD



Because lines _

BE and _




mangCGD = 55deg



3x ___ 3 = 126deg ____

3

x = 42deg





Guided Practice




so mangDGE = 30deg





value by 3














measures are equal

mangKMI = mangHMG

84 = 4x

84 ___ 4 = 4x ___

4

x = 21deg



x + 84 - 84 = 180 - 84

x = 96

mangKMH = 96deg



x + 62 - 62 = 180 - 62

x = 118

mangCBE = 118deg



x + 62 - 62 = 90 - 62

x = 28

mangABF = 28deg




x + 28 - 28 = 152

mangCBA = 152deg




2x ___ 2 = 86deg ___

2





6x ___ 6 = 180deg ____

6









_ -48deg268 _ -48deg268

mangK = 41deg3352






greater than 38deg











( 90 - ( 90 - xdeg ) ) = ( 90 - 90 + xdeg ) = xdeg

MODULE 8

Ready to Go On

1

Living


Actual


Blueprint





created




A point is another




mangFGE = 50deg




3 ( mangY ) ________ 3 = 120deg ____

3

mangY = 40deg

mangY = 40deg


rooms or gardens



Are You Ready

1 416

_ times 13

1248

_ +thinsp4160

5408

5408

2 647

_ times thinsp04

2588

2588

3 705

_ times thinsp94

2820

_ +thinsp63450

66270

6627

4 256

_ timesthinsp049

2304

_ +thinsp10240

12544

12544

5 1 __ 2 ( 14 ) ( 10 )

7 ( 10 )

70 i n 2

6 ( 35 ) ( 35 )

1225 ft 2

7 ( 8 1 __ 2 ) ( 6 )

17 ___ 1 2 sdot 6 3 __

1

51 i n 2

8 1 __ 2 ( 125 ) ( 24 )

1 __ 2 ( 24 ) ( 125 )

( 12 ) ( 125 )

15 m 2

LESSON 91

Your Turn

3 d = 11 cm

C = πd

C asymp 314 ( 11 )

C asymp 3454


6 C = πd

44 asymp 314d

44 ____ 314

asymp d

d asymp 1401 yards


rate

1401 divide 7 = 2001


Guided Practice

1 d = 9 in

C asymp 314 ( 9 )

C asymp 2826 in

2 r = 7 cm

C = 2πr

C asymp 2 ( 22 ___ 7 ) ( 7 )

C asymp 44 cm

3 d = 25 m

C = πd

C asymp 314 ( 25 )

C asymp 785 m

4 r = 48 yd

C = 2πr

C asymp 2 ( 314 ) ( 48 )

C asymp 3014 yd

5 r = 75 in

C = 2πr

C asymp 2 ( 314 ) ( 75 )

C asymp 471 in

6 Find the diameter

C = πd

66 asymp 314d

66 ____ 314

asymp 314d _____ 314

21 asymp d

Find the cost


25 times $045 = $1125



r = 05 yd

d = 1 yd


2πr = 788

2πr ___ 2π

= 788 ____ 2π

r asymp 788 _______ 2 ( 314 )

r asymp 1255 ft

d = 2r asymp 2 ( 1255 ft )

d asymp 2510 ft

9 d = 2r so r = d __ 2 asymp 34 ___

2

r asymp 17 in

C = πd asymp 314 ( 34 )

C = 1068 in





11 d = 59 ft

C = πd

C asymp 314 ( 59 )

C asymp 1853 ft

12 r = 56 cm

C = 2πr

C asymp 2 ( 22 ___ 7 ) ( 56 )

C asymp 352 cm

13 d = 35 in

C = πd

C asymp ( 22 ___ 7 ) ( 35 )

C asymp 110 in



15 r = 94 ft

d = 2r = 2 ( 94 )

d = 188 ft

C = πd

C asymp 314 ( 188 )

C asymp 590 ft

16 d = 475 in

r = d __ 2 = 475 ____

2

r = 2375 in

C = πd

C asymp 314 ( 475 )

C asymp 14915 in

17 d = 18 in

r = d __ 2 = 18 ___

2

r = 9 in

C = πd

C asymp 314 ( 18 )

C asymp 5652 in

18 r = 15 ft

C = 2πr

C asymp 2 ( 314 ) ( 15 ) = 942 ft


so ( 942 ) ( 075 ) = 7065 or about $707

19 C = πd

C asymp ( 22 ___ 7 ) ( 63 )

C asymp 198 ft




20 C = πd asymp 314 ( 2 )

C asymp 628 ft

Converting km to ft

2 km sdot ( 3280 ft _______

1 km ) = 6560 ft

6560 ft

_______ 628 ft

= 104459




1 __ 2 C = 1 __

2 πd asymp 1 __

2 sdot 314 ( 025 ) = 03925





Height 180 ft



_______ 2 ( 314 )

asymp 48 ft

Diameter d = 2r = 2 ( 48 ) = 96 ft



plus the diameter

1 __ 2 C = 1 __

2 πd asymp 1 __

2 sdot 314 ( 30 ) = 471



per linear foot

( 771 ft ) ( $925 _____

ft ) = $71318



C = πd asymp 314 ( 18 ) = 5652 ft


inches to feet

( 54 in ) ( 1 ft _____ 12 in

) = 45 ft



5652 ft _______ 45 ft

= 1256


must buy 13 strands


C inner

= πd asymp 314 ( 150 ) = 471 ft


C outer

= πd asymp 314 ( 154 ) = 48356 ft








smaller gear





314 ( 75 ) - 314 ( 732 ) = 314 ( 018 ) asymp 057

057 m asymp 187 ft

LESSON 92

Your Turn

4 A = π r 2 A = π ( 10 ) 2

A asymp 314 ( 10 ) 2


A asymp 314 f t 2

Guided Practice

1 r = d __ 2 = 14 ___

2 = 7 m

A = π r 2 A = π ( 7 ) 2

A asymp 314 ( 7 ) 2

A asymp 314 sdot 49

A asymp 1539 m 2

2 A = π r 2 A = π ( 12 ) 2

A asymp 314 ( 12 ) 2


A asymp 4522 m m 2

3 r = d __ 2 = 20 ___

2 = 10 yd

A = π r 2 A = π ( 10 ) 2

A asymp 314 ( 10 ) 2


A asymp 314 y d 2

4 A = π r 2 A = π ( 8 ) 2

A asymp 314 ( 8 ) 2

A asymp 314 sdot 64

A asymp 20096 i n 2

5 r = d __ 2 = 12 ___

2 = 6 cm

A = π r 2 A = π ( 6 ) 2

A asymp 314 ( 6 ) 2

A asymp 314 sdot 36

A asymp 11304 c m 2

6 r = d __ 2 = 13 ___

2 = 65 in

A = π r 2 A = π ( 65 ) 2

A asymp 314 ( 65 ) 2


A asymp 13267 i n 2

7 C = 4π = 2πr

4π ___ 2π

= 2πr ___ 2π

r = 2

A = π r 2 A = π ( 2 ) 2


8 C = 12π = 2πr

12π ____ 2π

= 2πr ___ 2π

r = 6

A = π r 2 A = π ( 6 ) 2


9 C = π __ 2 = 2πr

π __ 2 divide 2π = 2πr ___

2π

π __ 2 sdot 1 ___

2π = r

1 __ 4 = r

A = π r 2

A = π ( 1 __ 4 ) 2 = π ( 1 ___

16 )

A = π ___ 16

square units

10 A = π r 2 = 64π

π r 2 ___ π = 64π ____ π

r 2 = 64

r = 8

C = 2πr

= 2π ( 8 )

=16π yd

11 A = π r 2


12 r = d __ 2 = 10 ___

2 = 5 in

A = π r 2 A = π ( 5 ) 2

A asymp 314 ( 5 ) 2

A asymp 314 sdot 25

A asymp 785 i n 2

13 A = π r 2 A = π ( 16 ) 2

A asymp 314 ( 16 ) 2


A asymp 80384 c m 2


diameter 36 in

r = d __ 2 = 36 ___

2 = 18 in

A semicircle

= 1 __ 2 π r 2

A semicircle

= 1 __ 2 π ( 18 ) 2

A semicircle

asymp 1 __ 2 ( 314 ) ( 18 ) 2

A semicircle


A asymp 50868 i n 2




A = π r 2 A = π ( 3 ) 2

A asymp 314 ( 3 ) 2



A r = 75 mi

- A r = 50 mi

π ( 75 ) 2 - π ( 50 ) 2



greater







s 2 minus π r 2 = 1 2 2 minus π ( 6 ) 2

= 144 minus π ( 36 )

asymp 144 minus 11304 = 3096










16π in 2





about $20

_____ π ( 9 ) 2



_____ π ( 6 ) 2

asymp $009






A = π r 2 = π ( 8 ) 2

= π ( 64 )

asymp 20096


201 mi 2




A new

minus A old

= π ( 10 ) 2 - π ( 8 ) 2

= π ( 1 0 2 - 8 2 ) = π ( 100 - 64 )

= π ( 36 ) asymp 11304


more area









A


A whole target

=

π ( 15 ) 2 ______

π ( 75 ) 2

= ( 15 ) 2

_____ ( 75 ) 2

= 225 _____ 5625

= 004


LESSON 93

Your Turn


two right triangles





A = ℓw = 11 sdot 4 = 44 f t 2


A = 1 __ 2 bh = 1 __



A = 1 __ 2 bh = 1 __

2 sdot 3 sdot 3 = 45 f t 2


44 + 3 + 45 = 515 f t 2


semicircle



or 10 ___ 2 = 5 m


A = s 2 = 1 0 2 = 100 m 2


A = 1 __ 2 π r 2

A asymp 1 __ 2 sdot 314 sdot ( 5 ) 2


A asymp 3925 m 2


100 + 3925 = 13925 m 2







4 __ 2 = 2 ft


A = ℓw = 5 sdot 4 = 20 f t 2


A = π r 2 A asymp 314 sdot ( 2 ) 2



two areas

20 + 1256 = 3256 f t 2



( 3256 f t 2 ) ( $28 ____

f t 2 ) = $91168


Guided Practice


a parallelogram



2 ( 4 ) ( 2 ) = 4




2 parallelogram

15 cm 2


4 + 15 + 15 = 34 cm 2


2 Method 1

A 1 = ℓw A

2 = ℓw

= 12 sdot 9 = 20 sdot 9 = 108 = 180


Method 2

A 1 = ℓw A

2 = ℓw

= 9 sdot 8 = 12 sdot 8 = 72 = 216






1 + b

2 )

A = 1 __ 2 ( 5 ) ( 7 + 4 )

A = 1 __ 2 ( 5 ) ( 11 ) = 275 f t 2



275 + 16 = 435 ft 2


find the cost

( 435 f t 2 ) ( $225 _____

f t 2 ) = $9788


simpler figures




A asymp 1 __ 2 sdot 314 sdot ( 13 ) 2


A asymp 26533 i n 2


676 + 26533 = 94133 in 2






A = 1 __ 2 sdot 6 sdot 7

A = 1 __ 2 sdot 42

A = 21 f t 2


40 + 21 = 61 f t 2


square foot

( 61 f t 2 ) ( $250 _____

f t 2 ) = $15250

7

O 42-2-4

2

-4

y

A (-2 4) B (0 4)

C (2 1)D (5 1)

E (5 -2)F (-2 -2)










Area of trapezoid

A = 1 __ 2 h ( b

1 + b

2 )

A = 1 __ 2 ( 3 ) ( 4 + 2 )

A = 1 __ 2 ( 3 ) ( 6 ) = 9 square units











A = 1 __ 2 sdot 8 sdot 8

A = 1 __ 2 sdot 64

A = 32 m 2


A asymp 1 __ 4 sdot 314 sdot ( 8 ) 2


A asymp 5024 f t 2


64 + 32 + 5024 = 14624 m 2









48 + 1256 = 6056 cm 2






A = 1 __ 2 sdot 1 sdot 1

A = 1 __ 2 sdot 1

A = 05 f t 2


3 + 05 = 35 ft 2





( 42 f t 2 ) ( $125 _____

f t 2 ) = $5250


area of triangle

325 ft 2 - 75 ft 2 = 25 ft 2



square is 5 ft






20 ( 15 ) or 300 carrots








triangle



A = 1 __ 2 sdot 12 sdot 8

A = 1 __ 2 sdot 96

A = 48 i n 2


144 + 48 = 192 in 2










420 - 176625 = 243375 in 2 or 243 3 __

8 i n 2










A asymp 1 __ 2 sdot 314 sdot ( 20 ) 2


A asymp 628 i n 2


1600 + 628 = 2228 in 2






40 + 2 sdot 4 = 48 in




total of 40 + 4 = 44 in






A asymp 1 __ 2 sdot 314 sdot ( 24 ) 2


A asymp 90432 i n 2


the sum

2112 + 90432 asymp 3016 in 2

LESSON 94

Your Turn


B = l times w

= 9 times 2

= 18 square inches


P = 2 ( 9 ) + 2 ( 2 )

= 18 + 4 = 22 inches


S = Ph + 2B

S = 22 ( 1 1 __ 2 ) + 2 ( 18 )

= 33 + 36

= 69



B = times w

= 12 times 12

= 144 square inches


P = 4 ( 12 )

= 48 inches


S = Ph + 2B

S = 48 ( 12 ) + 2 ( 144 )

= 576 + 288

= 864 square inches


B = l times w

= 8 times 8

= 64 square inches


P = 4 ( 8 )

= 32 inches


S = Ph + 2B

S = 32 ( 8 ) + 2 ( 64 )

= 256 + 128

= 384 square inches








Guided Practice



Height = 7 ft

Base area = 1 __ 2 ( 3 ) ( 8 ) = 12 ft 2

Surface area

S = ( 18 ft ) ( 7 ft ) + 2 ( 12 ft 2 ) = 150 ft 2


B = l times w

= 25 times 25

= 625 m 2


P = 4 ( 25 )

= 10 m


S = Ph + 2B

S = 10 ( 25 ) + 2 ( 625 )

= 25 + 125

= 375


S = 375 m 2


B = l times w

= 11 times 9

= 99 m 2


prism

P = 2 ( 11 ) + 2 ( 9 )

= 22 + 18

= 40 m


S = Ph + 2B

S = 40 ( 7 ) + 2 ( 99 )

= 280 + 198

= 478


S = 478 m 2


A = ( 25 ) ( 25 ) = 625



= 375 + 478 -2 ( 625 ) = 503 m 2




surface




B = l times w

= 10 times 3

= 30 in 2


P = 2 ( 10 ) + 2 ( 3 )

= 20 + 6

= 26 in


S = Ph + 2B

S = 26 ( 4 ) + 2 ( 30 )

=104 + 60

= 164 in 2



B = l times w

= 20 times 15

= 300 cm 2


P = 2 ( 20 ) + 2 ( 15 )

= 40 + 30

= 70 cm


S = Ph + 2B

S = 70 ( 9 ) + 2 ( 300 )

= 630 + 600

= 1230 cm 2


1230 - 300 = 930 cm 2



Convert cm 2 to mm

2


2 ________

1 cm 2 = 93000 mm

2


93000 divide 25 = 3720




= 2 + 3 = 5 in 2


Perimeter = 3 + 3 + 1 + 2 + 2 + 1

= 12 in


S = Ph + 2B

S = 12 ( 3 ) + 2 ( 5 )

= 36 + 10

= 46 in 2



Perimeter = 25 + 25 + 3 = 8 ft

Base area = 1 __ 2 ( 2 ) ( 3 ) = 3 ft 2


= 8 ( 4 ) + 2 ( 3 )

= 32 + 6 = 38 ft 2


Perimeter = 2 ( 3 ) + 2 ( 4 ) = 14 ft



= 14 ( 2 ) + 2 ( 12 )

= 28 + 24 = 52 ft 2



Surface area = 38 + 52 - 12 - 12 = 66 ft 2







1 + b

2 ) h

1 __ 2 ( 16 + 48 ) 12 = 384 in

2


P = 48 + 20 + 16 + 20 = 104 in


S = Ph + 2B

S = 104 ( 24 ) + 2 ( 384 )

= 2496 + 768

= 3264 in 2



B = l times w

= 7 times l

= 7 ft 2


P = 2 ( 7 ) + 2 ( 1 )

= 14 + 2

= 16 ft


S = Ph + 2B

S = 16 ( 2 ) + 2 ( 7 )

= 32 + 14

= 46 f t 2


B = l times w

= 1 times 1

= 1 ft 2


P = 2 ( 1 ) + 2 ( 1 )

= 2 + 2 = 4 ft


S = Ph + 2B

S = 4 ( 3 ) + 2 ( 1 )

= 12 + 2

= 14 ft 2



Surface area = 46 + 14 - 1 - 1 = 58 ft 2



58 divide 25 = 232


needed


3 times 679 = 2037




B = l times w

= 27 times 24

= 648 cm 2


P = 2 ( 27 ) + 2 ( 24 )

= 54 + 48

= 102 cm


S = Ph + 2B

S = 102 ( 10 ) + 2 ( 648 )

= 1020 + 1296

= 2316 cm 2






2 ( 2l + 2w ) = 2P


New S = 2Ph + 2 ( 4B )


doubles



B = l times w

= 25 times 25

= 625 ft 2


P = 4 ( 25 )

= 10 ft


S = Ph + 2B

S = 10 ( 35 ) + 2 ( 625 )

= 35 + 135

= 485 ft 2



485 - 625 = 4225 ft 2



4225 _____ 485

times 100 asymp 87




15


r = 2 in

9 in


A = πr 2

asymp 31 4 ( 2 ) 2 = 1256 in 2


C = πd

asymp 314 ( 4 ) = 1256 in 2




S = Ch + 2B

asymp 1256 ( 9 ) + 2 ( 1256 ) = 13816 in 2





1500 times 1382 = 207300 in 2



( 207300 in 2 ) 1 ft 2 _______

144 in 2 asymp 1440 ft 2






show

LESSON 95

Your Turn


B = 1 __ 2 bh

= 1 __ 2 ( 24 ) 7

= 84 m 2


V = Bh

= ( 84 ) ( 22 )

= 1848 m 3



B = 1 __ 2 ( b 1 + b 2 ) h

= 1 __ 2 ( 8 + 12 ) 10

= 1 __ 2 ( 20 ) 10 = 100 cm

2


V = Bh

= ( 100 ) ( 22 )

= 2200 cm 3




B = bh

= ( 13 ) 13

= 169 in 2


V = Bh

= ( 169 ) ( 30 )

= 5070 in 3



B = 1 __ 2 bh

= 1 __ 2 ( 9 ) 13

= 585 in 2


V = Bh

= ( 585 ) ( 30 )

= 1755 in 3


5070 + 1755 = 6825 in 3


Guided Practice

1 B = 1 __ 2 bh = 1 __

2 ( 8 ) ( 3 ) = 12 ft 2

V = Bh = ( 12 times 7 ) ft 3 = 84 ft 3

2 B = 1 __ 2 ( b 1 + b 2 ) h = 1 __

2 ( 15 + 5 ) 3 = 30 m

2

V = Bh = ( 30 times 11 ) m 3 = 330 m 3


B = bh

= ( 4 ) 6 = 24 ft 2


V = Bh

= ( 24 ) ( 12 ) = 288 ft 3



B = 1 __ 2 bh

= 1 __ 2 ( 6 ) 4 = 12 ft 2


V = Bh

= ( 12 ) ( 6 ) = 72 ft 3



288 + 72 = 360 ft 3



B = bh

= ( 40 ) ( 50 ) = 2000 ft 2


V = Bh

= ( 2000 ) ( 15 ) = 30000 ft 3


B = 1 __ 2 bh

= 1 __ 2 ( 40 ) ( 10 ) = 200 ft 2


V = Bh

= ( 200 ) ( 50 ) = 10000 ft 3


30000 + 10000 = 40000 ft 3



B = 1 __ 2 ( b 1 + b 2 ) h

= 1 __ 2 ( 10 + 12 ) 5

= 1 __ 2 ( 22 ) 5 = 55 cm

2


V = Bh

= ( 55 ) ( 7 ) = 385 cm 3







V = Bh

= ( 35 ) ( 5 ) = 175 in 3




B = 1 __ 2 bh

= 1 __ 2 ( 7 ) ( 6 ) = 21 in

2


V = Bh

= ( 75 ) ( 7 ) = 525 in 3



B = 1 __ 2 bh

= 1 __ 2 ( 8 ) ( 4 ) = 16 ft 2


V = Bh

= ( 16 ) ( 24 ) = 384 ft 3



B = 1 __ 2 ( b 1 + b 2 ) h

= 1 __ 2 ( 7 + 5 ) 4

= 1 __ 2 ( 12 ) 4 = 24 in

2


V = Bh

= ( 24 ) ( 8 ) = 192 in 3



V = Bh

= ( 20 ) ( 15 ) = 300 in 3


300 cubic inches


given B = 234 in 3


V = Bh

= ( 234 ) ( 3 ) = 702 in 3



B = bh

= ( 3 ) ( 3 ) = 9 in 2


V = Bh

= ( 9 ) ( 3 ) = 27 in 3


702 + 27 = 972 in 3



B = bh

= ( 75 ) 375 = 28125 m 2


V = Bh

= ( 28125 ) ( 75 ) asymp 21094 cm 3


prism


15 - 75 = 75


B = bh

= ( 75 ) 375 = 28125 m 2


V = Bh

= ( 28125 ) ( 375 ) asymp 10547 cm 3


21094 + 10547 = 31641 m 3




V = Bh

= ( 21 ) ( 8 ) = 168 cm 3



260 - 168 = 92 cm 3


V = Bh

= ( 7 ) ( 14 ) = 98 cm 3



260 - 168 = 92 cm 3


a height of 14 cm

V = Bh

92 = B ( 14 )

92 ___ 14

= B ( 14 ) _____ 14

6 8 ___ 14

= B asymp 657





V = Bh

= ( 36 ) ( 5 ) = 180 in 3



prism V = Bh

= ( 32 ) ( 6 ) = 192 in 3





V = Bh

286 = B ( 8 )

286 ____ 8 = B ( 8 )

3575 = B


trapezoidal prism

1 __ 2 ( 2 + b 2 ) 13 = 3575

1 __ 2 ( 2 + b 2 ) ( 13 ___

13 ) = 3575 _____

13

( 2 ) 1 __ 2 ( 2 + b 2 ) = ( 2 ) 275

2 + b 2 = 55

_ -2 _ -2

b 2 = 35 ft



B = 1 __ 2 bh

= 1 __ 2 ( 10 ) 6 = 30 cm

2


V = Bh

= ( 30 ) ( 25 ) = 75 cm 3



_____ cm

3 )

asymp ( 75 cm 3 ) ( 86 g

_____ cm

3 ) = 645 g


about 645 g







of 120 cm 3

V = Bh

V = [ 1 __ 2 ( b 1 + b 2 ) h 1 ] h 2

120 ≟ [ 1 __ 2 ( 2 + 6 ) 4 ] 75

= [ 1 __ 2 ( 8 ) 4 ] 75

= [ 16 ] ( 75 ) = 120


V = Bh

V = [ 1 __ 2 ( b 1 + b 2 ) h 1 ] h 2

120 ≟ [ 1 __ 2 ( 1 + 7 ) 25 ] 12

= [ 1 __ 2 ( 8 ) 25 ] 12

= [ 10 ] 12 = 120






MODULE 9

Ready to Go On




2 d = 12 cm d = 6 cm so r = 12 ___ 2 = 6 ft



A asymp 11304 ft 2





A asymp 1 __ 2 sdot 314 sdot ( 8 ) 2


A asymp 10048 m 2


A = 1 __ 2 sdot 16 sdot 10

A = 1 __ 2 sdot 160

A = 80 m 2


80 + 10048 = 18048 m 2





A = 20 sdot 45

A = 90 c m 2

Area of rectangle

A = ℓw = 20 sdot 55 = 110 c m 2


90 + 110 = 200 cm 2



1 __ 2 ( 4 ) 3 = 6 cm 2


P = 3 + 4 + 5 = 12 cm


S = Ph + 2B

S = 12 ( 10 ) + 2 ( 6 )

thinsp=120 + 12

thinsp= 132 cm 2


V = Bh

= ( 6 ) 10

= 60 cm 3




1 __ 2 ( 4 ) 15 = 3 yd 2


( 4 ) 2 = 8 yd 2



P = 4 + 2 + 25 + 25 + 2 = 13 yd


S = Ph + 2B

S = 13 ( 25 ) + 2 ( 11 )

thinsp= 325 + 22

thinsp= 545 yd 2


is given

B = 234 yd 3


V = Bh

= ( 11 ) 25

= 275 yd 3






unit


Are You Ready

1 x ___16

=45___40

40x=720

40x ____40

=720____40

   x=18

2 x __5=1__

4

4x=5

4x ___4

=5__4

  x=5__4=125

3 25___10

=x ___10

125=10x

125____10

=10x ____10

125=x

4 x __6

=2__9

9x= 12

9x ___9

=12___9

   x=12___9=4__

3

5 4748495152575960range=60-47=13

6 4566689121213range=13-4=9

7 95979799100106108115range=115-95=20

8 121319273539476671range=71-12=59

9 mean=3+5+7+3+6+4+8+6+9+5_________________________________10

=56

10 mean=81+94+113+67+62+75____________________________6

=82

LESSON 101

Your Turn




Guided Practice




Jimmy 80

Darnell 90

Ping 75

Zach 85

Jamar 80

BSampleanswer

75+80+90+75+85+80___________________________6

=485____6

asymp81

Meanasymp81



Stan 80 Marcus 90

Alejandro 90 Tio 85

BSampleanswer

85+80+90+85+90+85____________________________6

=515____6 =86

Mean=size86




















b 35___60

= x ____100

xasymp58


=58



LESSON 102

Your Turn


______________________sizeofsample



6___50

= x_____3500

6sdot70______50sdot70

= x _____3500

420_____3500

= x_____3500


Guided Practice

1

6 7 8 9 10 11 12 13 14 1550 1 2 3 4


6 7 7 107 114 4 54

Leastvalue

4

Lower quartile

4

Median

65

Upper quartile

7

Greatestvalue11

Drawaboxplot

10 1550





______________________sizeofsample



4___60

= x_____4200

4sdot70______60sdot70

= x_____4200

280_____4200

= x_____4200






8___50

= x_____4500

8sdot90______50sdot90

= x_____4500

720_____4500

= x_____4500



divide060

divide060







_______________________________________ size of sample

=



4 ___ 50

= x ____ 600

4 sdot 12 ______ 50 sdot 12

= x ____ 600

48 ____ 600

= x ____ 600

x = 48



_______________________________________________ size of sample

=



2 ___ 20

= x ____ 130

2 sdot 65 _______ 20 sdot 65

= x ____ 130

13 ____ 130

= x ____ 130

x = 13



________________ size of sample



12 ___ 60

= x _____ 1200

12 sdot 20 ______ 60 sdot 20

= x _____ 1200

240 _____ 1200

= x _____ 1200

x = 240


shelters


__________________________ size of sample



12 ___ 72

= x ______ 10800

12 sdot 150 _______ 72 sdot 150

= x ______ 10800

1800

______ 10800

= x ______ 10800

x = 1800



_______ 2 = 25


14 Order the data

11 12 12 12 13 13 13 14 14 14 15 17 18 18

19 22



12 ___ 16

= x ____ 100

12 sdot 625 ________ 16 sdot 625

= x ____ 100

75 ____ 100

= x ____ 100

x = 75



15

6 7 8 9 1050 1 2 3 4


fewer siblings




















9 a 56 + 43 + 62 + 63 + 33 + 34 + 38 + 51 + 59 + 59

___________________________________________ 10

= 498


b 498 sdot 64 = 31872



10 55 + 57 + 57 + 58 + 59 + 59 + 59 + 59 + 59 + 61 + 62 + 62 + 63 + 64 + 66

_________________________________________________________________ 15

= 60






accurately

LESSON 103

Guided Practice

1 (1 600) 20

2 50 51 600








5 Shop A 10 ___ 50

times 500 = 100

Shop B 23 ____ 100

times 500 = 115

Shop C 7 ___ 25

times 500 = 140








fewest bagels










count of 75


MODULE 10

Ready to Go On




service


__________________________________________ size of sample


18 ____ 270

= x ______ 30330

18 sdot 337 ____

3 ________

270 sdot 337 ____ 3

= x ______ 30330

2022

______ 30330

= x ______ 30330

x = 2022


languages





= defective players

______________ shipment

2 ___ 10

= x _____ 5000

2 middot 500 _______ 10 middot 500

= x _____ 5000

1000

_____ 5000

= x _____ 5000

x = 1000


defective


the shipment





Are You Ready

0875

1 8 ⟌ _

7000

_ -6 400

600

_ -560

40

_ -40

0

0875 875

08

2 5 ⟌ _

40

_ -4 0

0

08 80

025

3 4 ⟌ _

100

_ -80

20

_ -20

0

025 25

03

4 10 ⟌ _

30

_ -3 0

0

03 30

5 4 6 7 7 9 11 15 17

7 + 9

_____ 2 = 8

Median = 8

Mode = 7

6 36 37 40 43 44 49 50 51 56

Median = 44

Mode none

7 9 + 16 + 13 + 14 + 10 + 16 + 17 + 9

________________________________ 8

= 13

Mean = 13

8 108 + 95 + 104 + 96 + 97 + 106 + 94

________________________________ 7 = 100

Mean = 100

LESSON 111

Your Turn








in order

1 4 4 4 5 5 5 6 6 6 6 7 7 8 11


range 10 h



range for exercise

Guided Practice




one area




no data


4 Class A

4 4 4 4 4 5 5 5 6 6 12 13 13 13 13 14 14

median 6

Class B

3 4 4 4 5 5 5 5 6 6 7 7 7 7 7 8 8 9

median 6








at 8 letters




3 + 4 + 4 + 5 + 5 + 6 + 7 + 7 + 8 + 8 + 8 + 9

________________________________________ 12

74 ___ 12

asymp 617

Mean asymp 617

3 3 4 5 5 6 7 7 8 8 8 9


average

6 + 7

_____ 2 = 13 ___

2 = 65

Median 65

Range 9 - 3 = 6


the left


interval













LESSON 112

Your Turn



Guided Practice


2 Median79

3 Range88-72=16 IQR85-75=10






























does not




LESSON 113

Your Turn

1 Team 1

Mean

44 + 47 + 67 + 89 + 55 + 76 +85 + 80 + 87 + 69 + 47 + 58 = 804

804 divide 12 = 67


ǀ 44 - 67 ǀ = 23 ǀ 47 - 67 ǀ = 20

ǀ 67 - 67 ǀ = 0 ǀ 89 - 67 ǀ = 22

ǀ 55 - 67 ǀ = 12 ǀ 76 - 67 ǀ = 9

ǀ 85 - 67 ǀ = 18 ǀ 80 - 67 ǀ = 13

ǀ 87 - 67 ǀ = 20 ǀ 69 - 67 ǀ = 2

ǀ 47 - 67 ǀ = 20 ǀ 58 - 67 ǀ = 11


23 + 20 + 0 + 22 + 12 + 9 +18 + 13 + 20 + 2 + 20 + 11 = 170


Team 2

Mean

40 + 32 + 52 + 75 + 65 + 70 +72 + 61 + 54 + 43 + 29 + 32 = 625



ǀ 40 - 521 ǀ = 121 ǀ 32 - 521 ǀ = 201

ǀ 52 - 521 ǀ = 01 ǀ 75 - 521 ǀ = 229

ǀ 65 - 521 ǀ = 129 ǀ 70 - 521 ǀ = 179

ǀ 72 - 521 ǀ = 199 ǀ 61 - 521 ǀ = 89

ǀ 54 - 521 ǀ = 19 ǀ 43 - 521 ǀ = 91

ǀ 29 - 521 ǀ = 231 ǀ 32 - 521 ǀ = 201


121 + 201 + 01 + 229 +129 + 179 + 199 + 89 +19 + 91 + 231 + 201 = 169


Difference in means

67 - 521 = 149



MAD


distributions

Guided Practice

1 Class 1 mean

12 + 1 + 6 + 10 + 1 + 2 + 3 +10 + 3 + 8 + 3 + 9 + 8 + 6 + 8 = 90

90 divide 15 = 6

Class 2 mean

11 + 14 + 11 + 13 + 6 + 7 + 8 + 6 +8 + 13 + 8 + 15 + 13 + 17 + 15 = 165

165 divide 15 = 11


ǀ 12 - 6 ǀ = 6 ǀ 1 - 6 ǀ = 5 ǀ 6 - 6 ǀ = 0

ǀ 10 - 6 ǀ = 4 ǀ 1 - 6 ǀ = 5 ǀ 2 minus 6 ǀ = 4

ǀ 3 - 6 ǀ = 3 ǀ 10 - 6 ǀ = 4 ǀ 3 - 6 ǀ = 3

ǀ 8 - 6 ǀ = 2 ǀ 3 - 6 ǀ = 3 ǀ 9 - 6 ǀ = 3

ǀ 8 - 6 ǀ = 2 ǀ 6 - 6 ǀ = 0 ǀ 8 - 6 ǀ = 2

6 + 5 + 0 + 4 + 5 + 4 + 3 + 4 +3 + 2 + 3 + 3 + 2 + 0 + 2 = 46



ǀ 11 - 11 ǀ = 0 ǀ 14 - 11 ǀ = 3 ǀ 11 - 11 ǀ = 0

ǀ 13 - 11 ǀ = 2 ǀ 6 - 11 ǀ = 5 ǀ 7 - 11 ǀ = 4

ǀ 8 - 11 ǀ = 3 ǀ 6 - 11 ǀ = 5 ǀ 8 - 11 ǀ = 3

ǀ 13 - 11 ǀ = 2 ǀ 8 - 11 ǀ = 3 ǀ 15 - 11 ǀ = 4

ǀ 13 - 11 ǀ = 2 ǀ 17 - 11 ǀ = 6 ǀ 15 - 11 ǀ = 2

0 + 3 + 0 + 2 + 5 + 4 + 3 + 5 +3 + 2 + 3 + 4 + 2 + 6 + 2 = 44



11 minus 6 = 5




comparison


different samples


5 23 + 38 + 39 + 48 + 55 + 56 + 71 +86 + 57 + 53 + 43 + 31 = 600

600 divide 12 = 50

ǀ 23 - 50 ǀ = 27 ǀ 38 - 50 ǀ = 12

ǀ 39 - 50 ǀ = 11 ǀ 48 - 50 ǀ = 2

ǀ 55 - 50 ǀ = 5 ǀ 56 - 50 ǀ = 6

ǀ 71 - 50 ǀ = 21 ǀ 86 - 50 ǀ = 36

ǀ 57 - 50 ǀ = 7 ǀ 53 - 50 ǀ = 3

ǀ 43 - 50 ǀ = 7 ǀ 31 - 50 ǀ = 19

27 + 12 + 11 + 2 + 5 + 6 + 21 +36 + 7 + 3 + 7 + 19 = 156

156 divide 12 = 13



6 ǀ 23 - 8 ǀ = 15 ǀ 38 - 23 ǀ = 15

ǀ 39 - 24 ǀ = 15 ǀ 48 - 33 ǀ = 15

ǀ 55 - 40 ǀ = 15 ǀ 56 - 41 ǀ = 15

ǀ 71 - 56 ǀ = 15 ǀ 86 - 71 ǀ = 15

ǀ 57 - 42 ǀ = 15 ǀ 53 - 38 ǀ = 15

ǀ 43 - 28 ǀ = 15 ǀ 31 - 16 ǀ = 15




7 50 - 15 = 35




8 50 - 35 = 15




9

0 4 8 12 16 20 24 28 32 36 40 44

Medians

School B

School A

0 4 8 12 16 20 24 28 32 36 40 44

Means

School B

School A




10 State A 48 - 38 = 10


State B 50 - 42 = 8

8 divide 4 = 2





well


Median 665


Median 77

77 - 665 = 105

105 divide 6 = 175


ranges













not very similar

MODULE 11

Ready to Go On


5 + 6 + 6 + 7 + 7 + 7 + 7 + 8 + 8 + 8 + 8 + 9 + 9 + 10

________________________________________________ 14

= 105 ____ 14

= 75 mi


6 + 6 + 7 + 7 + 8 + 8 + 8 + 8 + 9 + 9 + 9 + 10 + 10 + 10

__________________________________________________ 14

= 115 ___ 14

asymp 82 mi




5 6 6 7 7 7 7 8 8 8 8 9 9 10


average

7 + 8

_____ 2 = 15 ___

2 = 75

Median 75


6 6 7 7 8 8 8 8 9 9 9 10 10 10




Median 8













7 + 11 + 11 + 12 + 9 + 12 + 8 + 10

______________________________ 8

= 10


21 + 24 + 19 + 19 + 22 + 23 + 24 + 24

__________________________________ 8 = 22




12 ___ 5

= 24




groups



Are You Ready

1 6 ___ 10

= 6 divide 2 ______ 10 divide 2

= 3 __ 5

2 9 ___ 15

= 9 divide 3 ______ 15 divide 3

= 3 __ 5

3 16 ___ 24

= 16 divide 8 ______ 24 divide 8

= 2 __ 3

4 9 ___ 36

= 9 divide 9 ______ 36 divide 9

= 1 __ 4

5 45 ___ 54

= 45 divide 9 ______ 54 divide 9

= 5 __ 6

6 30 ___ 42

= 30 divide 6 ______ 42 divide 6

= 5 __ 7

7 36 ___ 60

= 36 divide 12 _______ 60 divide 12

= 3 __ 5

8 14 ___ 42

= 14 divide 14 _______ 42 divide 14

= 1 __ 3

075

9 4 ⟌ _

300

_ -2 80

20

_ -20

0

075

0875

10 8 ⟌ _

7000

_ -6400

600

_ -560

40

_ -40

0

0875

015

11 20 ⟌ _

300

_ -2 00

100

_ -100

0

015

038

12 50 ⟌ _

1900

_ -15 00

4 00

_ -4 00

0

038

13 67 = 67 ____ 100

= 067

14 31 = 31 ____ 100

= 031

15 7 = 7 ____ 100

= 007

16 146 = 100 + 46

= 100 ____ 100

+ 46 ____ 100

= 1 + 046

= 146

17 013 = 13

18 055 = 55

19 008 = 8

20 116 = 116

LESSON 121

Your Turn







is 10 ___ 20

or 1 __ 2





3


UNIT

6



P(5) + P(not 5) = 1

1 __ 8 + P(not 5) = 1

P(not 5) = 7 __ 8




1 __ 2 + P(odd) = 1

P(odd) = 1 __ 2


Guided Practice













impossible 0
















= 1 __ 4


P(5) + P(not 5) = 1

1 __ 6 + P(not 5) = 1

P(not 5) = 5 __ 6




1 __ 3 + P(not blue) = 1




P(4) + P(not 4) = 1

1 __ 5 + P(not 4) = 1

P(not 4) = 4 __ 5




4 ___ 52

+ P(not queen) = 1

P(not blue) = 48 ___ 52

= 12 ___ 13









selecting


or 2 ___ 13



9 ___ 12



or 1 __ 4



or 1 __ 4













or 5 __ 7



have red hair




or 4 __ 7





coin is 9 ___ 16














landing on blue

LESSON 122

Your Turn


Red 10 ___ 30

= 1 __ 3

Yellow 14 ___ 30

= 7 ___ 15

Blue 6 ___ 30

= 1 __ 5






Guided Practice


A 14 ___ 40

= 7 ___ 20

= 035 = 35

B 7 ___ 40

= 0175 = 175

C 11 ___ 40

= 0275 = 275

D 8 ___ 40

= 1 __ 5 = 020 = 20







4 6 ___ 10








= 8 ___ 48

= 1 __ 6





chosen is 19 ___ 20


1 ___ 20

+ P(not Ryan) = 1

P(not Ryan) = 19 ___ 20


patterns




times



get a hit next time


is 4 ___ 10





or about 417


7 ___ 12



or 417











pocket


LESSON 123

Your Turn



= 60 ____ 400

= 3 ___ 20

= 15



= 12 ___ 75

or 4 ___ 25

Guided Practice




= 50 ____ 400

or 1 __ 8











number of trials








= 33 ____ 330

= 1 ___ 10



= 60 ____ 400

= 3 ___ 20


= 55 + 60 + 23

____________ 400

= 138 ____ 400

= 69 ____ 200


and 4 color choices


P(7th grade + 100 pages) = 85 ____ 250

= 17 ___ 50




7th grade




likely





12 P(male + open toe) = 11 ____ 300











heads and 3 or 4

LESSON 124

Your Turn








Guided Practice








too high

5 98 ____ 100

= x ___ 40

= 39 ___ 40

or 39 times




6 18 ____ 100

= x _____ 5000

= 900 _____ 5000



accepted

times04

times04

times50

times50





events


8 4 ____ 100

= x ____ 200

= 8 ____ 200



9 Yes 6th grade 2 ____ 100

= x ____ 250

= 5 ____ 250

or 5 students

7th grade 4 ____ 100

= x ____ 200

= 8 ____ 200

or 8 students

8th grade 8 ____ 100

= x ____ 150

= 12 ____ 150

or 12 students



10 6 ____ 100

= x ____ 300

= 18 ____ 300










1 ___ 30

= x ____ 180




normal gas pump







4 ____ 100

= x _____ 2400

= 96 _____ 2400



MODULE 12

Ready to Go On

1 H1 H2 T1 T2

2 6 ___ 10

= 3 __ 5

3 13 ___ 20




because 3 ___ 10

= x ___ 80

= 24 ___ 80

or 24 times




times15

times15

times24

times24

times2

times2

times3

times3

times2

times2

times25

times25

times8

times8



Simulations

Are You Ready

075

1 4 ⟌ _

300

_ -2 80

20

_ -20

0

075 = 75

04

2 5 ⟌ _

20

_ -2 0

0

04 = 40

09

3 10 ⟌ _

90

_ -9 0

0

09 = 90

035

4 20 ⟌ _

700

_ -6 00

1 00

_ -1 00

0

035 = 35

0875

5 8 ⟌ _

7000

_ thinsp-6 400

600

_ -560

40

_ -40

0

0875 = 875

005

6 20 ⟌ _

100

_ -1 00

0

005 = 5

076

7 25 ⟌ _

1900

_ -17 50

1 50

_ -1 50

0

076 = 76

046

8 50 ⟌ _

2300

_ -20 50

3 00

_ -3 00

0

046 = 46

9 1 - 1 __ 5 = 5 __

5 - 1 __

5

= 4 __ 5

10 1 - 2 __ 9 = 9 __

9 - 2 __

9

= 7 __ 9

11 1 - 8 ___ 13

= 13 ___ 13

- 8 ___ 13

= 5 ___ 13

12 1 - 3 ___ 20

= 20 ___ 20

- 3 ___ 20

= 17 ___ 20

13 8 ___ 15

times 5 __ 8 =

18 ___ 315

times 5 1 ___

8 1

= 1 __ 3

14 2 __ 9 times 3 __

4 =

12 __ 39

times 3 1 ___

4 2

= 1 __ 6

15 9 ___ 16

times 12 ___ 13

= 9 ___ 416

times 12 3 _____

13

= 27 ___ 52

16 7 ___ 10

times 5 ___ 28

= 17 ___

210 times 5

1 ____

28 4

= 1 __ 8

LESSON 131

Your Turn






= 2 __ 6 = 1 __

3



probability


Guided Practice

1

Basket A Basket B


= 16

7 + 4 + 9

= 20


P(win) =

Number of red balls


3 ___

16 4 ___

20 = 1 __

5


16 use


1 __ 5 = 16 ___

80

3 ___ 16

= 15 ___ 80

Therefore 16 ___ 80

gt 15 ___ 80

so 1 __ 5 gt 3 ___

16


winning




= 6 ___ 11




= 5 ___ 11




= 2 __ 6 = 1 __

3


close


by 20




= 2 __ 6

= 1 __ 3 033 or 33



= 8 ___ 12

= 2 __ 3 067 or 67



= 4 ___ 14

= 2 __ 7 029 or 29


= 26 ___ 52

= 1 __ 2 050 or 50


= 12 - 5 ______ 12

= 7 ___ 12

058 or 58



7 adventure)

P(not a comedy)


= 5 + 7 _________

5 + 7 + 8 = 12 ___

20

= 3 __ 5 060 or 60






= 2 __ 6

= 1 __ 3 033 or 33







= 6 ___ 16

or 3 __ 8







5 ______ 5 + 15

= 5 ___ 20

= 1 __ 4

times16

times16

times5

times5




P(seventh grader) =



= 20 ___ 35

= 4 __ 7


P(eighth grader) =



= 15 ___ 35

= 3 __ 7



more likely










= 8 ___ 20


14 ___ 40

or 7 ___ 20



marble is 8 ___ 20

- 7 ___ 20

= 1 ___ 20



= 10 ___ 20


= 8 ___ 20



marble is 10 ___ 20

- 8 ___ 20

= 2 ___ 20

= 1 ___ 10




= 2 ___ 20


= 5 ___ 20



marble is 5 ___ 20

- 2 ___ 20

= 3 ___ 20



LESSON 132

Your Turn

3 P(ham sandwich) =



= 4 ___ 12

= 1 __ 3




= 6 ___ 12

= 1 __ 2




0 0 0 0

0 0 0 1

0 0 1 0

0 0 1 1


second digit

0 1 0 0

0 1 0 1

0 1 1 0

0 1 1 1


second digit

1 0 0 0

1 0 0 1

1 0 1 0

1 0 1 1


second digit

1 1 0 0

1 1 0 1

1 1 1 0

1 1 1 1



0 0 1 1

0 1 0 1

0 1 1 0

1 0 0 1

1 0 1 0

1 1 0 0





= 6 ___ 16

= 3 __ 8


Guided Practice

1

1 2 3 4 5 6

11 sdot 1

= 1

1 sdot 2

= 2

1 sdot 3

= 3

1 sdot 4

= 4

1 sdot 5

= 5

1 sdot 6

= 6

22 sdot 1

= 2

2 sdot 2

= 4

2 sdot 3

= 6

2 sdot 4

= 8

2 sdot 5

= 10

2 sdot 6

= 12

33 sdot 1

= 3

3 sdot 2

= 6

3 sdot 3

= 9

3 sdot 4

= 12

3 sdot 5

= 15

3 sdot 6

= 18

44 sdot 1

= 4

4 sdot 2

= 8

4 sdot 3

= 12

4 sdot 4

= 16

4 sdot 5

= 20

4 sdot 6

= 24

55 sdot 1

= 5

5 sdot 2

= 10

5 sdot 3

= 15

5 sdot 4

= 20

5 sdot 5

= 25

5 sdot 6

= 30

66 sdot 1

= 6

6 sdot 2

= 12

6 sdot 3

= 18

6 sdot 4

= 24

6 sdot 5

= 30

6 sdot 6

= 36





= 15 ___ 36




= 23 ___ 36

4 H

HHH HHT

H

H

Coin 1

List

Coin 2

Coin 3 T

T

HTH HTT

H T

T

H

H T

THH THT

T

H T

TTH TTT

Coin 1

List

Coin 2

Coin 3




= 1 __ 8


HHT HTH THH



= 3 __ 8




10

Checkered

Red

Checkered

Red

Blue

Black

Checkered

Red

Checkered

Red

Blue

Black

Checkered

Red

Checkered

Red

Blue

Black

Shirt Pants Shoes

Yellow

Red

Green




= 6 ___ 12

= 1 __ 2


Shirt Pants Shoes






= 4 ___ 12

= 1 __ 3



Rhee Pamela

Rhee A

Rhee B

Rhee C

Pamela A

Pamela B

Pamela C

A B

A C

B C



P(Rhee and Pamela)


= 1 ___ 10




1 2 3 4 5 6

11 + 1

= 2

1 + 2

= 3

1 + 3

= 4

1 + 4

= 5

1 + 5

= 6

1 + 6

= 7

22 + 1

= 3

2 + 2

= 4

2 + 3

= 5

2 + 4

= 6

2 + 5

= 7

2 + 6

= 8

33 + 1

= 4

3 + 2

= 5

3 + 3

= 6

3 + 4

= 7

3 + 5

= 8

3 + 6

= 9

44 + 1

= 5

4 + 2

= 6

4 + 3

= 7

4 + 4

= 8

4 + 5

= 9

4 + 6

= 10

55 + 1

= 6

5 + 2

= 7

5 + 3

= 8

5 + 4

= 9

5 + 5

= 10

5 + 6

= 11

66 + 1

= 7

6 + 2

= 8

6 + 3

= 9

6 + 4

= 10

6 + 5

= 11

6 + 6

= 12


are 10 less than 6



= 10 ___ 36

= 5 ___ 18


diagram

Khakis

Shorts

Shirt Pants Shoes

Collared Jeans

Sneakers

Flip-flops

Sandals

Sneakers

Flip-flops

Sandals

Sneakers

Flip-flops

Sandals

Khakis

Shorts

T-shirt Jeans

Sneakers

Flip-flops

Sandals

Sneakers

Flip-flops

Sandals

Sneakers

Flip-flops

Sandals







= 4 ___ 18

= 2 __ 9






outcomes



Therefore




= 7 ___ 30






diagram

Carrots

Sweet potato

Pasta

Peas

Asparagus





Carrots

Sweet potato

Peas

Asparagus





Carrots

Sweet potato

Peas

Asparagus





Carrots

Sweet potato

Peas

Asparagus





Salmon

Beef

Pork



salmon Therefore


= 1 __ 4





Carrots

Sweet potato

PastaPeas

Asparagus

Carrots

Sweet potato

Peas

Asparagus

Carrots

Sweet potato

Peas

Asparagus

Carrots

Sweet potato

Peas

Asparagus

Salmon

Beef

Pork


salmon Therefore


= 1 __ 4















codes













12453 12534 12543 13245 13254 13425

13452 13524 13542 14235 14253 14325

14352 14523 14532 15234 15243 15324













114 115 221 223 224 225 331 332 334 335

441 442 443 445 551 552 553 554 There























LESSON 133

Your Turn




3






heads is 1 __ 2

1 __ 2 = x ___

18

1 __ 2 = x ___

18

x = 9

about 9 times


P(red) = 8 ___ 17

P(not red) = 1 - 8 ___ 17

= 9 ___ 17




Therefore




Guided Practice






3 House 1 __

3



1 __ 3 = x ___

18

1 __ 3 = x ___

18

x = 6














P(hazel) = 9 ___ 28

P(brown) = 10 ___ 28

P(blue) = 7 ___ 28

P(green) = 2 ___ 28






unknown quantity




P(white or gray) = 3 __ 9 = 1 __

3


prediction is then








Y GRR

R R

RR





card is 12 ___ 52


52 use the least


52 Given

that 12 ___ 52

lt 26 ___ 52





P(ace) = 4 ___ 52

= 1 ___ 13


prediction is then


times 39 = 3



P(red card) = 26 ___ 52

= 1 __ 2








times6

times6

times9

times9


1 2 3 4 5 6

1 2 3 4 5 6 7

2 3 4 5 6 7 8

3 4 5 6 7 8 9

4 5 6 7 8 9 10

5 6 7 8 9 10 11

6 7 8 9 10 11 12




P(sum of 8) = 5 ___ 36

P(sum of 11) = 2 ___ 36



gt 2 ___ 36




= 1 __ 4




1 __ 4 times 180 = 45





so P(sum of 3) = 3 ___ 36

= 1 ___ 12


prediction is then


middot 36 = 3





time









that is not green



green is 3 + 9 _________

3 + 8 + 9 = 12 ___



20 = 12 ___

40






6 = 1 ___

12



P(5 or heads) = 1 __ 6 + 1 __

2 - 1 __

6 times 1 __

2 = 7 ___

12





LESSON 134

Your Turn



1 0 0 1 No

2 0 1 No

3 1 No

4 0 1 No

5 1 No

6 0 0 0 1 Yes

7 0 0 1 No

8 0 1 No

9 1 No

10 0 0 0 0 1 Yes




or 20



1 1 0 1 1 0 3

2 0 1 0 0 1 2

3 0 0 0 0 1 1

4 0 0 1 1 0 2

5 1 1 1 1 1 5

6 1 0 0 0 0 1

7 1 0 1 1 0 3

8 1 0 1 0 0 2

9 0 1 1 1 1 4

10 0 0 0 0 0 0



= 70


Guided Practice







numbers each time

2


1 10 3 5 1 2

2 10 4 6 5 0

3 3 2 10 3 3

4 2 10 4 4 1

5 7 3 6 3 2

6 8 4 8 5 0

7 6 2 2 8 2

8 6 5 2 4 1

9 2 2 3 2 4

10 6 3 1 5 2




8 ___ 10

= 80









= 10




= 20














1 3 1

2 4 2 2

3 2 1

4 1 1

5 2 1

6 4 5 3 2

7 4 2 2

8 4 5 2 1

9 4 4 3 3

10 5 1 2


1 + 2 + 1 + 1 + 1 + 2 + 2 + 1 + 3 + 2

_________________________________ 10

= 16 ___ 10

= 1 3 __ 5

















MODULE 13

Ready to Go On


= 12 ___________________ 12 + 12 + 15 + 9 + 12

= 12 ___ 60

= 1 __ 5 020 or 20




= 13 + 13

_______ 52

= 26 ___ 52

= 1 __ 2 050 or 50








or

40





24 15 + ( -15 ) + 200 = 200

25 -500 + ( -600 ) + 1200 = 100
















is 8 feet deep








LESSON 13

Your Turn

4 -7 - 2 = -7 + ( -2 )

-7 + ( -2 ) = -9

5 -1 - ( -3 ) = -1 + 3

-1 + 3 = 2

6 3 - 5 = 3 + ( -5 )

3 + ( -5 ) = -2

7 -8 - ( -4 ) = -8 + 4

-8 + 4 = -4

Guided Practice







3 -4 - 5 = -4 + ( -5 ) = -9

0-1-2-3-4-5-6-7-8-9 4 1 - 4 = 1 + -4 = -3

0 1 2 3 4-1-2-3-4 5 8 - 11 = 8 + ( -11 ) = -3

6 -3 - ( -5 ) = -3 + 5 = 2

7 15 - 21 = 15 + ( -21 ) = -6

8 -17 - 1 = -17 + ( -1 ) = -18

9 0 - ( -5 ) = 0 + 5 = 5

10 1 - ( -18 ) = 1 + 18 = 19

11 15 - 1 = 14

12 -3 - ( -45 ) = -3 + 45 = 42

13 19 - ( -19 ) = 19 + 19 = 38

14 -87 - ( -87 ) = -87 + 87 = 0


example 6 - 8 = 6 + ( -8 ) = -2




25 - ( -4 ) = 25 + 4 = 29





-127 - ( -225 ) = -127 + 225 = 98



temperature 90degF

90 - ( -2 ) = 92






-425 - ( -275 ) = -425 + 275 = -150



in temperature

Gas A -8 - ( -21 ) = -8 + 21 = 13

13degC increase

Gas B 12 - ( -12 ) = 12 + 12 = 24

24degC increase

Gas C -15 - ( -19 ) = -15 + 19 = 4

4degC increase













-11 + 4 = -7




LESSON 14

Your Turn




Guided Practice


2 -23+5-7=-18-7  =-25-25degF

3 50-40+87-30=10+87-30  =97-30  =6767points

4 -6+15+15=-6+30  =24

5 9- 4- 17= 9- 21  =-12

6 50-42+10=8+10  =18

7 6+13+7-5=19+2  =21

8 65+43-11=108-11  =97

9 -35-14+45+31=-49+76  =27

10 -12+6-4=-6-4  =-10-34-3+39=-37+39  = 2  -10lt2( -12+6-4)lt( -34-3+39)

11 21-3+8=18+8  =26-14+ 31- 6= 17- 6  =11 26gt11( 21-3+8)gt( -14+31-6)



13 a 5-1+6-1=9






b 45gt-55Barry

17 a 300to400


18 100-18+22-53=51$51

19 45-17-22+18=24$24






MODULE 1

Ready to Go On

1 -8+( -6)=-14

2 -4+( -7)=-11

3 -9+( -12)=-21





4 5 + ( -2 )

ǀ 5 ǀ - ǀ -2 ǀ = 3

5 + ( -2 ) = 3

5 -8 + 4

ǀ -8 ǀ - ǀ 4 ǀ = 4

-8 + 4 = -4

6 15 + ( -8 )

ǀ 15 ǀ - ǀ -8 ǀ = 7

15 + ( -8 ) = 7

7 2 - 9 = 2 + ( -9 )

2 + ( -9 ) = -7

8 -3 - ( -4 ) = -3 + 4-3 + 4 = 1

9 11 - ( -12 ) = 11 + 12

11 + 12 = 23

10 -15 + 9 - 4 = -6 - 4

= -10


11 24 + 8 - 12 - 9 = 24 + 8 - ( 12 + 9 ) = 32 - 21

= 11




after she pays them

-10 + ( -5 ) = -15 $15 decrease



Are You Ready

1 9 times 3 = 27

2 7 times 10 = 70

3 9 times 8 = 72

4 15 times 10 = 150

5 6 times 9 = 54

6 10 times 23 = 230

7 9 times 9 = 81

8 10 times 20 = 200

9 54 divide 9 = 6

10 42 divide 6 = 7

11 24 divide 3 = 8

12 64 divide 8 = 8

13 90 divide 10 = 9

14 56 divide 7 = 8

15 81 divide 9 = 9

16 110 divide 11 = 10

17 12 + 8 divide 212 + 4

16

18 15 - ( 4 + 3 ) times 2

15 - 7 times 2

15 - 14

1

19 18 - ( 8 - 5 ) 2

18 - ( 3 ) 2

18 - 9

9

20 6 + 7 times 3 - 5

6 + 21 - 5

27 - 5

22

21 9 + ( 2 2 + 3 ) 2 times 2

9 + ( 4 + 3 ) 2 times 2

9 + ( 7 ) 2 times 2

9 + 49 times 2

9 + 98

107

22 6 + 5 - 4 times 3 divide 2

6 + 5 - 12 divide 2

6 + 5 - 6

11 - 6

5

LESSON 21

Your Turn


will be negative


-3 ( 5 ) = -15


will be positive

ǀ -10 ǀ times ǀ -2 ǀ = 10 times 2 = 20

( -10 ) ( -2 ) = 20


0 ( -22 ) = 0


will be positive

8 ( 4 ) = 32

Guided Practice

1 -1 ( 9 ) = -9

2 14 ( -2 ) = -28

3 ( -9 ) ( -6 ) = 54

4 ( -2 ) ( 50 ) = -100

5 ( -4 ) ( 15 ) = -60

6 -18 ( 0 ) = 0

7 ( -7 ) ( -7 ) = 49

8 -15 ( 9 ) = -135

9 ( 8 ) ( -12 ) = -96

10 -3 ( -100 ) = 300

11 0 ( -153 ) = 0

12 -6 ( 32 ) = -192

13 7 ( -75 ) = -525 -$525



15 6 ( -2 ) = -12 -12degF








19 5 ( -4 ) = -20 $20 decrease





22 9 ( -6 ) = -54 -54 ( 2 ) = -108 Casey has $108

less in his savings

23 7 ( -8 ) = -56 7 ( -5 ) = -35





160 points


25 a 3 ( 3 ) ( -3 ) = 9 ( -3 ) = -27

b 3 ( -3 ) ( -3 ) = -9 ( -3 ) = 27

c -3 ( -3 ) ( -3 ) = 9 ( -3 ) = -27

d 3 ( 3 ) ( 3 ) ( -3 ) = 9 ( 3 ) ( -3 ) = 27 ( -3 ) = -81

e 3 ( 3 ) ( -3 ) ( -3 ) = 9 ( -3 ) ( -3 ) = -27 ( -3 ) = 81

f 3 ( -3 ) ( -3 ) ( -3 ) = -9 ( -3 ) ( -3 ) = 27 ( -3 ) = -81




negative



3 ( 3 ) ( -3 ) ( -3 ) = 9 ( -3 ) ( -3 ) = 81 the sign of the

product is positive


26 -1 ( 3 ) ( 1 ) 1 ( -3 ) ( 1 ) -1 ( -3 ) ( -1 )









negative

LESSON 22

Your Turn


0 divide ( -6 ) = 0


will be negative

38 divide ( -19 ) = -2


will be positive

-13 divide ( -1 ) = 13



Guided Practice

1 -14 ____ 2 = -7

2 21 divide ( -3 ) = -7

3 26 ____ -13

= -2

4 0 divide ( -4 ) = 0

5 -45 ____ -5 = 9

6 -30 divide ( 10 ) = -3

7 -11 ____ -1

= 11

8 -31 divide ( -31 ) = 1

9 0 ___ -7 = 0

10 -121 _____ -11

= 11

11 84 divide ( -7 ) = -12

12 500 ____ -25

= -20


undefined

14 -63 ____ -21

= 3

15 -40 divide ( 4 ) = -10 $10

16 -22 divide ( 11 ) = -2 2 points

17 -75 divide ( -15 ) = 5 5 targets

18 -99 divide ( -9 ) = 11 11 times





20 -24 divide ( 12 ) = -2 $2







is -200 ft _______ 10 min



= -15 ftmin







-20 divide 5 = -4 and -20 times 5 = -100

-100 lt -4



negative





incorrectly

29 a divide ( -3 ) = 8

a = -24

8 divide b = -4






integers

LESSON 23

Your Turn


3 ( -30 ) + 200 = -90 + 200

= 110

2 -6 ( 13 ) - 21 = -78 - 21

= -99

4 ( -12 ) divide 6 + 2 = -2 + 2

= 0

5 -87 divide ( -3 ) -9 = 29 - 9

= 20

6 40 divide ( -5 ) + 30 = -8 + 30

= 22

7 -39 divide 3 -15 = -13 - 15

= -28



moved further back

9 ( -10 ) divide 2 - 2 = -5 - 2 = -7

( -28 ) divide 4 + 1 = -7 + 1 = -6

10 42 divide ( -3 ) + 9 = -14 + 9 = -5

( -36 ) divide 9 - 2 = -4 - 2 = -6

Guided Practice

1 -6 ( -5 ) + 12 = 30 + 12

= 42

2 3 ( -6 ) - 3 = -18 - 3

= -21

3 -2 ( 8 ) + 7 = -16 + 7

= -9

4 4 ( -13 ) + 20 = -52 + 20

= -32

5 -4 ( 0 ) - 4 = 0 - 4

= -4

6 -3 ( -5 ) - 16 = 15 - 16

= -1

7 7 ( -5 ) + 20 = -35 + 20

= -15

15 dollars less

8 7 ( -10 ) + ( -100 ) = -70 + ( -100 )

= -170

170 fewer points

9 6 ( -4 ) + 10 = -24 + 10

= -14

Ned lost 14 points

10 4 ( -12 ) + 10 = -48 + 10

= -38

$38 less

11 -3 ( -2 ) + 3 = 6 + 3

= 9

3 ( -4 ) + 9 = -12 + 9

= -3

9 gt -3

-3 ( -2 ) + 3 gt 3 ( -4 ) + 9

12 -8 ( -2 ) -20 = 16 -20

= -4

3 ( -2 ) + 2 = - 6 + 2

= -4

-4 = -4

-8 ( -2 ) -20 = 3 ( -2 ) + 2

13 -7 ( 5 ) - 9 = -35 - 9

= -44

-3 ( 20 ) + 10 = -60 + 10

= -50

-44 gt -50

-7 ( 5 ) -9 gt -3 ( 20 ) + 10

14 -16 ( 0 ) -3 = 0 -3

= -3

-8 ( -2 ) -3 = 16 -3

= 13

-3 lt 13

-16 ( 0 ) -3 lt -8 ( -2 ) -3





16 -12 ( -3 ) + 7 = 36 + 7

= 43

17 -42 divide ( -6 ) + 5 -8 = 7 + 5 -8

= 12 -8

= 4

18 10 ( -60 ) -18 = -600 -18

= -618

19 ( -11 ) ( -7 ) + 5 - 82 = 77 + 5 - 82

= 82 - 82

= 0

20 35 divide ( -7 ) + 6 = -5 + 6

= 1

21 -13 ( -2 ) - 16 - 8 = 26 - 16 - 8

= 10 - 8

= 2

22 a 5 ( 2 ) -12 + 3 = 10 -12 + 3

= -2 + 3

= 1

b -3 ( 2 ) -1 + 6 + 7 = -6 -1 + 6 + 7

= -7 + 6 + 7

= -1 + 7

= 6


the game

23 5 ( -4 ) -8 = -20 - 8 = -28

24 -36 divide ( -4 ) + 9 = 9 + 9 = 18


25 a 4 ( -35 ) -9 = -140 -9

= -149

$149 less

b Yes $200 - $149 = $51 $51 gt $50 so Arleen

has enough money

26 a 2 ( -10 ) + 3 = -20 + 3= -17

b 7 + 2 + ( -7 ) = 2




7 of clubs





had change








MODULE 2

Ready to Go On


will be negative

( -2 ) ( 3 ) = -6


will be positive

( -5 ) ( -7 ) = 35



( 8 ) ( -11 ) = -88

4 ( -3 ) ( 2 ) ( -2 ) = ( -6 ) ( -2 ) = 12

5 5 ( -3 ) = -15 -15degC

6 -63 ____ 7 = -9

7 -15 ____ -3

= 5

8 0 ____ -15

= 0

9 96 ____ -12

= -8

10 -24 divide 6 = -4 -4 Ib

11 ( -4 ) ( 5 ) + 8 = -20 + 8

= -12

12 ( -3 ) ( -6 ) -7 = 18 -7

= 11

13 -27 ____ 9 - 11 = -3 - 11

= -14

14 -24 ____ -3

- ( -2 ) = 8 + 2

= 10




( -3 ) ( 5 ) + 10 = -15 + 10 = -5 He had $05 less

than before



Are You Ready

1 9 ___ 14

times 7 __ 6 =

3

2

9 ___ 14

times 7 __ 6 1

2

= 3 __ 4

2 3 __ 5 times 4 __

7 = 12 ___

35

3 11 ___ 8

times 10 ___ 33

= 1

4

11 ___ 8 times 10 ___

33 5

3

= 5 ___ 12

4 4 __ 9 times 3 =

3

4 __ 9 times 3 __

1 1

= 4 __ 3 or 1 1 __

3

5 1 __ 2 divide 1 __

4 = 1 __

2 times 4 __

1

=

1 1 __ 2 times 4 __

1 2

= 2 __ 1 = 2

6 3 __ 8 divide 13 ___

16 = 3 __

8 times 16 ___

13

= 1 3 __ 8 times 16 ___

13 2

= 6 ___ 13

7 2 __ 5 divide 14 ___

15 = 2 __

5 times 15 ___

14

= 1

1 2 __ 5 times 15 ___

14 3

7

= 3 __ 7

8 4 __ 9 divide 16 ___

27 = 4 __

9 times 27 ___

16

= 1

1 4 __ 9 times 27 ___

16 3

4

= 3 __ 4

9 3 __ 5 divide 5 __

6 = 3 __

5 times 6 __

5

= 18 ___ 25

10 1 __ 4 divide 23 ___

24 = 1 __

4 times 24 ___

23

= 1 1 __ 4 times 24 ___

23 6

= 6 ___ 23

11 6 divide 3 __ 5 = 6 __

1 times 5 __

3

= 2

6 __ 1 times 5 __

3 1

= 10 ___ 1 = 10

12 4 __ 5 divide 10 = 4 __

5 times 1 ___

10

= 2

4 __ 5 times 1 ___

10 5

= 2 ___ 25

13 21 - 6 divide 3

21 - 2

19

14 18 + ( 7 - 4 ) times 3

18 + 3 times 3

18 + 9

27

15 5 + ( 8 - 3 ) 2

5 + ( 5 ) 2

5 + 25

30

16 9 + 18 divide 3 + 10

9 + 6 + 10

15 + 10

25

17 60 - ( 3 - 1 ) 4 times 3

60 - ( 2 ) 4 times 3

60 - 16 times 3

60 - 48

12

18 10 - 16 divide 4 times 2 + 6

10 - 4 times 2 + 6

10 - 8 + 6

2 + 6

8

LESSON 31

Your Turn

0 _

571428

4 7 ⟌ _


_ -35

50

_ -49

10

_ -7

30

_ -28

20

_ -14

60

_ -56




-0 _

571428 or -0571428571428hellip


0 _ 3

5 3 ⟌ _


_ -3




0333hellip

045

6 20 ⟌ _

900

_ -8 0

1 00

_ -1 00

0

-045

7 -2 3 __ 4 = -thinsp 4 times 2 + 3

_________ 4 = -11 ____

4

275

4 ⟌ _

1100

_ -8

30

_ -28

20

_ -20

0

-275 terminating

8 7 1 __ 3 =

3 times 7 + 1 _________

3 = 22 ___

3

7 _ 3

3 ⟌ _


_ -21





Guided Practice

06

1 5 ⟌ _

30

_ -3 0

0

06 terminating

089

2 100 ⟌ _

8900

_ -80 0

9 00

_ -9 00

0

-089 terminating


4 ___ 12

= 4 times 1 _____ 4 times 3

= 1 __ 3

0 _ 3

3 ⟌ _


_ -3





0 _

25

4 99 ⟌ _


_ -19 8

520

_ -495




25 or


0 _ 7

5 9 ⟌ _


_ -63





036

6 25 ⟌ _

900

_ -7 5

1 50

_ -1 50

0

-036 terminating

004

7 25 ⟌ _

100

_ -1 00

0

004 terminating

01420 _

45

8 176 ⟌ _

250000000

_ -17 6

7 40

_ -7 04

360

_ -352

80

_ -0


_ -704

960

_ -880




-01420 _


0012

9 1000 ⟌ _

12000

_ -10 00

2 000

_ -2 000

0

0012 terminating


10 -11 1 __ 6 = -thinsp 6 times 11 + 1

_________ 6 = -67 ____

6

111 _ 6

6 ⟌ _

67000

_ -6

07

_ -6

1 0

_ -6


_ -36




- 67 ___ 6

-111 _ 6 or -111666hellip

11 2 9 ___ 10

= 10 times 2 + 9

__________ 10

= 29 ___ 10

29

10 ⟌ _

290

_ -20

9 0

_ -9 0

0

29 ___ 10

29

12 -8 23 ____ 100

= - 100 times 8 + 23

____________ 100

= -823 _____ 100

823

100 ⟌ _

82300

_ -800

23 0

_ -20 0

3 00

_ -3 00

0

-823 _____ 100

-823

13 7 3 ___ 15

= 15 times 7 + 3

__________ 15

= 108 ____ 15

72

15 ⟌ _

1080

_ -105

3 0

_ -3 0

0

108 ____ 15

72

14 54 3 ___ 11

= 11 times 54 + 3

__________ 11

= 597 ____ 11

54 _

27

11 ⟌ _

597000

_ -55

47

_ -44


_ -22

80

_ -77




597 ____ 11

54 _

27 or 542727hellip

15 -3 1 ___ 18

= -thinsp 18 times 3 + 1 __________

18 = -55 ____

18

30 _ 5

18 ⟌ _

55000

_ -54

1 0

_ -0


_ -90




-55 ____ 18

-30 _ 5 or -30555hellip

16 3 2 __ 3 =

3 times 3 + 2 _________

3 = 11 ___

3

3 _ 6

3 ⟌ _

1100

_ -9


_ -1 8





17 -2 7 __ 8 = -

8 times 2 + 7 _________

8 = -23 ____

8

2875

8 ⟌ _

23000

_ -16

7 0

_ -6 4

60

_ -56

40

_ -40

0

-2875 lb




3 ___ 47








= 5 ___ 11

0 _

45

11 ⟌ _


_ -4 4

60

_ -55




5 ___ 11

0 _


20 hockey players


= 6 ___ 10

06

10 ⟌ _

60

_ -6 0

0

6 ___ 10

06 terminating

21 polo players


= 4 ___ 11

036

11 ⟌ _


_ -3 3

70

_ -66




4 ___ 11

0 _


22 lacrosse players


= 10 ___ 15

= 5 times 2 _____ 5 times 3

= 2 __ 3

0 _ 6

3 ⟌ _


_ -1 8




10 ___ 15


23 football players


= 11 ___ 11

= 1

11 ___ 11

1 terminating







25 a -4 7 __ 8 = -thinsp 8 times 4 + 7

_________ 8 = - 39 ___

8

b 4875

8 ⟌ _

39000

_ -32

7 0

_ -6 4

60

_ -56

40

_ -40

0

-4875








is equal

to 85 ___ 16


is

equal to 127 ____ 24

or 52916hellip ft




















090625











0121212hellip


LESSON 32

Your Turn

2

50 1 2 3 4

3 + 1 1 __ 2 = 4 1 __

2

3

0-7 -6 -5 -4 -3 -2 -1

-25 + ( -45 ) = -7

6

0 1 2-5-6-7-8 -4 -3-2-1

-8 + 5 = -3

7

10-1

1 __ 2 + ( - 3 __

4 ) = - 1 __

4

8

3 4 5 6 7 80 1 2-3-2-1

-1 + 7 = 6

9

3 4 50 1 2-5-4 -3-2-1

2 1 __ 2 + ( -2 1 __

2 ) = 0

10

3 4 50 1 2-5-4 -3-2-1

-45 + 45 = 0

11

1-1 0

3 __ 4 + ( - 3 __

4 ) = 0


12 -15 + 35 + 2

-15 + 55

55 - 15

4

13 3 1 __ 4 + ( -2 ) + ( -2 1 __

4 )

3 1 __ 4 + ( -4 1 __

4 )

3 1 __ 4 - 4 1 __

4

-1

14 -275 + ( 325 ) + 5

-6 + 5

-1

15 15 + 8 + ( -3 )

23 + 3

20

Guided Practice

1

3 4 50 1 2-5-4 -3-2-1

-3 + ( -15 ) = -45

2

0 54321-5-4-3-2-1

15 + 35 = 5

3

0 105-1 -05

1 __ 4 + 1 __

2 = 3 __

4

4

0 54321-5-4-3-2-1

-1 1 __ 2 + ( -1 1 __

2 ) = -3

5

0 54321-5-4-3-2-1

3 + ( -5 ) = -2

6

0 54321-5-4-3-2-1

-15 + 4 = 25

7 -2150 + 2150 = 0 $0

8 -874 + 874 = 0 $0

9 275 + ( -2 ) + ( -525 )

275 + ( -725 )

- ( 725 - 275 )

-45

10 -3 + 1 1 __ 2 + 2 1 __

2 = -3 + 4 = 1

11 124 + 92 + 1

-124 + 102

- ( 124 - 102 )

-22

12 -12 + 8 +13

-12 + 21

21 - 12

9

13 45 + ( -12 ) + ( -45 )

45 + ( -45 ) + ( -12 )

0 + ( -12 )

-12

14 1 __ 4 + ( - 3 __

4 ) = - ( 3 __

4 - 1 __

4 ) = - 2 __

4 = - 1 __

2


15 -4 1 __ 2 + 2 = - ( 4 1 __

2 - 2 ) = -2 1 __

2

16 -8 + ( -1 1 __ 8 ) = -9 1 __

8


The sum is 2



19 -$225 + $1500 = $1500 - $225 = $1275

20 -3525 m + ( -85 ) = -4375 m

21 4 3 __ 4 mi + ( -3 1 __

4 mi ) = 1 2 __

4 mi = 1 1 __

2 mi


23 30 + 15 - 25 = 45 - 25 = 20 pts

24 January

Income - Expenses

$1205 - $129060

- ( $129060 - $1205 ) -$8560

February

Income - Expenses

$1183 - $134544

-($134544 - $1183)

-$16244


February

25 June

Income - Expenses

$2413 - $210623

$30677

July

Income - Expenses

$2260 - $195850

$30150

August

Income - Expenses

$2183 - $184512

$33788


$33788 in August






the end of August

Income = $1205 + $1183 + $1664 + $2413

$2260 + $2183 = $10908

Expenses = $129060 + $134544 + $1664 +$210623 + $195850 + $184512

= $1020989

Profit = $10908 - $1020989 + $250

= $94811


28 a 7 ( 10 ) + 3 ( -15 ) = 70 - 45 = 25 pts

b 2 ( 10 ) + 8 ( -15 ) = 20 - 120 = -100 pts








the positive number







LESSON 33

Your Turn

1

-9 -8 -7 -6 -5 -4

-65 - 2 = -85

2

42 30-1 1

1 1 __ 2 - 2 = - 1 __

2

3

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0

-225 - 55 = -775

6

1 2-1 0

025 - ( -150 ) = 175

7

1-1 0

- 1 __ 2 - ( - 3 __

4 ) = 1 __

4

Guided Practice

1

1312111098765 14 15

5 - ( -8 ) = 13

2

-9 -8 -7 -6 -5 -4 -3

3 1 __ 2 - 4 1 __

2 = -8


3

-15 -13 -11 -9 -5-7

-7 - 4 = -11

4

-6 -5 -4 -3 -2 -1 0 1

-05 - 35 = -4

5 -14 - 22 = -36

6 -125 - ( -48 )

-125 + 48

- ( 125 - 48 )

-77

7 1 __ 3 - ( - 2 __

3 ) = 1 __

3 + 2 __

3 = 1

8 65 - ( -14 ) = 65 + 14 = 79

9 - 2 __ 9

- ( -3 )

- 2 __ 9

+ 3

3 - 2 __ 9

2 9 __ 9 - 2 __

9

2 7 __ 9

10 24 3 __ 8

- ( -54 1 __ 8 )

24 3 __ 8

+ 54 1 __ 8

78 4 __ 8

78 1 __ 2

11 -1 m + ( 105 m ) = -15 m


12 -12 1 __ 2 + ( -5 ) = -17 1 __

2

17 1 __ 2

or 175 yards


533 ft - ( -10 ft ) = 533 ft + 10 ft = 543 ft

14 -4500 + (-3015) = -7515 $7515






16 -126degC - 75degC = -201degC

17 -2565 ft - 165 ft + 1245 ft = -297 ft


18 -9500 ft - ( -26000 ft ) = 16500 ft

19 29035 ft - ( -36198 ft ) = 65233 ft

70000 ft - ( -26000 ft ) = 96000 ft


96000 ft - ( 65233 ft ) = 30767 ft


b 78degF - 32degF


21 a -$1258 + ( -$3072 ) = -$4330

b -$4330 + ( -$25 ) = -$6830

c $6830 since -$6830 + $6830 = 0



23 a 5 ft - 72 ft + 22 ft

b 5 ft - 72 ft + 22 ft

5 ft + 22 ft - 72 ft

72 ft - 72 ft



24 a Yes

$425 + $089 + $1099

= $1613 lt $20

b $20 - $1613 = $387 left over





- 7 ___ 16

- 1 __ 4 - 5 ___

16 = ( - 7 ___

16 ) + ( - 1 __

4 ) + ( - 5 ___

16 )

( - 7 ___ 16

) + ( - 5 ___ 16

) + ( - 1 __ 4 ) by CPA

( -7 + ( -5 ) __________

16 ) + ( - 1 __

4 )

( -12 ____ 16

) + ( - 1 __ 4 )

( - 4 times 3 _____ 4 times 4

) + ( - 1 __ 4 )

( - 3 __ 4 ) + ( - 1 __

4 )

( -3 + ( -1 ) __________

4 )

( -4 ___ 4 ) = -1





and c __ d

Both fractions









LESSON 34

Your Turn

1

-8 -7 -6 -5 -2 -1 0-4 -3

2 ( -35 ) = -7

2

-2 -1 0 1 2 3 4-4 -3

-3 ( -125 ) = 375

4 ( - 3 __ 4 ) ( - 4 __

7 ) ( - 2 __

3 ) = -



= - 2 __ 7

5 ( - 2 __ 3 ) ( - 3 __

4 ) ( 4 __


__________ 13 times 41 times 5


= 2 __ 5

6 ( 2 __ 3 ) ( - 9 ___

10 ) ( 5 __

6 ) = -


____________ 13 times 210 times 63


= - 1 __ 2

Guided Practice

1

-5 -2 -1 0-4 -3

5 ( - 2 __ 3 ) = 5 __

1 times ( - 2 __

3 )

= - 5 times 2 _____ 1 times 3

= - 10 ___ 3

= -3 1 __ 3

2

-1 -05 0-2 -15

3 ( - 1 __ 4 ) = 3 __

1 times - 1 __

4

= - 3 times 1 _____ 1 times 4

= - 3 __ 4

3

0 1 2-2 -1

-3 ( - 4 __ 7 ) = 3 __

1 times 4 __

7

= 3 times 4 _____ 1 times 7

= 12 ___ 7

= 1 5 __ 7

4

-2 -1 0 1 2 3 4-4 -3

- 3 __ 4 ( -4 ) = 3 __

4 times 4 __

1

= 3 times 41

______ 14 times 1

= 3 times 1 _____ 1 times 1

= 3 __ 1

= 3

5 4 ( -3 ) = -12

6 -18 ( 5 ) = -9

7 -2 ( -34 ) = 68

8 054 ( 8 ) = 432

9 -5 ( -12 ) = 6

10 -24 ( 3 ) = -72

11 1 __ 2 times 2 __

3 times 3 __

4 = ( 1 times 21

______ 12 times 3

) ( 3 __ 4 )

= ( 1 __ 3 ) ( 3 __

4 )

= 1

1 __ 3 times 3 __

4 1

= 1 __ 4

12 - 4 __ 7 ( -thinsp 3 __

5 ) ( - 7 __

3 ) = ( - 4 times 3 _____

7 times 5 ) ( - 7 __

3 )

= 12 ___ 35

( - 7 __ 3 )

= - 4

5 12 times 7 ______ 35 times 3

1

1

= - 4 times 1 _____ 5 times 1

= - 4 __ 5

13 ( - 1 __ 8 ) times 5 times 2 __

3 = ( - 1 __

8 ) times 5 __

1 times 2 __

3


__________ 48 times 1 times 3


= - 5 ___ 12


14 ( - 2 __ 3

) ( 1 __ 2 ) ( - 6 __


__________ 13 times 21 times 7


= 2 __ 7


16 18 ( -100 ) = -1800 or a $1800 change









amount

b 200 + 6 ( -1998 )

= 200 - 11988

= 8012 $8012





which is 6

20 8 ( -3 1 __ 4 ) = -8 ( 13 ___

4 )

= - 1

8 __ 1 times 13 ___

4 1

= - 2 times 13 ______ 1 times 1

= - 26 ___ 1





(below the surface)

22 5 + ( -3 ) ( 15 )

= 5 + ( -45 )

= 05 cups left





a positive



25 Total score is

2 times ( 6 ) + 16 times ( 05 )

+ 7 times ( -05 ) + 2 times ( -15 )

= 12 + 8 - 35 - 3

= 20 - 65

= 135 pts




= 12 + 5 ( -68 )

= 12 + ( -34 )

= -22degC

27 a b c d

+ + + +

+ + - +

+ - + +

- + + +

- - - +

- - + -

- + - -

+ - - -









LESSON 35

Your Turn

3 28 ___ -4

= - 28 ___ 4 = -07

4 -664 ______ -04

= 664 ____ 04

= 166

5 - 55 ___ 05

= - 55 ___ 5 = -11

6 -4256 _______ 112

= -38


per minute

7 - 5 __

8 ___

- 6 __ 7 = - 5 __

8 divide - 6 __

7

= - 5 __ 8 times - 7 __

6

= 35 ___ 48

8 - 5 ___

12 ____

2 __ 3 = - 5 ___

12 divide 2 __

3

= - 5 ___ 12

times 3 __ 2

= - 15 ___ 24

= - 5 __ 8


9 -4__5

___1__2 =-4__5divide1__

2

=-4__5times2__1

=-8__5

=-13__5

Guided Practice

1 072_____-09=-72___

9 =-08

2 -1__5

___7__5 =-1__

15times5

1__

7=-1times1_____

1times7=-1__7

3 56___-7=-56___7=-8

4 251____4 divide(-3__

8)=251____

4 times-8__

3

=-251times82________

14times3


=-502____3

5 75____-1__5

=-75___1times5__

1=-75times5______

1times1=-375

6 -91____-13=91___

13=7

7 -3__7

___9__4 =-

13__7times4__93


=-4___21

8 - 12____003

=-1200_____

3 =-400


changeindays

=-35L______4day

=-0875 L____day

or-0875Lperday


changeindays

=-$4575________5day



numberofminutes

=-044mi________08min

=-44mi______8min

=-055mileperminute



13 5___-2__

8=-5__

1times8__

24

1=-5times4_____

1times1=-20

14 51__3divide(-11__

2)


2

=-16___3divide3__

2

=-16___3times2__

3


=-32___9

15 -120_____-6 =120____

6 =20

16 -4__5

___-2__

3=

24__5times3__

21=2times3_____

5times1=6__

5

17 103divide(-103)=-103____1 times 1____

103

=-103times1________1times103

=-103____103

=-103____103

=-01

18 -04_____80

=-04___80

=-0005

19 1divide9__5=1__

1times5__

9=5__

9

20 -1___4 ___

23___24

=-1__

14times246

___23


=-6___23

21 -1035_______-23 =1035_____

23 =45


= 21h______7days

=3 h____day


times3days=9hours




=-4times15+3___________4 times1__

9

yd___run

=-763___4 times1__

91yd

___run

=-153__

4yd______

9runs

=-153__4times1__

9

yd___run

=-7__4or-13__

4yardsperrun





_____________________________________ 4

= 414degC ______ 4

= -1035degC per day

25 a total profit


= $1750

______ 7 days

= $250 per day

b $150

_____ day


c total change


= - $490

______ 7 days

= -$70 per day


= 996 m ______ 12 s

= 83 ms





- 3 __

4 ___

4 __ 3

= - 3 __

4 times 3 __

4 = - 9 ___

16



= -629 m





-85degF divide 15 d

= - 1785 ____ 315

degF __ d

= - 17 ___ 3 degF __

d or -5 2 __

3 degF __


d


every day





definition

LESSON 36

Your Turn


3 times 2 1 __ 2 = 7 1 __

2


30 - 7 1 __ 2 = 22 1 __

2


22 1 __ 2 divide 4 = 5 5 __

8











12 3 __ 5 = 126

= 0126


750 times 0126 = 945

750 + 945 = 8445


8445 times 0126 asymp 10641

8445 + 10641 = 95091


95091 times 0126 asymp 11981

95091 + 11981 = 107072


Guided Practice











78 times 3 = 234


234 divide 4 = 585




12 - 3 1 __ 2 = 8 1 __

2

Find half the width

8 1 __ 2 divide 2 = 4 1 __

4


of the page


11 times 1 __ 3 = 3 2 __

3

10 times 3 __ 4 = 7 1 __

2

3 2 __ 3 + 7 1 __

2 = 11 1 __

6


box

11 1 __ 6 lt 12





41 3 __ 4 divide 2 = 20 7 __

8


50 - 20 7 __ 8 = 29 1 __

8




( 78 + 10 ) = 88


88 = 88 ____ 100

= 44 ___ 50


Donovan

44 - 39 = 5


Donovan







19 ___ 37


15 times ( - 1 __ 2 ) = -075







-79 9 ___ 10

divide ( -188 ) = 425


19 1 __ 8 - 1275 - 425 = 2 1 __

8


-28 9 ___ 10

- ( -79 9 ___ 10

) = 51


51 divide 2 1 __ 8 = 24


ascent was 24 ftmin

15 Sample answer



the result by 037



(276 + 159)037 = (276)(037) + (159)(037)




make errors








MODULE 3

Ready to Go On

1 4 1 __ 5 =

5 times 4 + 1 _________

5 = 21 ___

5

42

5 ⟌ _

210

_ -20

1 0

_ -1 0

0

42


2 12 14 ___ 15

= 15 times 12 + 14

___________ 15

= 194 ____ 15

129 _ 3

15 ⟌ _

194000

_ -15

44

_ -30

14 0

_ -13 5

50 first 50

_ -45

50 second 50



129 _ 3 or 12933

3 5 5 ___ 32

= 32 times 5 + 5

__________ 32

= 165 ____ 32

515625

32 ⟌ _

16500000

_ -160

5 0

_ -3 2

1 80

_ -1 60

200

_ -192

80

_ -64

160

_ -160

0

515625

4 45 + 71 = 116

5 5 1 __ 6 + ( -3 5 __

6 ) = 4

6+1 ____

6 -3 5 __

6

= 1 2 __ 6

= 1 1 __ 3

6 - 1 __ 8 -6 7 __

8 = - 1 __

8 + ( -6 7 __

8 )

= -6 8 __ 8

= -7

7 142 - ( -49 ) = 142 + 49

= 191

8 -4 ( 7 ___ 10

) = - 4 __ 1 times 7 ___

10

= - 24 times 7 _______ 1 times 105

= - 2 times 7 _____ 1 times 5

= - 14 ___ 5 or -2 4 __

5

9 -32 ( -56 ) ( 4 ) = 32 times 56 times 4

= 7168

10 - 19 ___ 2 divide 38 ___

7 = -

119 times 7 _______ 2 times 382

= - 1 times 7 _____ 2 times 2

= - 7 __ 4

11 -3201 _______ -33

= 3201 _____ 33

97

33 ⟌ _

3201

_ -297

23 1

_ -23 1

0

97


second day

$8360 + $1535 = $9895


-4 3 __ 4 = -475 or -00475




price

$9895 times -00475 asymp -$47

$9895 - $47 = $9425






prices



Are You Ready

1 3 __ 4 divide 4 __

5 = 3 __

4 times 5 __

4

= 15 ___ 16

2 5 __ 9 divide 10 ___

11 = 5 __

9 times 11 ___

10

= 1

5 __ 9 times 11 ___

10 2

= 11 ___ 18

3 3 __ 8 divide 1 __

2 = 3 __

8 times 2 __

1

= 4

3 __ 8 times 2 __

1 1

= 3 __ 4

4 16 ___ 21

divide 8 __ 9 = 16 ___

21 times 9 __

8

=thinsp 2

7 16 ___ 21

times 9 __ 8 3

1

= 6 __ 7

5 B ( -4 1 )

6 C ( 3 0 )

7 D ( 5 4 )

8 E ( -2 -2 )

9 F ( 0 0 )

10 G ( 0 -4 )

LESSON 41

Your Turn

3 1 __ 6 acre divide ( 1 __

4 hour ) = 1 __

6 times 4 __

1

= 3


2

= 1 times 2 _____ 3 times 1


4 3 cups divide ( 3 __ 4 cups ) = 3 __

1 divide 3 __

4

= 3 __ 1 times 4 __

3

= 1


1

= 1 times 4 _____ 1 times 1

= 4 cups


5 = 3 __

4 times 5 __

1 = 15 ___

4 = 3 3 __

4


6 = 2 ___

1 3 times 6

2 __

1 = 4 __

1 = 4






flavor

Guided Practice

1

Distance (mi) 8 1 __ 2 17 25 1 __

2 34 42 1 __

2

Time (h) 1 __ 2 1 1 1 __

2 2 2 1 __

2

2 3 1 __ 2 miles divide ( 1 1 __

4 hours ) = 7 __

2 divide 5 __

4 mi ___ h

= 7 times 4 _____ 2 times 5

= 1 7 times 4 _____ 2 times 5

2

= 7 times 2 _____ 1 times 5

= 14 ___ 5 mi ___

h


3 5 __ 8 page divide ( 2 __

3 minute ) = 5 __

8 times 3 __

2

= 15 ___ 16

page per minute

4 1 __ 6 foot divide ( 1 __

3 hour ) = 1 __

6 times 3 __

1

= 2 1 times 3 _____ 6 times 1

1

= 1 times 1 _____ 2 times 1


5 5 __ 8 sq ft divide ( 1 __

4 hour ) = 5 __

8 times 4 __

1

= 2 5 times 4 _____ 8 times 1

1

= 5 times 1 _____ 2 times 1

= 5 __ 2 or 2 1 __



UNIT

2



1 divide 1 __

3

= 240 ____ 1 times 3 __

1

= 720 ____ 1



1 divide 1 __

2

= 325 ____ 1 times 2 __

1

= 650 ____ 1




1 __ 4 cup divide ( 2 __

3 serving ) = 1 __

4 times 3 __

2

= 3 __ 8

cup _______

serving


1 __ 3 cup divide ( 3 __

4 serving ) = 1 __

3 times 4 __

3

= 4 __ 9

cup _______

serving




72 and 4 __

9 = 32 ___

72




the rate


1 __ 2 hour

= 1 __




$10 divide ( 35 hours ) = 10 ___ 35

$ __



$125 divide ( 1 __ 2 hours ) = 125 ____

05 $ __





multiply by 60


= 005 ____ 1

$ ____


1 h

= $3 per hour



one


8 cup






originally

c 1 __ 2 divide 1 __

8 = 1 ___

1 2 times 8

4 __

1 = 4 __

1 = 4


sunflower seeds

11 10 songs


= 5 songs ____________

1 commercials


6 mi divide ( 1 __ 2 h ) = 6 __

1 times 2 __

1

= 12 miles per hour

Jessersquos rate


4

= 2 __ 1 times 4 __

1 mi ___ h

= 8 miles per hour

b Terrance

50 mi divide ( 12 mi ___ h ) = 50 ___

1 times 1 ___

12

= 50 ___ 12

h

= 4 1 __ 6 h

= 4 10 ___ 60

h


Jesse

50 mi divide ( 8 mi ___ h ) = 50 ___

1 times 1 __

8

= 50 ___ 8 h

= 6 1 __ 4 h

= 6 15 ___ 60

h



4

= 8 __ 1 times 4 __

3

= 32 ___ 3





13 1 ___ 10

h = 6 ___ 60

h = 6 min

300 words _________ 6 min

= 50 words per min

1 ___ 12

h = 5 ___ 60

h = 5 min

300 words _________ 5 min

= 60 words per min










b For the 10-pack



For the 12-pack








2 day ) = 1 room _____

day so at the same





LESSON 42

Your Turn


was not constant




= 12 ___ 1 = 36 ___

3 = 60 ___




s or s = 12a

Guided Practice

1 45 ___ 1 = 45 90 ___

2 = 45 135 ____

3 = 45 180 ____

4 = 45


2 k = y __ x = 10 ___

2 = 5 y = 5x

3 k = y __ x = 2 __

8 = 1 __

4 y = 1 __

4 x


of proportionality


5 k = y __ x = 74 ___

4 = 1850 y = 1850x

6 $1099

_______ 05 days

= $2198 per day


($1850)

8 100 ft _____ 08 s

= 1000 _____ 8 ft __ s = 125 ft __ s

500 ft _____ 31 s

= 5000 _____ 31


1875 ft ______ 15 s

= 1875 ______ 15





9 $3125

______ 5 h


______ 8 h

= $625 per







12 y = $625 ( 3 ) = $1875

13 300 ft _____ 2 min

= 6750

_____ 45


150 ft _____ min

times 60 min ______ 1 h


14 y = 150x



hours




same factor




of corn

LESSON 43

Your Turn

1 No because 11 ___ 1 ne 16 ___





b k = 60 mi _____ 4 h

= 15 mi ___ h


distance in miles

Guided Practice

1

Time (h) 3 5 9 10

Pages 195 325 585 650


per hour

2

Time (h) 2 3 5 8

Earnings 15 2250 3750 60








5 k = 28 ft ____ 8 s

= 7 __ 2 ft __ s = 35 ft __ s y = 7 __



6 k = $2 ______

8 items = 1 __

4

$ _____

items = 025

$ _____

items so y = 1 __

4 x or


y = cost in dollars


origin



0 minutes





x or 2 __ 5 x




5 = 48




2

2

4

6

8

10

4 6 8 10Time (min)

Dis

tanc

e (m

i)

A

B

O








equation

15 a

2

8

16

24

32

40

4 6 8 10DVDs

Cost

($)

O



cost $20






18 k = 8 ft ___ 4 s










because 65 ___ 1 ne 85 ___

2





distance column

MODULE 4

Ready to Go On

1 $140

_____ 18 ft 2


2 $299

_____ 14 lb


3 $56 ______


$3205

______ 15 gal


4 $160

_____ 5 g


$315

_____ 9 g




3


6 k = $9

___ 8euro

= $27 ____

24euro = 9 __

8 $ __

euro or 1125

$ __

euro So y = 9 __

8 x or





_______ pt

or k = 25 servings

_______ pt

Therefore

y = 5 __ 2




2

2

4

6

8

10

4 6 8 10Pints

Serv

ings

Frozen Yogurt

O





constant rate



Are You Ready

1 22 = 22 ____ 100

= 022

2 75 = 75 ____ 100

= 075

3 6 = 6 ____ 100

= 006

4 189 = 100 + 89

= 100 ____ 100

+ 89 ____ 100

= 1 + 089

= 189

5 059 = 59

6 098 = 98

7 002 = 2

8 133 = 133

9 64

_ timesthinsp05

320

32

10 30

_ timesthinsp007

210

21

11 160

_ timesthinsp015

800

_ +1600

2400

24

12 62

_ timesthinsp032

124

_ +thinsp1860

1984

1984

13 4

_ timesthinsp12

8

_ +thinsp40

48

48

14 1000

_ timesthinsp006

6000

60

LESSON 51

Your Turn

2 x = ( $64 - 52 )

__________ $52

x = $12

____ $52

asymp 23

4 x = ( 18 - 12 )

________ 18

x = 6 ___ 18

asymp 33

5 x = ( 16 - 10 )

________ 16

x = 6 ___ 16

= 375

8 010 times $499 = $4990

$499 + $4990 = $54890

9 030 times $499 = $14970

$499 - $14970 = $34930

Guided Practice

1 x = ( $8 - $5 )

_________ $5

x = $3

___ $5

= 60

2 x = ( 30 - 20 )

_________ 20

x = 10 ___ 20

= 50

3 x = ( 150 - 86 )

__________ 86

x = 64 ___ 86

asymp 74

4 x = ( $389 - $349 )

______________ $349

x = $040

_____ $349

asymp 11

5 x = ( 14 - 13 )

________ 13

x = 1 ___ 13

asymp 8

6 x = ( 16 - 5 )

________ 5

x = 11 ___ 5 = 220

7 x = ( 64 - 36 )

_________ 36

x = 28 ___ 36

asymp 78

8 x = ( 80 - 64 )

_________ 80

x = 16 ___ 80

= 20

9 x = ( 95 - 68 )

_________ 95

x = 27 ___ 95

asymp 28


10 x=( 90-45)_________

90

x=45___90

=50

11 x=( 145-132)__________

145

x=13____145

asymp9

12 x=( 64-21)_________

64

x=43___64

asymp67

13 x=( 16-0)________

16

x=16___16

=100

14 x=( 3-1__

2)_______

3

x=21__

2___

3 asymp83

15 010times$900=$090 $900+$090=$990

16 025times48=12 48-12=36cookies

17 020times340=68 $340-68=272pages

18 050times28=14 28+14=42members

19 004times$29000=$1160 $29000-$1160=$27840

20 130times810=1053 810+1053=1863songs

21 030times20=6 20+6=26miles



ItemOriginal

PriceNew Price

Percent Change

Increase or





24 a 55

x=( 8-3)_______

8 =5__

8=625

x=( 12-7)________

12 =5___

12asymp417



x=( 12-3)________

3

x=9__3=300increase



b $100_____5 =$020each$100_____

4 =$025each



=25

26 Percenterror=( 136-133)___________

136 times100

=03____136

times100asymp2







LESSON 52

Your Turn

2 a 1c+01c11c

b s=11times$28=$3080

3 a 200

b 1c+2c3c

5 a

1b - 024b

1b024b

b 1b-024b=076b

6 a 1p-005p095p

b 095p=$1425




Guided Practice

1 a 035s

b 1s + 035s 135s

c 135 times $3200 = $4320

d 035 times $3200 = $1120


Price

2 Hat $18 15 $270 $2070

3 Book $2250 42 $945 $3195

4 Shirt $3375 75 $2531 $5906

5 Shoes $7499 33 $2475 $9974

6 Clock $4860 100 $4860 $9720

7 Painting $18500 125 $23125 $41625

8 $4500 - 022 ( $4500 ) = $3510

9 $8900 - 033 ( $8900 ) = $5963

10 $2399 - 044 ( $2399 ) = $1343

11 $27999 - 075 ( $27999 ) = $7000





13 a 046b

b 1b - 046b 054b

c 054 times $2900 = $1566

d 046 times $2900 = $1334


Sale Price $201

Regular Price $419

Sale Price $245

Regular Price $279

Sale Price $115

Regular Price $309

Sale Price $272

Regular Price $377

Sale Price $224


$050


$9950


$350

16 p = 127 ( $7400 ) = $9398

s = 127 ( $4800 ) = $6096

j = 127 ( $32500 ) = $41275

2 ( 9398 ) + 3 ( $6096 ) + $41275 = $78359









greater




the coat

LESSON 53

Your Turn

1 005 times $2000 = $100 $100 + $2000 = $2100

3 005 times $40000 = $2000

$2000 times 4 years = $8000

$40000 + $8000 = $48000


Total $2200 + $16875 = $236875

Guided Practice

1 005 times $3000 = $150

2 015 times $7000 = $1050

3 0004 times $10000 = $040

4 15 times $2200 = $3300

5 001 times $8000 = $080

6 20 times $500 = $1000

7 a 007 times $4399 = $308

b $4399 + $308 = $4707

8 115 times $7550 = $8683

9 007 times $2000 = $140


10 003 times $550 = $1650

$1650 times 10 years = $165

$550 + $165 = $715

11 a 090 times $20 = $18

b 1085 times $18 = $1953

12 020 times $2999 = $600 tip

00625 times $2999 = $187 tax

$2999 + $600 + $187 = $3786 total



to the price


14 $3275 + $3988 = $7263 total meal cost

014 times $7263 = $1017 tip

$7263 + $1017 = $8280 total with tip


$7865 times 020 = $1573 tip

$7865 + $1573 - $1180 = $8258 total


0075 times $29375 = $2203 tax

$29375 + $2203 = $31578 total with tax


17 $7999 times 012 = $960 discount

$7999 - $960 = $7039 price before tax





19 $4500 + 00725 = $32625 commission

$750 + $32625 = $107625 total income


$475 + $3850 = $51350 total income










nearest inch

22 a $4998 times 05 = $2499 50 discount

$2499 - $1000 = $1499 $10 discount

b $4998 - $1000 = $3998 $10 discount

$3998 times 05 = $1999 50 discount


$8550 + $1599 = $10149 total


$95 + $1439 = $10939 total



d $10149 times 008 = $812 tax

$10149 + $812 = $10961 total

24 a Store 1 $22 divide 2 = $11

Store 2 $1299 times 09 = $1169




b Store 3 $2098 times 045 = $944






to $2050 per month


____________ 137

times 100 = 05 ____ 137

asymp 36

MODULE 5

Ready to Go On

1 x = ( 63 - 36 )

_________ 36

x = 27 ___ 36

= 75 increase

2 x = ( 50 - 35 )

_________ 50

x = 15 ___ 50

= 30 decrease

3 x = ( 72 - 40 )

_________ 40

x = 32 ___ 40

= 80 increase

4 x = ( 92 - 69 )

_________ 92

x = 23 ___ 92

= 25 decrease

5 $60 times 015 = $9

$60 + $9 = $69

6 $32 times 0125 = $4

$32 + $4 = $36

7 $50 times 022 = $11

$50 - $11 = $39

8 $125 times 030 = $3750

$12500 - $3750 = $8750


$325 + $312 = $637 total income

10 $5310

______ $1735

asymp 31



$700 times 020 = $140

$700 + $140 = $840


5 less than Priya

$840 times 005 = $042

$840 - $042 = $798





$45 times 026 = $1170

$45 + $1170 = $5670






Are You Ready

1 5 + x

2 11 - n

3 -9 ___ y

4 2x - 13

5 2x + 3

= 2 ( 3 ) + 3

= 6 + 3

= 9

6 -4x + 7

= -4 ( 1 ) + 7

= -4 + 7

= 11

7 15x - 25

= 15 ( 3 ) - 25

= 45 - 25

= 2

8 04x + 61

= 04 ( -5 ) + 61

= -20 + 61

= 41

9 2 __ 3 x - 12

= 2 __ 3

( 18 ) - 12

= 2 __ 3

times ( 18 ___ 1 ) - 12

= 36 ___ 3 - 12

= 0

10 - 5 __ 8

x + 10

= - 5 __ 8 ( -8 ) + 10

= - 5 __ 8 times- 8 __

1 + 10

= - 5 ___ 1 8

times- 8 1 __

1 + 10

= - 5 __ 1 times- 1 __

1 + 10

= 5 + 10

= 15

11 1 __ 2 divide 1 __

4

= 1 times 4 _____ 2 times 1

= 1 times 4 2 ______

1 2 times 1

= 1 times 2 _____ 1 times 1

= 2

12 3 __ 8 divide 13 ___

16

= 3 __ 8 times 16 ___

13

= 3 times 16 2 _______

1 8 times 13

= 3 times 2 ______ 1 times 13

= 6 ___ 13

13 2 __ 5 divide 14 ___

15

= 2 __ 5 times 15 ___

14

= 1 2 times 15

3 ________

1 5 times 14 7

= 1 times 3 _____ 1 times 7

= 3 __ 7

14 4 __ 9 divide 16 ___

27

= 4 __ 9 times 27 ___

16

= 1 4 times 27

3 ________

1 9 times 16 4

= 1 times 3 _____ 1 times 4

= 3 __ 4

LESSON 61

Your Turn

2 ( 3x + 1 __ 2 ) + ( 7x - 4 1 __

2 )

= 3x + 7x + 1 __ 2 - 4 1 __

2

= 10x - 4

3 ( -025x - 3 ) - ( 15x + 14 ) = -025x - 3 - 15x - 14

= -175x - 44

4 02(3b - 15c) + 6c

= 06b - 3c + 6c

= 06b + 3c

5 2 __ 3 (6e + 9f - 21g) - 7f

= 4e + 6f - 14g - 7f

= 4e - f - 14g

6 5x - 3(x - 2) - x

= 5x - 3x + 6 - x

= x + 6

7 83 + 34y - 05(12y - 7)

= 83 + 34y - 6y + 35

= 118 - 26y


UNIT

3


Guided Practice


14 + 12n + 23 + 16n

14 + 23 + 12n + 16n

37 + 28n


37 + 28n

2 37 + 28n

37 + 28 ( 9 )

= 37 + 252

= 289

3 14 + 5(x + 3) - 7x = 14 + 5x + 15 - 7x

= 29 - 2x

4 3 ( t - 4 ) - 8 ( 2 - 3t ) = 3t - 12 - 16 + 24t

= 27t - 28

5 63c - 2 ( 15c + 41 ) = 63c - 3c - 82

= 33c - 82

6 9 + 1 __ 2 ( 7n - 26 ) - 8n = 9 + 35n - 13 - 8n

= -4 - 4 1 __ 2 n

7 2x + 12

2 ( x + 6 )

8 12x + 24

12 ( x + 2 )

9 7x + 35

7 ( x + 5 )







15 ( 100 + 5d ) + 20 ( 50 + 7d ) = 15 ( 100 ) + 15 ( 5d ) + 20 ( 50 ) + 20 ( 7d )

= 1500 + 75d + 1000 + 140d

= 1500 + 1000 + 75d + 140d

= 2500 + 215d


New width 60 + w


2(96 + l) + 2(60 + w)

=2(96) + 2l + 2(60) + 2w

192 + 2l + 120 + 2w

192 + 120 + 2l + 2w

312 + 2l + 2w

13 Width 3


Factors 3 and x + 2

Product 3 ( x + 2 ) = 3x + 6

14 Width 4



Product 4 ( 2x - 1 ) = 8x - 4




and 6 times 4 ) So 6 ( 9 ) = 6 ( 5 ) + 6 ( 4 )


6x = ( x + 3 ) + ( 2x + 4 ) +

6x = 3x + 7 +

-3x = _ -3x

3x = 7 +

_ -7 = _ -7

3x - 7 =



10x + 6 = 2 ( 3x - 3 ) + 2 ( )

10x + 6 = 6x - 6 + 2

_ -6x = _ -6x

4x + 6 = - 6 + 2

_ + 6 = _ + 6

4x + 12 = 2

( 4x + 12 ) divide 2 = ( 2 ) divide 2

2x + 6 =


18 a P = 2l + 2w


2(2x + 6) + 2(x)

= 4x + 12 + 2x

= 6x + 12


2(3x - 14) + 2( 1 __ 2 x + 32)

= 6x - 28 + x + 64

= 7x + 36

b (7x + 36) - (6x + 12)

= 7x + 36 - 6x - 12

= x + 24


Let x = 36

2x + 6 = 2 ( 36 ) + 6

= 72 + 6

= 78


Let x = 36

1 __ 2 x + 32 = 1 __

2 ( 36 ) + 32

= 18 + 32

= 50


Let x = 36

3x - 14 = 3 ( 36 ) - 14

= 108 - 14

= 94





( x ) ( x ) = x 2

( x ) 1 = x

( 1 ) 1 = 1


x

x

1

11

1 1

x2 x x x

x 1 1 1x 1 1 1

Area =

x 2 + x + x + x + x + x + 1 + 1 + 1 + 1 + 1 + 1

= x 2 + 5x + 6

( x + 3 ) ( x + 2 ) = x 2 + 5x + 6




1160 = 1334 So 58 ( 23 ) = 58 ( 3 ) + 58 ( 20 )


8 ( 1000 - 3 ) = 8000 - 24 = 7976


Property 8 ( 900 + 90 + 7 ) = 7200 + 720 + 56 =

7976

LESSON 62

Your Turn

1 49 + z = -9

_ -49 _ -49

z = -139

2 r - 171 = -48

_ +171 _ +171

r = 123

3 -3c = 36

-3c ____ -3

= 36 ___ -3

c = -12

5 x - 15 = 525

_ +15 _ +15

x = 675


6 x ___ 35

= -12

x ___ 35

( 35 ) = -12 ( 35 )

x = -42


7 25x = 75

25x ____ 25

= 75 ___ 25

x = 3


Guided Practice



x + ( -134 ) = -17 or x - 134 = -17

x - 134 = -17

_ +134 _ +134

x = 117


warmer



-1 1 __ 2 x = -9

( - 2 __ 3 ) ( - 3 __

2 x ) = ( - 2 __

3 ) ( -9 )

x = 18 ___ 3

x = 6


3 -2x = 34

-2x ____ -2

= 34 ___ -2

x = -17

4 y - 35 = -21

_ + 35 _ + 35

y = 14

y = 14

5 2 __ 3 z = -6

( 3 __ 2 ) 2z ___

3 = ( 3 __

2 ) ( -6 )

z = -9





x - 870737 = 203215

_ +870737 _ +870 737

x = 2902887



2825131 - x = 2320106

_ -2825131 _ -2825131

-x = - 505025

x = 505025




2825131 - x = 1119421

_ -2825131 _ -2825131

-x = -1705710

x = 1705710



1250 - 935 = 315

Use an equation


descends

( -22 1 __ 2 ) x = -315

( - 45 ___ 2 ) x = -315

( - 2 ___ 45

) ( - 45 ___ 2 ) x = -315 ( - 2 ___

45 )

x = 14



4106 - 3205 = 901




34x = 901

34x ____ 34

= 901 ____ 34

x = 265 = 26 1 __ 2




- 25 + x = -07

_ + 25 _ + 25

x = 18





181 - x = -07

_ - 181 _ -181

-x = -188

x = 188





125 + x = 181

_ -125 _ -125

x = 56



their next play

-26 1 __ 3

+ x = 10

+26 1 __ 3

______

+26 1 __ 3

______

x = 36 1 __ 3



( -2 1 __ 2 ) x = -156

( -25 ) x = -156

( -25 _____ -25

) x = -156 ______ -25

x = 624



rate and the time


x __ 5 = 455

( 5 ) x __ 5 = 455 ( 5 )

x = 2275


Sample answer


to $22750



below sea level



lower elevation

20 -4x = -48

( -4x ____ -4

) = -48 _____ -4

x = 12

- 1 __ 4 x = -48

( -4 ) ( - 1 __ 4 ) x = -48 ( -4 )

x = 192

192 ____ 12

= 16








$21085

LESSON 63

Your Turn


purchased






Equation 150 - 35x = 45





Guided Practice

1

+ + ++ ++

+++ + +

+++

2

----

+ ++ ++

- - -

























place 28 +1-tiles


bicycle





Equation 85d + 55 = 123






Equation 125r + 675 = 3175








Equation 45n + 60 = 285




means + 45





1 _ 2

bull n + 45 = 172

Equation 1 __ 2 n + 45 = 172





uniforms equipment


Equation 295u + 548 = 2023





weeks


Equation 500 - 20x = 220






Total bill $88


shirts bill















10 + 5c = 25

10 - 10 + 5c = 25 - 10

5c = 15

5c ___ 5 = 15 ___

5

c = 3

3 children



10 + 5 ( 5 ) = $35














bought

LESSON 64

Your Turn


+ ++ +

+ ++ ++ +

+ ++ ++ +

++


+ ++ +

+ ++ ++ +

+ ++ ++ +

++


++

+ ++ +

++


++ ++


+ + ++ + ++ +

+++

+++

__



+ + ++ + ++

++ +

+++

+++

__


+ + ++++ + +++


+ + +++


++++

______

______

____



++++

+

++

+

++

______

______

____


++++

____


++ __



____

________

++



________

________

++

____


________

________

We get -y = -1

____


tile to each side

++

__ ++ __


++++

__


+++

6 3n + 10 = 37


3n + 10 = 37

-10 ____

-10 ____

3n = 27

3n ___ 3 = 27 ___

3

n = 9


7 n __ 4 - 5 = 15


n __ 4 - 5 = 15

+5 ___

+5 ___

n __ 4 = 20

n __ 4 ( 4 ) = 20 ( 4 )

n = 80

The number is 80

8 -20 = 5 __ 9 ( x - 32 )


-20 = 5 __ 9 ( x - 32 )

-20 = 5 __ 9 x - 160 ____

9

+ 160 ____ 9

______

+ 160 ____ 9

______

- 20 ___ 9 = 5 __

9 x

- 20 ___ 9 divide ( 5 __

9 ) = 5 __

9 x divide ( 5 __

9 )

4 20 times 9

1 _______

9 1 times 5

1 = x

- 4 __ 1 = x

-4 = x


9 120 - 4x = 92


120 - 4x = 92

-120 _____

-120 _____

- 4x = -28

-4x ____ -4

= -28 ____ -4

x = 7



Guided Practice





++++

+ +++++++++


++++

++++++++


++ + + + +




Solve the equation

2 ( 18 ) + 2w = 58

36 + 2w = 58

36 - 36 + 2w = 58 - 36

2w = 22

2w ___ 2 = 22 ___

2

w = 11


4 1200 minus 25x = 500


1200 - 25x = 500

_ -1200 _ -1200

-25x = -700

-25x _____ -25

= -700 _____ -25

x = 28






equation


6 9s + 3 = 57

9s + 3 - 3 = 57 - 3

9s = 54

9s ___ 9 = 54 ___

9

s = 6

7 4d + 6 = 42

4d + 6 - 6 = 42 - 6

4d = 36

4d ___ 4 = 36 ___

4

d = 9

8 115 - 3y = -485

115 - 115 - 3y = -485 - 115

thinsp-3y = -60

-3y

____ -3

= -60 ____ -3

y = 20

9 k __ 2 + 9 = 30

k __ 2 + 9 - 9 = 30 - 9

k __ 2 = 21

2 sdot k __ 2 = 2 sdot 21

k = 42

10 g

__ 3 - 7 = 15

g

__ 3 - 7 + 7 = 15 + 7

g

__ 3 = 22

3 sdot g

__ 3 = 3 sdot 22

g = 66

11 z __ 5 + 3 = -35

z __ 5 + 3 - 3 = -35 - 3

z __ 5 = -38

5 sdot z __ 5 = 5 ( -38 )

z = -190

12 -9h - 15 = 93

-9h - 15 + 15 = 93 + 15

-9h = 108

-9h ____ -9 = 108 ____

-9

h = -12

13 - 1 __ 3 (n + 15) = -2

- 1 __ 3 n - 5 = -2

- 1 __ 3 n - 5 + 5 = -2 + 5

- 1 __ 3 n = 3

-3 sdot - 1 __ 3 n = -3 sdot 3

n = -9

14 -17 + b __ 8 = 13

-17 + 17 + b __ 8 = 13 + 17

b __ 8 = 30

8 sdot b __ 8 = 8 sdot 30

b = 240


15 7 ( c - 12 ) = -21

7c - 84 = -21

_ +84 _ +84

7c = 63

7c ___ 7 = 63 ___

7

c = 9

16 -35 + p

__ 7 = -52

-35 + 35 + p

__ 7 = -52 + 35

p

__ 7 = -17

7 sdot p

__ 7 = -17 sdot 7

p = -119

17 46 = -6t - 8

46 + 8 = -6t - 8 + 8

54 = -6t

54 ___ -6

= -6t ____ -6

t = -9





2 (a + $26) = $264

Solve the equation

2 ( a + 26 ) = 264

2 ( a + 26 )

_________ 2 = 264 ____

2

a + 26 = 132

a + 26 - 26 = 132 - 26

a = 106






Solve the equation

2t - 6 = 20

2t - 6 + 6 = 20 + 6

2t = 26

2t __ 2 = 26 ___

2

t = 13


20 -35 = 5 __ 9 ( x - 32 )

-35 = 5 __ 9 x - 160 ____

9

+ 160 ____ 9

______

+ 160 ____ 9

- 155 ____ 9 = 5 __

9 x

thinsp- 155 ____ 9 divide ( 5 __

9 ) = 5 __

9 x divide ( 5 __

9 )

-thinsp 31

155 times 9

1

= x

9 1

times 5

1

- 31 ___ 1 = x

-31 = x




Solve the equation

-a + 40 = 28

-a + 40 - 40 = 28 - 40

-a = -12

-a ___ -1

= -12 ____ -1

a = 12






Solve the equation

2c + 11 = 73

2c + 11 - 11 = 73 - 11

2c = 62

2c ___ 2 = 62 ___

2

c = 31




price paid


1 __ 2

middot p -6 = 88

Solve the equation

1 __ 2 p - 6 = 88

1 __ 2 p - 6 + 6 = 88 + 6

1 __ 2 p = 94

2 sdot 1 __ 2 p = 2 sdot 94

p = 188



24 115 minus 8n = 19


115 - 8n = 19

_ -115 _ -115

-8n = -96

-8n _____ -8

= -96 _____ -8

n = 12


25 -55x + 056 = -164

-55x + 056 - 056 = -164 - 056

-55x = -22

-55x ______ -22

= -22 _____ -22

x = 04

26 -42x + 315 = -651

-42x + 315 - 315 = -651 - 315

-42x = -966

-42x ______ -42

= -966 ______ -42

x = 23

27 k ___ 52

+ 819 = 472

k ___ 52

+ 819 - 819 = 472 - 819

k ___ 52

= -347

52 sdot k ___ 52

= 52 ( -347 )

k = -18044




divide 2 by 3

3x + 2 = 15

3x ___ 3 + 2 __

3 = 15 ___

3

x + 2 __ 3 = 5

- 2 __ 3

___

- 2 __ 3

___

x = 5 - 2 __ 3

x = 5 times3

___ 1

times3 - 2 __

3

x = 15 ___ 3 - 2 __

3

x = 13 ___ 3 or 4 1 __

3


31 a 2(x + 40) = 234


2x + 80 = 234

2x + 80 - 80 = 234 - 80

2x = 154

2x ___ 2 = 154 ____

2

x = 77

Trey saved $77






32 F = 18c + 32

F - 32 = 18c + 32 - 32

F - 32 = 18c

F - 32 ______ 18

= 18c ____ 18

F - 32 ______ 18

= c

33 P = 2 ( ℓ + w ) P = 2ℓ + 2w

P - 2ℓ = 2ℓ - 2ℓ + 2w

P - 2ℓ = 2w

P - 2ℓ ______ 2 = 2w ___

2

P - 2ℓ ______ 2 = w

34 ax + b = c

ax + b - b = c - b

ax = c - b

ax ___ a = c - b ______ a

x = c - b ______ a

MODULE 6

Ready to Go On




15n + 60 + 12n + 95



2 h + 97 = -97

_ -97 _ -97

h = -194

3 - 3 __ 4 + p = 1 __

2

+ 3 __ 4 + 3 __

4

p = 1 __ 2 + 3 __

4

p = 1 times2

___ 2

times2 + 3 __

4

p = 2 __ 4 + 3 __

4

p = 5 __ 4

4 -15 = -02k

-15 _____ -02

= -02k ______ -02

75 = k


5 y ___

-3 = 1 __

6

y ___

-3 ( -3 ) = 1 __

6 ( -3 )

y = 1 __ 6 times -3 ___

1

y = -3 ___ 6

y = -1 ___ 2

6 - 2 __ 3

m = -12

- 2 __

3 m _____

- 2 __ 3 = -12 ____

- 2 __ 3

m = -12 divide - 2 __ 3

m = -12 ____ 1 divide - 2 __

3

m = -12 ____ 1 times - 3 __

2

m = -36 ____ -2

m = 18

7 24 = - t ___ 45

24 ( 45 ) = - t ___ 45

( 45 )

108 = -t

-108 = t







2 middot d + 15 = 33


9 5n + 8 = 43

5n + 8 - 8 = 43 - 8

5n = 35

5n ___ 5 = 35 ___

5

n = 7

10 y __

6 - 7 = 4

y __

6 - 7 + 7 = 4 + 7

y __

6 = 11

6 sdot y __

6 = 6 sdot 11

y = 66

11 8w - 15 = 57

8w - 15 + 15 = 57 + 15

8w = 72

8w ___ 8 = 72 ___

8

w = 9

12 g

__ 3 + 11 = 25

g

__ 3 + 11 - 11 = 25 - 11

g

__ 3 = 14

3 sdot g

__ 3 = 3 sdot 14

g = 42

13 f __ 5 - 22 = -25

f __ 5 - 22 + 22 = -25 + 22

f __ 5 = -03

5 sdot f __ 5 = 5 ( -03 )

f = -15

14 - 1 __ 4 (p + 16) = 2

- 1 __ 4 p - 4 = 2

- 1 __ 4 p - 4 + 4 = 2 + 4

- 1 __ 4 p = 6

-4 sdot - 1 __ 4 p = 6 sdot -4

p = -24




situation



Are You Ready

1 9w = -54

9w ___ 9 = -54 ____

9

w = -6

2 b - 12 = 3

thinsp _ + 12 = _ + 12

b = 15

3 n __ 4

= -11

4 times n __ 4

= 4 ( -11 )

n = -44

4-7


75 4 6

8 3 - (-5)

3 + 5

8

9 -4 - 5

-9

10 6 - 10

-4

11 -5 - (-3)

-5 + 3

-2

12 8 - (-8)

8 + 8

16

13 9 - 5

4

14 -3 - 9

-12

15 0 - (-6)

0 + 6

6

LESSON 71

Your Turn


_ +5 _ +5

y ge minus2

-4-5 -3 -2-1 0 1 2 3 4 5


minus1 ge -8


2 le 16

5 21 gt 12 + x

_ -12 _ minus12

9 gt x

x lt 9

10 2 3 4 5 6 7 8 9 10


21 gt 12 + 8

21 gt 12 + 8

21 gt 20

6 -10y lt 60

-10y

_____ -10

lt 60 ____ -10

y gt -6

-10-9 -8 -7 -6 -5 -4 -3 -2-1 0 1


-10y lt 60

-10(-5) lt 60

50 lt 60

7 7 ge - t __ 6

7(-6) le - t __ 6 (-6)

-42 le t

t ge -42

-46 -45 -44 -43 -42 -41 -40-47


7 ge - t __ 6

7 ge - ( -36 ____

6 )

7 ge 6



35m le 315

35m ____ 35

le 315 ____ 35

m le 9



Guided Practice

1 -5 le -2

_ +7 _ +7

2 le 5

2 -6 lt -3

-6 ___ -3

gt -3 ___ -3

2 gt 1

3 7 gt -4

_ -7 _ -7

0 gtthinsp -11


4 -1 ge -8

-1 ( -2 ) le -8 ( -2 )

2 le 16

5 n - 5 ge -2

_ +5 _ +5

n ge 3

-5 -4 -3 -2-1 0 3 4 51 2


n - 5 ge -2

4 - 5 ge -2

-1 ge -2

6 3 + x lt 7

_ -3 _ -3

x lt 4

-2-1 0 3 4 5 6 7 81 2


3 + x lt 7

3 + 3 lt 7

6 lt 7

7 -7y le 14

-7y

____ -7 ge 14 ___ -7

y ge -2

-5-6-7 -4 -3 -2-1 0 1 2 3


-7y le 14

-7 ( -1 ) le 14

7 le 14

8 b __ 5 gt -1

b __ 5 ( 5 ) gt -1 ( 5 )

b gt -5

-5-6-7-8 -4 -3 -2-1 0 1 2


b __ 5 gt -1

0 __ 5 gt

-1

0 gt -1

9 a -4t ge -80

b -4t ge -80

-4t ____ -4

le -80 ____ -4

t le 20








number


11 x - 35 gt 15

_ + 35 _ +35

x gt 50

100 20 30 40 50 60 70 80 90100


x - 35 gt 15

51 minus 35 gt 15

16 gt 15

12 193 + y ge 201

_ -193 _ minus193

y ge 8

10 2 3 4 5 6 7 8 9 10


193 + y ge 201

193 + 9 ge 201

202 ge 201

13 - q

__ 7 ge -1

- q

__ 7 ( -7 ) le -1 ( -7 )

q le 7

8 9 105 6 70 1 2 3 4


- q

__ 7 ge -1

- -14 ____ 7 ge

-1

2 ge -1

14 -12x lt 60

-12x _____ -12

gt 60 ____ -12

x gt -5

0-10-9 -8 -7 -6 -5 -4 -3 -2-1


-12x lt 60

-12 ( -4 ) lt 60

48 lt 60

15 5 gt z -3

_ +3 _ +3

8 gt z

z lt 8

10 2 3 4 5 6 7 8 9 10


5 gt z - 3

5 gt 7 - 3

5 gt 4


16 05 le y __

8

05 ( 8 ) le y __

8 ( 8 )

4 le y

y ge 4

8 9 105 6 70 1 2 3 4


05 le y __

8

05 le 8 __

8

05 le 1



12 + x le 28

_ -12 _ -12

x le 16




w __ 7 lt 35

w __ 7 ( 7 ) lt 35 ( 7 )

w lt 245





6s le 42

6s ___ 6 le 42 ___

6

s le 7




3025 + x ge 50

_ -3025 _ -3025

x ge 1975




155w ge 1705

155w ______ 155

ge 1705 _____ 155

w ge 11




thinsp-12t lt -120

-12t _____ -12

gt -120 _____ -12

t gt 10






3s le 10

3s ___ 3 le 10 ___

3

s le 3 1 __ 3


pounds



m ___ 05

le 55

m ___ 05

( 05 ) le 55 ( 05 )

m le 275




125x le 3

125x _____ 125

le 3 ____ 125

x le 24



buy 25 pounds







not true





prism

V = lwh



( 13 ) ( 1 __ 2 ) h lt 65

65h lt 65

65h ____ 65

lt 65 ___ 65

h lt 10





LESSON 72Your Turn


raise



Target amount $6000



must raise equal to




can go on

Starting amount $40

Admission price $6




equal to




are looking for




10 is added to 3x



than 30








looking for












Guided Practice

1

- -- -

-

lt

++++++

+ + ++ + +

+

2

---

gt

+ + ++ + +

+ + ++ + +

+ + +


raise








1250 + 92a ge 7000




greater than 32







inequality






3a + 28 gt 200




cheese to has


075n + 129 le 700












120 + 32n le 720




month month


2100 + 005s ge 2400






668 + 7n gt 2000


day



buys to a month


$7 + $10 middot c le $100

7 + 10c le 100






$22 + $17 middot n le $80

22 + 17n le 80














is given by

95 + 86 + 89 + 3s

________________ 6


tests



95 + 86 + 89 + 3s

________________ 6 ge 90 or

95 + 86 + 89 + 3s ge 540 or

270 + 3s ge 540












So -m gt 0

25 n gt 1 __ n if n gt 1


n = 1 __ n if n = 1

LESSON 73

Your Turn


++

++++

+++

++++

++++

+++

gt


++

++++

+++

++++

++++

+++

gt

- -- -- --

- -- -- --


++

++++

gt


++

++++

gt



+ + +gt


+++++

----

+++++

+ +++++

ge


+++++

----

+++++

+ ++

++++

+++

++++

ge


+++++

+++++

+ +++++

++++

ge


+++++

+++++

+ +++++

++++

ge


+ + + +ge


5 - p

__ 6 le 4

5 - 5 - p

__ 6 le 4 - 5

thinsp- p

__ 6 le -1

thinsp-6 ( - p

__ 6 ) ge -6 ( -1 )

p ge 6


arrow

0 1 4 5 72 3 6 8 9 10



3v - 8 gt 22

v = 9 v = 10 v = 11

3 ( 9 ) - 8 gt 22 3 ( 10 ) - 8 gt 22 3 ( 11 ) - 8 gt 22


results

3 ( 9 ) - 8 gt 22 3 ( 10 ) - 8 gt

22 3 ( 11 ) - 8 gt

22

27 - 8 gt 22 30 - 8 gt

22 33 - 8 gt

22

19 gt 22 22 gt

22 25 gt

22


v = 11


5h + 12 le -3

h = -3 h = -4 h = -5

5 ( -3 ) + 12 le -3 5 ( -4 ) + 12 le -3 5 ( -5 ) + 12 le -3


results

5 ( -3 ) + 12 le -3 5 ( -4 ) + 12 le

-3 5 ( -5 ) + 12 le

-3

-15 + 12 le -3 -20 + 12 le

-3 -25 + 12 le

-3

-3 le -3 -8 le

-3 -13 le

-3

true true true

h = -3 h = -4 h = -5


Guided Practice




5d - 13 lt 32

5d - 13 + 13 lt 32 + 13

5d lt 45

5d ___ 5 lt 45 ___

5

d lt 9


20 6 84 10 12 14 16 18 20


-4b + 9 le -7

-4b + 9 - 9 le -7 - 9

-4b le -16

-4b ____ -4

ge -16 ____ -4

b ge 4


20 6 84 10 12 14 16 18 20


2m + 18 gt - 4

m = -12 m = -11 m = -10

2 ( -12 ) + 18 gt -4 2 ( -11 ) + 18 gt -4 2 ( -10 ) + 18 gt -4


results

2 ( -12 ) + 18 gt -4 2 ( -11 ) + 18 gt

- 4 2 ( -10 ) + 18 gt

- 4

- 24 + 18 gt -4 - 22 + 18 gt

- 4 - 20 + 18 gt

- 4

- 6 gt - 4 - 4 gt

- 4 - 2 gt

- 4


m = -10


- 6y + 3 ge 0

y = 1 y = 1 __ 2 y = 0

-6 ( 1 ) + 3 ge 0 -6 ( 1 __ 2 ) + 3 ge 0 -6 ( 0 ) + 3 ge 0


results

-6 ( 1 ) + 3 ge 0 - 6 ( 1 __

2 ) + 3 ge

0 - 6 ( 0 ) + 3 ge

0

-6 + 3 ge 0 -3 + 3 ge

0 0 + 3 ge

0

-3 ge 0 0 ge

0 3 ge

0

not true true true

y = 1 __ 2

y = 0


65 - 4t ge 15

65 - 65 - 4t ge 15 - 65

-4t ge -5

-4t ____ -4

le -5 ___ -4

t le 125


0 05 1 15 2 25



time






8 2s + 5 ge 49

2s + 5 - 5 ge 49 - 5

2s ge 44

2s ___ 2 ge 44 ___

2

s ge 22

10 14 1612 18 20 22 24 26 28 30

9 -3t + 9 ge -21

-3t + 9 - 9 ge -21 -9

-3t ge -30

-3t ____ -3

le -30 ____ -3

t le 10


10 55 gt -7v + 6

55 - 6 gt -7v + 6 - 6

49 gt - 7v

49 ___ -7 lt -7v ____ -7

v gt -7

-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0

11 21 1 __ 3 gt 3m - 2 2 __

3

21 1 __ 3 + 2 2 __

3 gt 3m - 2 2 __

3 + 2 2 __

3

24 gt 3m

24 ___ 3 gt 3m ___

3

8 gt m or m lt 8

0 1 4 5 72 3 6 8 9 10

12 a ___ -8

+ 15 gt 23

a ___ -8

+ 15 - 15 gt 23 - 15

a ___ -8

gt 8

-8 ( a ___ -8

) lt -8 ( 8 )

a lt -64

-70 -68 -66 -64 -62 -60


13 f __ 2 - 22 lt 48

f __ 2 - 22 + 22 lt 48 + 22

f __ 2 lt 70

2 ( f __ 2 ) lt 2 ( 70 )

f lt 140

100 110 120 130 140 150

14 -25 + t __ 2 ge 50

-25 + 25 + t __ 2 ge 50 + 25

t __ 2 ge 75

2 ( t __ 2 ) ge 2 ( 75 )

t ge 150

130 140 150 160 170 180

15 10 + g ___

-9 gt 12

10 - 10 + g ___

-9 gt 12 - 10

g ___

-9 gt 2

-9 ( g ___

-9 ) lt -9 ( 2 )

g lt -18

-20 -18 -14 -12 -10-16

16 252 le -15y + 12

252 - 12 le -15y + 12 - 12

24 le - 15y

24 ____ -15

ge -15y

_____ -15

y le -16

-20 -18 -14 -12 -10-16

17 -36 ge -03a + 12

-36 - 12 ge -03a + 12 - 12

-48 ge -03a

-48 _____ -03

le -03a ______ -03

a ge 16

10 11 12 13 14 16 17 18 19 2015

18 80 - 2w ge 50

80 - 80 - 2w ge 50 - 80

- 2w ge -30

-2w ____ -2

le -30 ____ -2

w le 15



11 12 13 14 and 15


7n - 25 ge 65

7n - 25 + 25 ge 65 + 25

7n ge 90

7n ___ 7 ge 90 ___

7

n ge 12 6 __ 7


be a whole number





21 a

10 3 42 5 6 7 8 9 10

b

10 3 42 5 6 7 8 9 10














MODULE 7

Ready to Go On

1 n + 7 lt -3

thinsp _ -7

_ -7

n lt -10

2 5p ge -30

5p

___ 5 ge -30 ____

5

p ge -6

3 14 lt k + 11

_ -11 _ -11

3 lt k

4 d ___ -3

le minus6

( -3 ) ( d ) ge ( -3 ) ( -6 )

d ge 18


5 c - 25 le 25

_ +25 _ +25

c le 5

6 12 ge -3b

12 ___ -3

le -3b _____ -3

-4 le b




562 + n ge 650

_ -562 _ -562

n ge 88


-20 - 20t ge -100

9 2s + 3 gt 15

_ -3 _ -3

2s gt 12

2s ___ 2

gt 12 ___ 2

s gt 6

10 - d ___ 12

- 6 lt 1

_ +6 _ +6

- d ___ 12

lt 7

12 ( - d ___ 12

) lt 12 ( 7 )

-d lt 84

d gt -84

11 -6w - 18 ge 36

_ +18 _ +18

thinsp-6w ge 54

-6w _____ -6

le 54 ___ -6

w le -9

12 z __ 4 + 22 le 38

_ -22 _ -22

z __ 4 le 16

4 ( z __ 4 ) le 4 ( 16 )

z le 64

13 b __ 9 - 34 lt -36

_ +34 _ +34

b __ 9 lt -2

9 ( b __ 9 ) lt 9 ( -2 )

b lt -18

14 -2p + 12 gt 8

-12 ____

-12 ____

-2p gt -4

-2p

____ -2 lt -4 ___

-2

p lt 2






Are You Ready

1 3x + 4 = 10

3x + 4 - 4 =10 - 4

3x = 6

3x ___ 3 = 6 __

3

x = 2

2 5x - 11 = 34

5x - 11 + 11 = 34 + 11

5x = 45

5x ___ 5 = 45 ___

5

x = 9

3 -2x + 5 = -9

-2x + 5 - 5 = -9 - 5

-2x = -14

-2x ____ -2

= -14 ____ -2

x = 7

4 -11 = 8x + 13

-11 - 13 = 8x + 13 - 13

-24 = 8x

-24 ____ 8 = 8x ___

8

-3 = x

5 4x - 7 = -27

4x - 7 + 7 = -27 + 7

4x = -20

4x ___ 4 = -20 ____

4

x = -5

6 1 __ 2 x + 16 = 39

1 __ 2 x + 16 - 16 = 39 - 16

1 __ 2 x = 23

( 2 ) 1 __ 2 x = ( 2 ) 23

x = 46

7 12 = 2x - 16

12 + 16 = 2x - 16 + 16

28 = 2x

28 ___ 2 = 2x ___

2

14 = x

8 5x - 15 = -65

5x - 15 + 15 = -65 + 15

5x = -50

5x ___ 5 = -50 ____

5

x = -10

9 x __ 5 = 18 ___

30


30x = 90

30x ____ 30

= 90 ___ 30

x = 3

10 x ___ 12

= 24 ___ 36


36x = 288

36x ____ 36

= 288 ____ 36

x = 8

11 3 __ 9 = x __

3


9 = 9x

9 __ 9 = 9x ___

9

1 = x

12 14 ___ 15

= x ___ 75


1050 = 15x

1050 _____ 15

= 15x ____ 15

70 = x

13 8 __ x = 14 ___ 7


56 = 14x

56 ___ 14

= 14x ____ 14

4 = x

14 14 ___ x = 2 __ 5


70 = 2x

70 ___ 2 = 2x ___

2

35 = x

15 5 __ 6 = x ___

15


75 = 6x

75 ___ 6 = 6x ___

6

125 = x


UNIT

4


16 81 ___ 33

= x ____ 55


4455 = 33x

4455 _____ 33

= 33x ____ 33

135 = x

LESSON 81

Your Turn


= 22 ft


= 10 ft


Guided Practice

1

Blueprint

length (in)3 6 9 12 15 18

Actual

length (ft)5 10 15 20 25 30



= 15 in







= 25 m


= 15 m


4 a


scales



the drawing


6 a 2 in times 40 cm ______ 1 in

= 80 cm

15 in times 40 cm ______ 1 in

= 60 cm


b 80 cm times 60 cm = 4800 c m 2

c 80 cm times 1 in _______ 254 cm

asymp 315 in

60 cm times 1 in _______ 254 cm

asymp 236 in


315 in by 236 in



= 24 units


= 15 units


15 units




larger



r = 810 m ______ 54 ft

r = 150 m ______ 1 ft



= 648 in



b = 162 bricks



h = 30 ft times 126 cm _______ 1 ft

h = 378 cm



_________ 63 cm

n = 6 toothpicks



asymp 5 swabs






s = 10 cm times 2 ft _____ 1 cm

s = 20 ft










original size


2

LESSON 82

Guided Practice















triangle






6 cm

3 cm120˚








same angle measures








between them






LESSON 83

Guided Practice


2 rectangle

3 triangle





















volume is 480 in 3





LESSON 84

Your Turn



intersecting lines




mangFGD and mangDGC



mangBGC and mangCGD



Because lines _

BE and _




mangCGD = 55deg



3x ___ 3 = 126deg ____

3

x = 42deg





Guided Practice




so mangDGE = 30deg





value by 3














measures are equal

mangKMI = mangHMG

84 = 4x

84 ___ 4 = 4x ___

4

x = 21deg



x + 84 - 84 = 180 - 84

x = 96

mangKMH = 96deg



x + 62 - 62 = 180 - 62

x = 118

mangCBE = 118deg



x + 62 - 62 = 90 - 62

x = 28

mangABF = 28deg




x + 28 - 28 = 152

mangCBA = 152deg




2x ___ 2 = 86deg ___

2





6x ___ 6 = 180deg ____

6









_ -48deg268 _ -48deg268

mangK = 41deg3352






greater than 38deg











( 90 - ( 90 - xdeg ) ) = ( 90 - 90 + xdeg ) = xdeg

MODULE 8

Ready to Go On

1

Living


Actual


Blueprint





created




A point is another




mangFGE = 50deg




3 ( mangY ) ________ 3 = 120deg ____

3

mangY = 40deg

mangY = 40deg


rooms or gardens



Are You Ready

1 416

_ times 13

1248

_ +thinsp4160

5408

5408

2 647

_ times thinsp04

2588

2588

3 705

_ times thinsp94

2820

_ +thinsp63450

66270

6627

4 256

_ timesthinsp049

2304

_ +thinsp10240

12544

12544

5 1 __ 2 ( 14 ) ( 10 )

7 ( 10 )

70 i n 2

6 ( 35 ) ( 35 )

1225 ft 2

7 ( 8 1 __ 2 ) ( 6 )

17 ___ 1 2 sdot 6 3 __

1

51 i n 2

8 1 __ 2 ( 125 ) ( 24 )

1 __ 2 ( 24 ) ( 125 )

( 12 ) ( 125 )

15 m 2

LESSON 91

Your Turn

3 d = 11 cm

C = πd

C asymp 314 ( 11 )

C asymp 3454


6 C = πd

44 asymp 314d

44 ____ 314

asymp d

d asymp 1401 yards


rate

1401 divide 7 = 2001


Guided Practice

1 d = 9 in

C asymp 314 ( 9 )

C asymp 2826 in

2 r = 7 cm

C = 2πr

C asymp 2 ( 22 ___ 7 ) ( 7 )

C asymp 44 cm

3 d = 25 m

C = πd

C asymp 314 ( 25 )

C asymp 785 m

4 r = 48 yd

C = 2πr

C asymp 2 ( 314 ) ( 48 )

C asymp 3014 yd

5 r = 75 in

C = 2πr

C asymp 2 ( 314 ) ( 75 )

C asymp 471 in

6 Find the diameter

C = πd

66 asymp 314d

66 ____ 314

asymp 314d _____ 314

21 asymp d

Find the cost


25 times $045 = $1125



r = 05 yd

d = 1 yd


2πr = 788

2πr ___ 2π

= 788 ____ 2π

r asymp 788 _______ 2 ( 314 )

r asymp 1255 ft

d = 2r asymp 2 ( 1255 ft )

d asymp 2510 ft

9 d = 2r so r = d __ 2 asymp 34 ___

2

r asymp 17 in

C = πd asymp 314 ( 34 )

C = 1068 in





11 d = 59 ft

C = πd

C asymp 314 ( 59 )

C asymp 1853 ft

12 r = 56 cm

C = 2πr

C asymp 2 ( 22 ___ 7 ) ( 56 )

C asymp 352 cm

13 d = 35 in

C = πd

C asymp ( 22 ___ 7 ) ( 35 )

C asymp 110 in



15 r = 94 ft

d = 2r = 2 ( 94 )

d = 188 ft

C = πd

C asymp 314 ( 188 )

C asymp 590 ft

16 d = 475 in

r = d __ 2 = 475 ____

2

r = 2375 in

C = πd

C asymp 314 ( 475 )

C asymp 14915 in

17 d = 18 in

r = d __ 2 = 18 ___

2

r = 9 in

C = πd

C asymp 314 ( 18 )

C asymp 5652 in

18 r = 15 ft

C = 2πr

C asymp 2 ( 314 ) ( 15 ) = 942 ft


so ( 942 ) ( 075 ) = 7065 or about $707

19 C = πd

C asymp ( 22 ___ 7 ) ( 63 )

C asymp 198 ft




20 C = πd asymp 314 ( 2 )

C asymp 628 ft

Converting km to ft

2 km sdot ( 3280 ft _______

1 km ) = 6560 ft

6560 ft

_______ 628 ft

= 104459




1 __ 2 C = 1 __

2 πd asymp 1 __

2 sdot 314 ( 025 ) = 03925





Height 180 ft



_______ 2 ( 314 )

asymp 48 ft

Diameter d = 2r = 2 ( 48 ) = 96 ft



plus the diameter

1 __ 2 C = 1 __

2 πd asymp 1 __

2 sdot 314 ( 30 ) = 471



per linear foot

( 771 ft ) ( $925 _____

ft ) = $71318



C = πd asymp 314 ( 18 ) = 5652 ft


inches to feet

( 54 in ) ( 1 ft _____ 12 in

) = 45 ft



5652 ft _______ 45 ft

= 1256


must buy 13 strands


C inner

= πd asymp 314 ( 150 ) = 471 ft


C outer

= πd asymp 314 ( 154 ) = 48356 ft








smaller gear





314 ( 75 ) - 314 ( 732 ) = 314 ( 018 ) asymp 057

057 m asymp 187 ft

LESSON 92

Your Turn

4 A = π r 2 A = π ( 10 ) 2

A asymp 314 ( 10 ) 2


A asymp 314 f t 2

Guided Practice

1 r = d __ 2 = 14 ___

2 = 7 m

A = π r 2 A = π ( 7 ) 2

A asymp 314 ( 7 ) 2

A asymp 314 sdot 49

A asymp 1539 m 2

2 A = π r 2 A = π ( 12 ) 2

A asymp 314 ( 12 ) 2


A asymp 4522 m m 2

3 r = d __ 2 = 20 ___

2 = 10 yd

A = π r 2 A = π ( 10 ) 2

A asymp 314 ( 10 ) 2


A asymp 314 y d 2

4 A = π r 2 A = π ( 8 ) 2

A asymp 314 ( 8 ) 2

A asymp 314 sdot 64

A asymp 20096 i n 2

5 r = d __ 2 = 12 ___

2 = 6 cm

A = π r 2 A = π ( 6 ) 2

A asymp 314 ( 6 ) 2

A asymp 314 sdot 36

A asymp 11304 c m 2

6 r = d __ 2 = 13 ___

2 = 65 in

A = π r 2 A = π ( 65 ) 2

A asymp 314 ( 65 ) 2


A asymp 13267 i n 2

7 C = 4π = 2πr

4π ___ 2π

= 2πr ___ 2π

r = 2

A = π r 2 A = π ( 2 ) 2


8 C = 12π = 2πr

12π ____ 2π

= 2πr ___ 2π

r = 6

A = π r 2 A = π ( 6 ) 2


9 C = π __ 2 = 2πr

π __ 2 divide 2π = 2πr ___

2π

π __ 2 sdot 1 ___

2π = r

1 __ 4 = r

A = π r 2

A = π ( 1 __ 4 ) 2 = π ( 1 ___

16 )

A = π ___ 16

square units

10 A = π r 2 = 64π

π r 2 ___ π = 64π ____ π

r 2 = 64

r = 8

C = 2πr

= 2π ( 8 )

=16π yd

11 A = π r 2


12 r = d __ 2 = 10 ___

2 = 5 in

A = π r 2 A = π ( 5 ) 2

A asymp 314 ( 5 ) 2

A asymp 314 sdot 25

A asymp 785 i n 2

13 A = π r 2 A = π ( 16 ) 2

A asymp 314 ( 16 ) 2


A asymp 80384 c m 2


diameter 36 in

r = d __ 2 = 36 ___

2 = 18 in

A semicircle

= 1 __ 2 π r 2

A semicircle

= 1 __ 2 π ( 18 ) 2

A semicircle

asymp 1 __ 2 ( 314 ) ( 18 ) 2

A semicircle


A asymp 50868 i n 2




A = π r 2 A = π ( 3 ) 2

A asymp 314 ( 3 ) 2



A r = 75 mi

- A r = 50 mi

π ( 75 ) 2 - π ( 50 ) 2



greater







s 2 minus π r 2 = 1 2 2 minus π ( 6 ) 2

= 144 minus π ( 36 )

asymp 144 minus 11304 = 3096










16π in 2





about $20

_____ π ( 9 ) 2



_____ π ( 6 ) 2

asymp $009






A = π r 2 = π ( 8 ) 2

= π ( 64 )

asymp 20096


201 mi 2




A new

minus A old

= π ( 10 ) 2 - π ( 8 ) 2

= π ( 1 0 2 - 8 2 ) = π ( 100 - 64 )

= π ( 36 ) asymp 11304


more area









A


A whole target

=

π ( 15 ) 2 ______

π ( 75 ) 2

= ( 15 ) 2

_____ ( 75 ) 2

= 225 _____ 5625

= 004


LESSON 93

Your Turn


two right triangles





A = ℓw = 11 sdot 4 = 44 f t 2


A = 1 __ 2 bh = 1 __



A = 1 __ 2 bh = 1 __

2 sdot 3 sdot 3 = 45 f t 2


44 + 3 + 45 = 515 f t 2


semicircle



or 10 ___ 2 = 5 m


A = s 2 = 1 0 2 = 100 m 2


A = 1 __ 2 π r 2

A asymp 1 __ 2 sdot 314 sdot ( 5 ) 2


A asymp 3925 m 2


100 + 3925 = 13925 m 2







4 __ 2 = 2 ft


A = ℓw = 5 sdot 4 = 20 f t 2


A = π r 2 A asymp 314 sdot ( 2 ) 2



two areas

20 + 1256 = 3256 f t 2



( 3256 f t 2 ) ( $28 ____

f t 2 ) = $91168


Guided Practice


a parallelogram



2 ( 4 ) ( 2 ) = 4




2 parallelogram

15 cm 2


4 + 15 + 15 = 34 cm 2


2 Method 1

A 1 = ℓw A

2 = ℓw

= 12 sdot 9 = 20 sdot 9 = 108 = 180


Method 2

A 1 = ℓw A

2 = ℓw

= 9 sdot 8 = 12 sdot 8 = 72 = 216






1 + b

2 )

A = 1 __ 2 ( 5 ) ( 7 + 4 )

A = 1 __ 2 ( 5 ) ( 11 ) = 275 f t 2



275 + 16 = 435 ft 2


find the cost

( 435 f t 2 ) ( $225 _____

f t 2 ) = $9788


simpler figures




A asymp 1 __ 2 sdot 314 sdot ( 13 ) 2


A asymp 26533 i n 2


676 + 26533 = 94133 in 2






A = 1 __ 2 sdot 6 sdot 7

A = 1 __ 2 sdot 42

A = 21 f t 2


40 + 21 = 61 f t 2


square foot

( 61 f t 2 ) ( $250 _____

f t 2 ) = $15250

7

O 42-2-4

2

-4

y

A (-2 4) B (0 4)

C (2 1)D (5 1)

E (5 -2)F (-2 -2)










Area of trapezoid

A = 1 __ 2 h ( b

1 + b

2 )

A = 1 __ 2 ( 3 ) ( 4 + 2 )

A = 1 __ 2 ( 3 ) ( 6 ) = 9 square units











A = 1 __ 2 sdot 8 sdot 8

A = 1 __ 2 sdot 64

A = 32 m 2


A asymp 1 __ 4 sdot 314 sdot ( 8 ) 2


A asymp 5024 f t 2


64 + 32 + 5024 = 14624 m 2









48 + 1256 = 6056 cm 2






A = 1 __ 2 sdot 1 sdot 1

A = 1 __ 2 sdot 1

A = 05 f t 2


3 + 05 = 35 ft 2





( 42 f t 2 ) ( $125 _____

f t 2 ) = $5250


area of triangle

325 ft 2 - 75 ft 2 = 25 ft 2



square is 5 ft






20 ( 15 ) or 300 carrots








triangle



A = 1 __ 2 sdot 12 sdot 8

A = 1 __ 2 sdot 96

A = 48 i n 2


144 + 48 = 192 in 2










420 - 176625 = 243375 in 2 or 243 3 __

8 i n 2










A asymp 1 __ 2 sdot 314 sdot ( 20 ) 2


A asymp 628 i n 2


1600 + 628 = 2228 in 2






40 + 2 sdot 4 = 48 in




total of 40 + 4 = 44 in






A asymp 1 __ 2 sdot 314 sdot ( 24 ) 2


A asymp 90432 i n 2


the sum

2112 + 90432 asymp 3016 in 2

LESSON 94

Your Turn


B = l times w

= 9 times 2

= 18 square inches


P = 2 ( 9 ) + 2 ( 2 )

= 18 + 4 = 22 inches


S = Ph + 2B

S = 22 ( 1 1 __ 2 ) + 2 ( 18 )

= 33 + 36

= 69



B = times w

= 12 times 12

= 144 square inches


P = 4 ( 12 )

= 48 inches


S = Ph + 2B

S = 48 ( 12 ) + 2 ( 144 )

= 576 + 288

= 864 square inches


B = l times w

= 8 times 8

= 64 square inches


P = 4 ( 8 )

= 32 inches


S = Ph + 2B

S = 32 ( 8 ) + 2 ( 64 )

= 256 + 128

= 384 square inches








Guided Practice



Height = 7 ft

Base area = 1 __ 2 ( 3 ) ( 8 ) = 12 ft 2

Surface area

S = ( 18 ft ) ( 7 ft ) + 2 ( 12 ft 2 ) = 150 ft 2


B = l times w

= 25 times 25

= 625 m 2


P = 4 ( 25 )

= 10 m


S = Ph + 2B

S = 10 ( 25 ) + 2 ( 625 )

= 25 + 125

= 375


S = 375 m 2


B = l times w

= 11 times 9

= 99 m 2


prism

P = 2 ( 11 ) + 2 ( 9 )

= 22 + 18

= 40 m


S = Ph + 2B

S = 40 ( 7 ) + 2 ( 99 )

= 280 + 198

= 478


S = 478 m 2


A = ( 25 ) ( 25 ) = 625



= 375 + 478 -2 ( 625 ) = 503 m 2




surface




B = l times w

= 10 times 3

= 30 in 2


P = 2 ( 10 ) + 2 ( 3 )

= 20 + 6

= 26 in


S = Ph + 2B

S = 26 ( 4 ) + 2 ( 30 )

=104 + 60

= 164 in 2



B = l times w

= 20 times 15

= 300 cm 2


P = 2 ( 20 ) + 2 ( 15 )

= 40 + 30

= 70 cm


S = Ph + 2B

S = 70 ( 9 ) + 2 ( 300 )

= 630 + 600

= 1230 cm 2


1230 - 300 = 930 cm 2



Convert cm 2 to mm

2


2 ________

1 cm 2 = 93000 mm

2


93000 divide 25 = 3720




= 2 + 3 = 5 in 2


Perimeter = 3 + 3 + 1 + 2 + 2 + 1

= 12 in


S = Ph + 2B

S = 12 ( 3 ) + 2 ( 5 )

= 36 + 10

= 46 in 2



Perimeter = 25 + 25 + 3 = 8 ft

Base area = 1 __ 2 ( 2 ) ( 3 ) = 3 ft 2


= 8 ( 4 ) + 2 ( 3 )

= 32 + 6 = 38 ft 2


Perimeter = 2 ( 3 ) + 2 ( 4 ) = 14 ft



= 14 ( 2 ) + 2 ( 12 )

= 28 + 24 = 52 ft 2



Surface area = 38 + 52 - 12 - 12 = 66 ft 2







1 + b

2 ) h

1 __ 2 ( 16 + 48 ) 12 = 384 in

2


P = 48 + 20 + 16 + 20 = 104 in


S = Ph + 2B

S = 104 ( 24 ) + 2 ( 384 )

= 2496 + 768

= 3264 in 2



B = l times w

= 7 times l

= 7 ft 2


P = 2 ( 7 ) + 2 ( 1 )

= 14 + 2

= 16 ft


S = Ph + 2B

S = 16 ( 2 ) + 2 ( 7 )

= 32 + 14

= 46 f t 2


B = l times w

= 1 times 1

= 1 ft 2


P = 2 ( 1 ) + 2 ( 1 )

= 2 + 2 = 4 ft


S = Ph + 2B

S = 4 ( 3 ) + 2 ( 1 )

= 12 + 2

= 14 ft 2



Surface area = 46 + 14 - 1 - 1 = 58 ft 2



58 divide 25 = 232


needed


3 times 679 = 2037




B = l times w

= 27 times 24

= 648 cm 2


P = 2 ( 27 ) + 2 ( 24 )

= 54 + 48

= 102 cm


S = Ph + 2B

S = 102 ( 10 ) + 2 ( 648 )

= 1020 + 1296

= 2316 cm 2






2 ( 2l + 2w ) = 2P


New S = 2Ph + 2 ( 4B )


doubles



B = l times w

= 25 times 25

= 625 ft 2


P = 4 ( 25 )

= 10 ft


S = Ph + 2B

S = 10 ( 35 ) + 2 ( 625 )

= 35 + 135

= 485 ft 2



485 - 625 = 4225 ft 2



4225 _____ 485

times 100 asymp 87




15


r = 2 in

9 in


A = πr 2

asymp 31 4 ( 2 ) 2 = 1256 in 2


C = πd

asymp 314 ( 4 ) = 1256 in 2




S = Ch + 2B

asymp 1256 ( 9 ) + 2 ( 1256 ) = 13816 in 2





1500 times 1382 = 207300 in 2



( 207300 in 2 ) 1 ft 2 _______

144 in 2 asymp 1440 ft 2






show

LESSON 95

Your Turn


B = 1 __ 2 bh

= 1 __ 2 ( 24 ) 7

= 84 m 2


V = Bh

= ( 84 ) ( 22 )

= 1848 m 3



B = 1 __ 2 ( b 1 + b 2 ) h

= 1 __ 2 ( 8 + 12 ) 10

= 1 __ 2 ( 20 ) 10 = 100 cm

2


V = Bh

= ( 100 ) ( 22 )

= 2200 cm 3




B = bh

= ( 13 ) 13

= 169 in 2


V = Bh

= ( 169 ) ( 30 )

= 5070 in 3



B = 1 __ 2 bh

= 1 __ 2 ( 9 ) 13

= 585 in 2


V = Bh

= ( 585 ) ( 30 )

= 1755 in 3


5070 + 1755 = 6825 in 3


Guided Practice

1 B = 1 __ 2 bh = 1 __

2 ( 8 ) ( 3 ) = 12 ft 2

V = Bh = ( 12 times 7 ) ft 3 = 84 ft 3

2 B = 1 __ 2 ( b 1 + b 2 ) h = 1 __

2 ( 15 + 5 ) 3 = 30 m

2

V = Bh = ( 30 times 11 ) m 3 = 330 m 3


B = bh

= ( 4 ) 6 = 24 ft 2


V = Bh

= ( 24 ) ( 12 ) = 288 ft 3



B = 1 __ 2 bh

= 1 __ 2 ( 6 ) 4 = 12 ft 2


V = Bh

= ( 12 ) ( 6 ) = 72 ft 3



288 + 72 = 360 ft 3



B = bh

= ( 40 ) ( 50 ) = 2000 ft 2


V = Bh

= ( 2000 ) ( 15 ) = 30000 ft 3


B = 1 __ 2 bh

= 1 __ 2 ( 40 ) ( 10 ) = 200 ft 2


V = Bh

= ( 200 ) ( 50 ) = 10000 ft 3


30000 + 10000 = 40000 ft 3



B = 1 __ 2 ( b 1 + b 2 ) h

= 1 __ 2 ( 10 + 12 ) 5

= 1 __ 2 ( 22 ) 5 = 55 cm

2


V = Bh

= ( 55 ) ( 7 ) = 385 cm 3







V = Bh

= ( 35 ) ( 5 ) = 175 in 3




B = 1 __ 2 bh

= 1 __ 2 ( 7 ) ( 6 ) = 21 in

2


V = Bh

= ( 75 ) ( 7 ) = 525 in 3



B = 1 __ 2 bh

= 1 __ 2 ( 8 ) ( 4 ) = 16 ft 2


V = Bh

= ( 16 ) ( 24 ) = 384 ft 3



B = 1 __ 2 ( b 1 + b 2 ) h

= 1 __ 2 ( 7 + 5 ) 4

= 1 __ 2 ( 12 ) 4 = 24 in

2


V = Bh

= ( 24 ) ( 8 ) = 192 in 3



V = Bh

= ( 20 ) ( 15 ) = 300 in 3


300 cubic inches


given B = 234 in 3


V = Bh

= ( 234 ) ( 3 ) = 702 in 3



B = bh

= ( 3 ) ( 3 ) = 9 in 2


V = Bh

= ( 9 ) ( 3 ) = 27 in 3


702 + 27 = 972 in 3



B = bh

= ( 75 ) 375 = 28125 m 2


V = Bh

= ( 28125 ) ( 75 ) asymp 21094 cm 3


prism


15 - 75 = 75


B = bh

= ( 75 ) 375 = 28125 m 2


V = Bh

= ( 28125 ) ( 375 ) asymp 10547 cm 3


21094 + 10547 = 31641 m 3




V = Bh

= ( 21 ) ( 8 ) = 168 cm 3



260 - 168 = 92 cm 3


V = Bh

= ( 7 ) ( 14 ) = 98 cm 3



260 - 168 = 92 cm 3


a height of 14 cm

V = Bh

92 = B ( 14 )

92 ___ 14

= B ( 14 ) _____ 14

6 8 ___ 14

= B asymp 657





V = Bh

= ( 36 ) ( 5 ) = 180 in 3



prism V = Bh

= ( 32 ) ( 6 ) = 192 in 3





V = Bh

286 = B ( 8 )

286 ____ 8 = B ( 8 )

3575 = B


trapezoidal prism

1 __ 2 ( 2 + b 2 ) 13 = 3575

1 __ 2 ( 2 + b 2 ) ( 13 ___

13 ) = 3575 _____

13

( 2 ) 1 __ 2 ( 2 + b 2 ) = ( 2 ) 275

2 + b 2 = 55

_ -2 _ -2

b 2 = 35 ft



B = 1 __ 2 bh

= 1 __ 2 ( 10 ) 6 = 30 cm

2


V = Bh

= ( 30 ) ( 25 ) = 75 cm 3



_____ cm

3 )

asymp ( 75 cm 3 ) ( 86 g

_____ cm

3 ) = 645 g


about 645 g







of 120 cm 3

V = Bh

V = [ 1 __ 2 ( b 1 + b 2 ) h 1 ] h 2

120 ≟ [ 1 __ 2 ( 2 + 6 ) 4 ] 75

= [ 1 __ 2 ( 8 ) 4 ] 75

= [ 16 ] ( 75 ) = 120


V = Bh

V = [ 1 __ 2 ( b 1 + b 2 ) h 1 ] h 2

120 ≟ [ 1 __ 2 ( 1 + 7 ) 25 ] 12

= [ 1 __ 2 ( 8 ) 25 ] 12

= [ 10 ] 12 = 120






MODULE 9

Ready to Go On




2 d = 12 cm d = 6 cm so r = 12 ___ 2 = 6 ft



A asymp 11304 ft 2





A asymp 1 __ 2 sdot 314 sdot ( 8 ) 2


A asymp 10048 m 2


A = 1 __ 2 sdot 16 sdot 10

A = 1 __ 2 sdot 160

A = 80 m 2


80 + 10048 = 18048 m 2





A = 20 sdot 45

A = 90 c m 2

Area of rectangle

A = ℓw = 20 sdot 55 = 110 c m 2


90 + 110 = 200 cm 2



1 __ 2 ( 4 ) 3 = 6 cm 2


P = 3 + 4 + 5 = 12 cm


S = Ph + 2B

S = 12 ( 10 ) + 2 ( 6 )

thinsp=120 + 12

thinsp= 132 cm 2


V = Bh

= ( 6 ) 10

= 60 cm 3




1 __ 2 ( 4 ) 15 = 3 yd 2


( 4 ) 2 = 8 yd 2



P = 4 + 2 + 25 + 25 + 2 = 13 yd


S = Ph + 2B

S = 13 ( 25 ) + 2 ( 11 )

thinsp= 325 + 22

thinsp= 545 yd 2


is given

B = 234 yd 3


V = Bh

= ( 11 ) 25

= 275 yd 3






unit


Are You Ready

1 x ___16

=45___40

40x=720

40x ____40

=720____40

   x=18

2 x __5=1__

4

4x=5

4x ___4

=5__4

  x=5__4=125

3 25___10

=x ___10

125=10x

125____10

=10x ____10

125=x

4 x __6

=2__9

9x= 12

9x ___9

=12___9

   x=12___9=4__

3

5 4748495152575960range=60-47=13

6 4566689121213range=13-4=9

7 95979799100106108115range=115-95=20

8 121319273539476671range=71-12=59

9 mean=3+5+7+3+6+4+8+6+9+5_________________________________10

=56

10 mean=81+94+113+67+62+75____________________________6

=82

LESSON 101

Your Turn




Guided Practice




Jimmy 80

Darnell 90

Ping 75

Zach 85

Jamar 80

BSampleanswer

75+80+90+75+85+80___________________________6

=485____6

asymp81

Meanasymp81



Stan 80 Marcus 90

Alejandro 90 Tio 85

BSampleanswer

85+80+90+85+90+85____________________________6

=515____6 =86

Mean=size86




















b 35___60

= x ____100

xasymp58


=58



LESSON 102

Your Turn


______________________sizeofsample



6___50

= x_____3500

6sdot70______50sdot70

= x _____3500

420_____3500

= x_____3500


Guided Practice

1

6 7 8 9 10 11 12 13 14 1550 1 2 3 4


6 7 7 107 114 4 54

Leastvalue

4

Lower quartile

4

Median

65

Upper quartile

7

Greatestvalue11

Drawaboxplot

10 1550





______________________sizeofsample



4___60

= x_____4200

4sdot70______60sdot70

= x_____4200

280_____4200

= x_____4200






8___50

= x_____4500

8sdot90______50sdot90

= x_____4500

720_____4500

= x_____4500



divide060

divide060







_______________________________________ size of sample

=



4 ___ 50

= x ____ 600

4 sdot 12 ______ 50 sdot 12

= x ____ 600

48 ____ 600

= x ____ 600

x = 48



_______________________________________________ size of sample

=



2 ___ 20

= x ____ 130

2 sdot 65 _______ 20 sdot 65

= x ____ 130

13 ____ 130

= x ____ 130

x = 13



________________ size of sample



12 ___ 60

= x _____ 1200

12 sdot 20 ______ 60 sdot 20

= x _____ 1200

240 _____ 1200

= x _____ 1200

x = 240


shelters


__________________________ size of sample



12 ___ 72

= x ______ 10800

12 sdot 150 _______ 72 sdot 150

= x ______ 10800

1800

______ 10800

= x ______ 10800

x = 1800



_______ 2 = 25


14 Order the data

11 12 12 12 13 13 13 14 14 14 15 17 18 18

19 22



12 ___ 16

= x ____ 100

12 sdot 625 ________ 16 sdot 625

= x ____ 100

75 ____ 100

= x ____ 100

x = 75



15

6 7 8 9 1050 1 2 3 4


fewer siblings




















9 a 56 + 43 + 62 + 63 + 33 + 34 + 38 + 51 + 59 + 59

___________________________________________ 10

= 498


b 498 sdot 64 = 31872



10 55 + 57 + 57 + 58 + 59 + 59 + 59 + 59 + 59 + 61 + 62 + 62 + 63 + 64 + 66

_________________________________________________________________ 15

= 60






accurately

LESSON 103

Guided Practice

1 (1 600) 20

2 50 51 600








5 Shop A 10 ___ 50

times 500 = 100

Shop B 23 ____ 100

times 500 = 115

Shop C 7 ___ 25

times 500 = 140








fewest bagels










count of 75


MODULE 10

Ready to Go On




service


__________________________________________ size of sample


18 ____ 270

= x ______ 30330

18 sdot 337 ____

3 ________

270 sdot 337 ____ 3

= x ______ 30330

2022

______ 30330

= x ______ 30330

x = 2022


languages





= defective players

______________ shipment

2 ___ 10

= x _____ 5000

2 middot 500 _______ 10 middot 500

= x _____ 5000

1000

_____ 5000

= x _____ 5000

x = 1000


defective


the shipment





Are You Ready

0875

1 8 ⟌ _

7000

_ -6 400

600

_ -560

40

_ -40

0

0875 875

08

2 5 ⟌ _

40

_ -4 0

0

08 80

025

3 4 ⟌ _

100

_ -80

20

_ -20

0

025 25

03

4 10 ⟌ _

30

_ -3 0

0

03 30

5 4 6 7 7 9 11 15 17

7 + 9

_____ 2 = 8

Median = 8

Mode = 7

6 36 37 40 43 44 49 50 51 56

Median = 44

Mode none

7 9 + 16 + 13 + 14 + 10 + 16 + 17 + 9

________________________________ 8

= 13

Mean = 13

8 108 + 95 + 104 + 96 + 97 + 106 + 94

________________________________ 7 = 100

Mean = 100

LESSON 111

Your Turn








in order

1 4 4 4 5 5 5 6 6 6 6 7 7 8 11


range 10 h



range for exercise

Guided Practice




one area




no data


4 Class A

4 4 4 4 4 5 5 5 6 6 12 13 13 13 13 14 14

median 6

Class B

3 4 4 4 5 5 5 5 6 6 7 7 7 7 7 8 8 9

median 6








at 8 letters




3 + 4 + 4 + 5 + 5 + 6 + 7 + 7 + 8 + 8 + 8 + 9

________________________________________ 12

74 ___ 12

asymp 617

Mean asymp 617

3 3 4 5 5 6 7 7 8 8 8 9


average

6 + 7

_____ 2 = 13 ___

2 = 65

Median 65

Range 9 - 3 = 6


the left


interval













LESSON 112

Your Turn



Guided Practice


2 Median79

3 Range88-72=16 IQR85-75=10






























does not




LESSON 113

Your Turn

1 Team 1

Mean

44 + 47 + 67 + 89 + 55 + 76 +85 + 80 + 87 + 69 + 47 + 58 = 804

804 divide 12 = 67


ǀ 44 - 67 ǀ = 23 ǀ 47 - 67 ǀ = 20

ǀ 67 - 67 ǀ = 0 ǀ 89 - 67 ǀ = 22

ǀ 55 - 67 ǀ = 12 ǀ 76 - 67 ǀ = 9

ǀ 85 - 67 ǀ = 18 ǀ 80 - 67 ǀ = 13

ǀ 87 - 67 ǀ = 20 ǀ 69 - 67 ǀ = 2

ǀ 47 - 67 ǀ = 20 ǀ 58 - 67 ǀ = 11


23 + 20 + 0 + 22 + 12 + 9 +18 + 13 + 20 + 2 + 20 + 11 = 170


Team 2

Mean

40 + 32 + 52 + 75 + 65 + 70 +72 + 61 + 54 + 43 + 29 + 32 = 625



ǀ 40 - 521 ǀ = 121 ǀ 32 - 521 ǀ = 201

ǀ 52 - 521 ǀ = 01 ǀ 75 - 521 ǀ = 229

ǀ 65 - 521 ǀ = 129 ǀ 70 - 521 ǀ = 179

ǀ 72 - 521 ǀ = 199 ǀ 61 - 521 ǀ = 89

ǀ 54 - 521 ǀ = 19 ǀ 43 - 521 ǀ = 91

ǀ 29 - 521 ǀ = 231 ǀ 32 - 521 ǀ = 201


121 + 201 + 01 + 229 +129 + 179 + 199 + 89 +19 + 91 + 231 + 201 = 169


Difference in means

67 - 521 = 149



MAD


distributions

Guided Practice

1 Class 1 mean

12 + 1 + 6 + 10 + 1 + 2 + 3 +10 + 3 + 8 + 3 + 9 + 8 + 6 + 8 = 90

90 divide 15 = 6

Class 2 mean

11 + 14 + 11 + 13 + 6 + 7 + 8 + 6 +8 + 13 + 8 + 15 + 13 + 17 + 15 = 165

165 divide 15 = 11


ǀ 12 - 6 ǀ = 6 ǀ 1 - 6 ǀ = 5 ǀ 6 - 6 ǀ = 0

ǀ 10 - 6 ǀ = 4 ǀ 1 - 6 ǀ = 5 ǀ 2 minus 6 ǀ = 4

ǀ 3 - 6 ǀ = 3 ǀ 10 - 6 ǀ = 4 ǀ 3 - 6 ǀ = 3

ǀ 8 - 6 ǀ = 2 ǀ 3 - 6 ǀ = 3 ǀ 9 - 6 ǀ = 3

ǀ 8 - 6 ǀ = 2 ǀ 6 - 6 ǀ = 0 ǀ 8 - 6 ǀ = 2

6 + 5 + 0 + 4 + 5 + 4 + 3 + 4 +3 + 2 + 3 + 3 + 2 + 0 + 2 = 46



ǀ 11 - 11 ǀ = 0 ǀ 14 - 11 ǀ = 3 ǀ 11 - 11 ǀ = 0

ǀ 13 - 11 ǀ = 2 ǀ 6 - 11 ǀ = 5 ǀ 7 - 11 ǀ = 4

ǀ 8 - 11 ǀ = 3 ǀ 6 - 11 ǀ = 5 ǀ 8 - 11 ǀ = 3

ǀ 13 - 11 ǀ = 2 ǀ 8 - 11 ǀ = 3 ǀ 15 - 11 ǀ = 4

ǀ 13 - 11 ǀ = 2 ǀ 17 - 11 ǀ = 6 ǀ 15 - 11 ǀ = 2

0 + 3 + 0 + 2 + 5 + 4 + 3 + 5 +3 + 2 + 3 + 4 + 2 + 6 + 2 = 44



11 minus 6 = 5




comparison


different samples


5 23 + 38 + 39 + 48 + 55 + 56 + 71 +86 + 57 + 53 + 43 + 31 = 600

600 divide 12 = 50

ǀ 23 - 50 ǀ = 27 ǀ 38 - 50 ǀ = 12

ǀ 39 - 50 ǀ = 11 ǀ 48 - 50 ǀ = 2

ǀ 55 - 50 ǀ = 5 ǀ 56 - 50 ǀ = 6

ǀ 71 - 50 ǀ = 21 ǀ 86 - 50 ǀ = 36

ǀ 57 - 50 ǀ = 7 ǀ 53 - 50 ǀ = 3

ǀ 43 - 50 ǀ = 7 ǀ 31 - 50 ǀ = 19

27 + 12 + 11 + 2 + 5 + 6 + 21 +36 + 7 + 3 + 7 + 19 = 156

156 divide 12 = 13



6 ǀ 23 - 8 ǀ = 15 ǀ 38 - 23 ǀ = 15

ǀ 39 - 24 ǀ = 15 ǀ 48 - 33 ǀ = 15

ǀ 55 - 40 ǀ = 15 ǀ 56 - 41 ǀ = 15

ǀ 71 - 56 ǀ = 15 ǀ 86 - 71 ǀ = 15

ǀ 57 - 42 ǀ = 15 ǀ 53 - 38 ǀ = 15

ǀ 43 - 28 ǀ = 15 ǀ 31 - 16 ǀ = 15




7 50 - 15 = 35




8 50 - 35 = 15




9

0 4 8 12 16 20 24 28 32 36 40 44

Medians

School B

School A

0 4 8 12 16 20 24 28 32 36 40 44

Means

School B

School A




10 State A 48 - 38 = 10


State B 50 - 42 = 8

8 divide 4 = 2





well


Median 665


Median 77

77 - 665 = 105

105 divide 6 = 175


ranges













not very similar

MODULE 11

Ready to Go On


5 + 6 + 6 + 7 + 7 + 7 + 7 + 8 + 8 + 8 + 8 + 9 + 9 + 10

________________________________________________ 14

= 105 ____ 14

= 75 mi


6 + 6 + 7 + 7 + 8 + 8 + 8 + 8 + 9 + 9 + 9 + 10 + 10 + 10

__________________________________________________ 14

= 115 ___ 14

asymp 82 mi




5 6 6 7 7 7 7 8 8 8 8 9 9 10


average

7 + 8

_____ 2 = 15 ___

2 = 75

Median 75


6 6 7 7 8 8 8 8 9 9 9 10 10 10




Median 8













7 + 11 + 11 + 12 + 9 + 12 + 8 + 10

______________________________ 8

= 10


21 + 24 + 19 + 19 + 22 + 23 + 24 + 24

__________________________________ 8 = 22




12 ___ 5

= 24




groups



Are You Ready

1 6 ___ 10

= 6 divide 2 ______ 10 divide 2

= 3 __ 5

2 9 ___ 15

= 9 divide 3 ______ 15 divide 3

= 3 __ 5

3 16 ___ 24

= 16 divide 8 ______ 24 divide 8

= 2 __ 3

4 9 ___ 36

= 9 divide 9 ______ 36 divide 9

= 1 __ 4

5 45 ___ 54

= 45 divide 9 ______ 54 divide 9

= 5 __ 6

6 30 ___ 42

= 30 divide 6 ______ 42 divide 6

= 5 __ 7

7 36 ___ 60

= 36 divide 12 _______ 60 divide 12

= 3 __ 5

8 14 ___ 42

= 14 divide 14 _______ 42 divide 14

= 1 __ 3

075

9 4 ⟌ _

300

_ -2 80

20

_ -20

0

075

0875

10 8 ⟌ _

7000

_ -6400

600

_ -560

40

_ -40

0

0875

015

11 20 ⟌ _

300

_ -2 00

100

_ -100

0

015

038

12 50 ⟌ _

1900

_ -15 00

4 00

_ -4 00

0

038

13 67 = 67 ____ 100

= 067

14 31 = 31 ____ 100

= 031

15 7 = 7 ____ 100

= 007

16 146 = 100 + 46

= 100 ____ 100

+ 46 ____ 100

= 1 + 046

= 146

17 013 = 13

18 055 = 55

19 008 = 8

20 116 = 116

LESSON 121

Your Turn







is 10 ___ 20

or 1 __ 2





3


UNIT

6



P(5) + P(not 5) = 1

1 __ 8 + P(not 5) = 1

P(not 5) = 7 __ 8




1 __ 2 + P(odd) = 1

P(odd) = 1 __ 2


Guided Practice













impossible 0
















= 1 __ 4


P(5) + P(not 5) = 1

1 __ 6 + P(not 5) = 1

P(not 5) = 5 __ 6




1 __ 3 + P(not blue) = 1




P(4) + P(not 4) = 1

1 __ 5 + P(not 4) = 1

P(not 4) = 4 __ 5




4 ___ 52

+ P(not queen) = 1

P(not blue) = 48 ___ 52

= 12 ___ 13









selecting


or 2 ___ 13



9 ___ 12



or 1 __ 4



or 1 __ 4













or 5 __ 7



have red hair




or 4 __ 7





coin is 9 ___ 16














landing on blue

LESSON 122

Your Turn


Red 10 ___ 30

= 1 __ 3

Yellow 14 ___ 30

= 7 ___ 15

Blue 6 ___ 30

= 1 __ 5






Guided Practice


A 14 ___ 40

= 7 ___ 20

= 035 = 35

B 7 ___ 40

= 0175 = 175

C 11 ___ 40

= 0275 = 275

D 8 ___ 40

= 1 __ 5 = 020 = 20







4 6 ___ 10








= 8 ___ 48

= 1 __ 6





chosen is 19 ___ 20


1 ___ 20

+ P(not Ryan) = 1

P(not Ryan) = 19 ___ 20


patterns




times



get a hit next time


is 4 ___ 10





or about 417


7 ___ 12



or 417











pocket


LESSON 123

Your Turn



= 60 ____ 400

= 3 ___ 20

= 15



= 12 ___ 75

or 4 ___ 25

Guided Practice




= 50 ____ 400

or 1 __ 8











number of trials








= 33 ____ 330

= 1 ___ 10



= 60 ____ 400

= 3 ___ 20


= 55 + 60 + 23

____________ 400

= 138 ____ 400

= 69 ____ 200


and 4 color choices


P(7th grade + 100 pages) = 85 ____ 250

= 17 ___ 50




7th grade




likely





12 P(male + open toe) = 11 ____ 300











heads and 3 or 4

LESSON 124

Your Turn








Guided Practice








too high

5 98 ____ 100

= x ___ 40

= 39 ___ 40

or 39 times




6 18 ____ 100

= x _____ 5000

= 900 _____ 5000



accepted

times04

times04

times50

times50





events


8 4 ____ 100

= x ____ 200

= 8 ____ 200



9 Yes 6th grade 2 ____ 100

= x ____ 250

= 5 ____ 250

or 5 students

7th grade 4 ____ 100

= x ____ 200

= 8 ____ 200

or 8 students

8th grade 8 ____ 100

= x ____ 150

= 12 ____ 150

or 12 students



10 6 ____ 100

= x ____ 300

= 18 ____ 300










1 ___ 30

= x ____ 180




normal gas pump







4 ____ 100

= x _____ 2400

= 96 _____ 2400



MODULE 12

Ready to Go On

1 H1 H2 T1 T2

2 6 ___ 10

= 3 __ 5

3 13 ___ 20




because 3 ___ 10

= x ___ 80

= 24 ___ 80

or 24 times




times15

times15

times24

times24

times2

times2

times3

times3

times2

times2

times25

times25

times8

times8



Simulations

Are You Ready

075

1 4 ⟌ _

300

_ -2 80

20

_ -20

0

075 = 75

04

2 5 ⟌ _

20

_ -2 0

0

04 = 40

09

3 10 ⟌ _

90

_ -9 0

0

09 = 90

035

4 20 ⟌ _

700

_ -6 00

1 00

_ -1 00

0

035 = 35

0875

5 8 ⟌ _

7000

_ thinsp-6 400

600

_ -560

40

_ -40

0

0875 = 875

005

6 20 ⟌ _

100

_ -1 00

0

005 = 5

076

7 25 ⟌ _

1900

_ -17 50

1 50

_ -1 50

0

076 = 76

046

8 50 ⟌ _

2300

_ -20 50

3 00

_ -3 00

0

046 = 46

9 1 - 1 __ 5 = 5 __

5 - 1 __

5

= 4 __ 5

10 1 - 2 __ 9 = 9 __

9 - 2 __

9

= 7 __ 9

11 1 - 8 ___ 13

= 13 ___ 13

- 8 ___ 13

= 5 ___ 13

12 1 - 3 ___ 20

= 20 ___ 20

- 3 ___ 20

= 17 ___ 20

13 8 ___ 15

times 5 __ 8 =

18 ___ 315

times 5 1 ___

8 1

= 1 __ 3

14 2 __ 9 times 3 __

4 =

12 __ 39

times 3 1 ___

4 2

= 1 __ 6

15 9 ___ 16

times 12 ___ 13

= 9 ___ 416

times 12 3 _____

13

= 27 ___ 52

16 7 ___ 10

times 5 ___ 28

= 17 ___

210 times 5

1 ____

28 4

= 1 __ 8

LESSON 131

Your Turn






= 2 __ 6 = 1 __

3



probability


Guided Practice

1

Basket A Basket B


= 16

7 + 4 + 9

= 20


P(win) =

Number of red balls


3 ___

16 4 ___

20 = 1 __

5


16 use


1 __ 5 = 16 ___

80

3 ___ 16

= 15 ___ 80

Therefore 16 ___ 80

gt 15 ___ 80

so 1 __ 5 gt 3 ___

16


winning




= 6 ___ 11




= 5 ___ 11




= 2 __ 6 = 1 __

3


close


by 20




= 2 __ 6

= 1 __ 3 033 or 33



= 8 ___ 12

= 2 __ 3 067 or 67



= 4 ___ 14

= 2 __ 7 029 or 29


= 26 ___ 52

= 1 __ 2 050 or 50


= 12 - 5 ______ 12

= 7 ___ 12

058 or 58



7 adventure)

P(not a comedy)


= 5 + 7 _________

5 + 7 + 8 = 12 ___

20

= 3 __ 5 060 or 60






= 2 __ 6

= 1 __ 3 033 or 33







= 6 ___ 16

or 3 __ 8







5 ______ 5 + 15

= 5 ___ 20

= 1 __ 4

times16

times16

times5

times5




P(seventh grader) =



= 20 ___ 35

= 4 __ 7


P(eighth grader) =



= 15 ___ 35

= 3 __ 7



more likely










= 8 ___ 20


14 ___ 40

or 7 ___ 20



marble is 8 ___ 20

- 7 ___ 20

= 1 ___ 20



= 10 ___ 20


= 8 ___ 20



marble is 10 ___ 20

- 8 ___ 20

= 2 ___ 20

= 1 ___ 10




= 2 ___ 20


= 5 ___ 20



marble is 5 ___ 20

- 2 ___ 20

= 3 ___ 20



LESSON 132

Your Turn

3 P(ham sandwich) =



= 4 ___ 12

= 1 __ 3




= 6 ___ 12

= 1 __ 2




0 0 0 0

0 0 0 1

0 0 1 0

0 0 1 1


second digit

0 1 0 0

0 1 0 1

0 1 1 0

0 1 1 1


second digit

1 0 0 0

1 0 0 1

1 0 1 0

1 0 1 1


second digit

1 1 0 0

1 1 0 1

1 1 1 0

1 1 1 1



0 0 1 1

0 1 0 1

0 1 1 0

1 0 0 1

1 0 1 0

1 1 0 0





= 6 ___ 16

= 3 __ 8


Guided Practice

1

1 2 3 4 5 6

11 sdot 1

= 1

1 sdot 2

= 2

1 sdot 3

= 3

1 sdot 4

= 4

1 sdot 5

= 5

1 sdot 6

= 6

22 sdot 1

= 2

2 sdot 2

= 4

2 sdot 3

= 6

2 sdot 4

= 8

2 sdot 5

= 10

2 sdot 6

= 12

33 sdot 1

= 3

3 sdot 2

= 6

3 sdot 3

= 9

3 sdot 4

= 12

3 sdot 5

= 15

3 sdot 6

= 18

44 sdot 1

= 4

4 sdot 2

= 8

4 sdot 3

= 12

4 sdot 4

= 16

4 sdot 5

= 20

4 sdot 6

= 24

55 sdot 1

= 5

5 sdot 2

= 10

5 sdot 3

= 15

5 sdot 4

= 20

5 sdot 5

= 25

5 sdot 6

= 30

66 sdot 1

= 6

6 sdot 2

= 12

6 sdot 3

= 18

6 sdot 4

= 24

6 sdot 5

= 30

6 sdot 6

= 36





= 15 ___ 36




= 23 ___ 36

4 H

HHH HHT

H

H

Coin 1

List

Coin 2

Coin 3 T

T

HTH HTT

H T

T

H

H T

THH THT

T

H T

TTH TTT

Coin 1

List

Coin 2

Coin 3




= 1 __ 8


HHT HTH THH



= 3 __ 8




10

Checkered

Red

Checkered

Red

Blue

Black

Checkered

Red

Checkered

Red

Blue

Black

Checkered

Red

Checkered

Red

Blue

Black

Shirt Pants Shoes

Yellow

Red

Green




= 6 ___ 12

= 1 __ 2


Shirt Pants Shoes






= 4 ___ 12

= 1 __ 3



Rhee Pamela

Rhee A

Rhee B

Rhee C

Pamela A

Pamela B

Pamela C

A B

A C

B C



P(Rhee and Pamela)


= 1 ___ 10




1 2 3 4 5 6

11 + 1

= 2

1 + 2

= 3

1 + 3

= 4

1 + 4

= 5

1 + 5

= 6

1 + 6

= 7

22 + 1

= 3

2 + 2

= 4

2 + 3

= 5

2 + 4

= 6

2 + 5

= 7

2 + 6

= 8

33 + 1

= 4

3 + 2

= 5

3 + 3

= 6

3 + 4

= 7

3 + 5

= 8

3 + 6

= 9

44 + 1

= 5

4 + 2

= 6

4 + 3

= 7

4 + 4

= 8

4 + 5

= 9

4 + 6

= 10

55 + 1

= 6

5 + 2

= 7

5 + 3

= 8

5 + 4

= 9

5 + 5

= 10

5 + 6

= 11

66 + 1

= 7

6 + 2

= 8

6 + 3

= 9

6 + 4

= 10

6 + 5

= 11

6 + 6

= 12


are 10 less than 6



= 10 ___ 36

= 5 ___ 18


diagram

Khakis

Shorts

Shirt Pants Shoes

Collared Jeans

Sneakers

Flip-flops

Sandals

Sneakers

Flip-flops

Sandals

Sneakers

Flip-flops

Sandals

Khakis

Shorts

T-shirt Jeans

Sneakers

Flip-flops

Sandals

Sneakers

Flip-flops

Sandals

Sneakers

Flip-flops

Sandals







= 4 ___ 18

= 2 __ 9






outcomes



Therefore




= 7 ___ 30






diagram

Carrots

Sweet potato

Pasta

Peas

Asparagus





Carrots

Sweet potato

Peas

Asparagus





Carrots

Sweet potato

Peas

Asparagus





Carrots

Sweet potato

Peas

Asparagus





Salmon

Beef

Pork



salmon Therefore


= 1 __ 4





Carrots

Sweet potato

PastaPeas

Asparagus

Carrots

Sweet potato

Peas

Asparagus

Carrots

Sweet potato

Peas

Asparagus

Carrots

Sweet potato

Peas

Asparagus

Salmon

Beef

Pork


salmon Therefore


= 1 __ 4















codes













12453 12534 12543 13245 13254 13425

13452 13524 13542 14235 14253 14325

14352 14523 14532 15234 15243 15324













114 115 221 223 224 225 331 332 334 335

441 442 443 445 551 552 553 554 There























LESSON 133

Your Turn




3






heads is 1 __ 2

1 __ 2 = x ___

18

1 __ 2 = x ___

18

x = 9

about 9 times


P(red) = 8 ___ 17

P(not red) = 1 - 8 ___ 17

= 9 ___ 17




Therefore




Guided Practice






3 House 1 __

3



1 __ 3 = x ___

18

1 __ 3 = x ___

18

x = 6














P(hazel) = 9 ___ 28

P(brown) = 10 ___ 28

P(blue) = 7 ___ 28

P(green) = 2 ___ 28






unknown quantity




P(white or gray) = 3 __ 9 = 1 __

3


prediction is then








Y GRR

R R

RR





card is 12 ___ 52


52 use the least


52 Given

that 12 ___ 52

lt 26 ___ 52





P(ace) = 4 ___ 52

= 1 ___ 13


prediction is then


times 39 = 3



P(red card) = 26 ___ 52

= 1 __ 2








times6

times6

times9

times9


1 2 3 4 5 6

1 2 3 4 5 6 7

2 3 4 5 6 7 8

3 4 5 6 7 8 9

4 5 6 7 8 9 10

5 6 7 8 9 10 11

6 7 8 9 10 11 12




P(sum of 8) = 5 ___ 36

P(sum of 11) = 2 ___ 36



gt 2 ___ 36




= 1 __ 4




1 __ 4 times 180 = 45





so P(sum of 3) = 3 ___ 36

= 1 ___ 12


prediction is then


middot 36 = 3





time









that is not green



green is 3 + 9 _________

3 + 8 + 9 = 12 ___



20 = 12 ___

40






6 = 1 ___

12



P(5 or heads) = 1 __ 6 + 1 __

2 - 1 __

6 times 1 __

2 = 7 ___

12





LESSON 134

Your Turn



1 0 0 1 No

2 0 1 No

3 1 No

4 0 1 No

5 1 No

6 0 0 0 1 Yes

7 0 0 1 No

8 0 1 No

9 1 No

10 0 0 0 0 1 Yes




or 20



1 1 0 1 1 0 3

2 0 1 0 0 1 2

3 0 0 0 0 1 1

4 0 0 1 1 0 2

5 1 1 1 1 1 5

6 1 0 0 0 0 1

7 1 0 1 1 0 3

8 1 0 1 0 0 2

9 0 1 1 1 1 4

10 0 0 0 0 0 0



= 70


Guided Practice







numbers each time

2


1 10 3 5 1 2

2 10 4 6 5 0

3 3 2 10 3 3

4 2 10 4 4 1

5 7 3 6 3 2

6 8 4 8 5 0

7 6 2 2 8 2

8 6 5 2 4 1

9 2 2 3 2 4

10 6 3 1 5 2




8 ___ 10

= 80









= 10




= 20














1 3 1

2 4 2 2

3 2 1

4 1 1

5 2 1

6 4 5 3 2

7 4 2 2

8 4 5 2 1

9 4 4 3 3

10 5 1 2


1 + 2 + 1 + 1 + 1 + 2 + 2 + 1 + 3 + 2

_________________________________ 10

= 16 ___ 10

= 1 3 __ 5

















MODULE 13

Ready to Go On


= 12 ___________________ 12 + 12 + 15 + 9 + 12

= 12 ___ 60

= 1 __ 5 020 or 20




= 13 + 13

_______ 52

= 26 ___ 52

= 1 __ 2 050 or 50








or

40





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