Austin Community College

Math Fundamentals

II 5TH EDITION

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Table of Contents

Understanding Decimals 6 Reading Decimals 7 Writing Decimals 8 Getting Rid of Unnessary Zeros 10 Changing Decimals to Fractions 11 Changing Fractions to Decimals 12 Comparing Decimals 13 Rounding Decimals 14 Adding Decimals 17 Review: Adding Decimals 18 Subtracting Decimals 20 Review: Subtracting Decimals 21 Multiplying Decimals 22 Multiplying Decimals by 10,100,1000,10000 23 Review: Multiplying Decimals 24 Dividing Decimals by Whole Numbers 25 Dividing Decimals by Decimals 26 Review: Dividing Decimals 27

Understanding Fractions 29 Ratios 33 Identifying Fractions 34 Changing Improper Fractions to Whole or Mixed Numbers 35 Changing Mixed Numbers to Improper Fractions 36 Raising Fractions to Higher Terms 37 Simplifying Fractions 38 Identifying the Size of Fractions 39 Adding Fractions with the Same Denominator 40 Adding Fractions with Different Denominators 42 Subtracting with the Same Denominator 44 Subtracting with Different Denominators 45 Borrowing and Subtracting Fractions 47 Review: Adding and Subtracting Fractions 49 Multiplication of Fractions 50 Cross Canceling Fractions in Multiplication 51 Multiplying Mixed and Whole Number Fractions 52

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Dividing Fractions 54 Dividing Fractions with Whole and Mixed Numbers 55 Review Test: Fraction Word Problems 57

Understanding Percent 62 Changing Fractions to Decimals 65 Changing Decimals to Percent 66 Changing Fractions to Percent 67 Changing Percent to Fractions 68 Finding a Number when a Fraction is Given 69 Finding a Percent of a Number 71 Finding what Percent One Number is of Another 73 Review: Applying your Skills 74 Solving Two-Step Percent Problems 75 Finding Percent of Change 78 Finding a Number When a Percent of it is Given 79 Review: Applying Your Skills 81 Recognizing Types of Percent Problems 83 Review: Percent 84

Special Topics Exponets 86 Order of Operation 87 Math Topics – Average, Mean, Mode 94 Conversions 99 Using Conversions 100 Conversions – Addition 101 Conversions – Subtraction 102 Conversions – Multiplication 103 Conversions – Division 104 Geometry- Perimeter 105 Geometry- Area 107 Graphing – Bar Chart 109 Graphing – Pie Chart 111 Graphing – Line Graph 113 Post Test: 115 Answers 110 Glossary 124

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Video1

Compare decimal decimal point

Circle the tenth place

2.334 5.944 25.0678 4.78857

Circle the thousandth place

7.878765 29.0045 46.08733 44.22134

Circle the hundred-thousandth place

12.08875 778.003455 .008786 3.97824545

Circle the hundredth place

24.0916 .10594 34.98642 123.8411 Circle the ten-thousandth place

11.26791 345.167391 16.093478 .247891

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.8 = .3 =

.5 = .9 =

.24 = .13 =

.45 = .87 =

.035 = .098 =

.0045 = .1322 =

.03255 = .02238 =

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Video

eight tenths =

fifteen hundredths =

one and three hundredths =

ten and thirty-two hundredths =

ten and five hundred twelve thousandths =

three hundred and seventeen thousandths =

seven thousandths = .

ninety nine and four hundred-thousandths =

three hundred two and two hundred two ten-thousandths =

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one ten-thousandths =

eighteen ten-thousandths =

two hundred-thousandths =

five and seventy one hundred-thousandths =

eight and eighty-eight millionths =

twenty ten-thousandths =

two hundred one thousandths =

seven and sixty two hundred-thousandths =

twenty-eight and one hundred forty-eight millionths =

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5.02320 = 023.03200 = 00.010 =

0.0110 = 0.010 = 00.000200 =

0003.0332100 = .80 = 0.520 =

01.010 = 00.0020 = 0.030 =

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Video

.8 = .5 = .2 =

.3 = .08 = .05 =

.22 = .35 = .003 =

.025 = .004 = .048 =

.006 = .008= .002=

.042= 2.2= 8.4=

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4

5=

3

8=

2

3=

5

12=

11

20=

5

8=

17

40=

3

4=

3

5=

7

25=

7

10=

1

8=

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Video

.04 or .006 .09 or .99 .12 or .012

.5 or .51 .67 or .76 .22 or .0227

.02 or .22 .17 or .017 .05 or .51

.1 or .11 .03 or .303 .3 or .333

.007 or .707 .2 or .3 .99 or .98

Put these in order from smallest to largest.

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.04, .4, .004, .0404=

.03, .33, .303, .003=

.02, .27, .027, .2727=

.5, .55, .005, .555=

.07, .4, .74, .47=

.09, .99, .909, .9999=

.9797, .097, .79, .797=

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Video

Round to tenth

4.076= 2.097= .99=

.0874= .22= .85=

5.099= .044= .999=

.089= .945= .06=

Round to hundredth

4.0765= 2.0974= .9994=

.0874= .2298= 5.099=

.044= .994= .089=

Round to thousandth

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4.0765= 2.0974= .9999=

.0874= .2295= 5.09954=

.04449= .99944= .08946=

Round to hundred-thousandth

4.076967= 2.097555=

.990058= .08740978=

.04459234= .9921965=

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Video

Align place value vertical

.089 + .007 + .0003= 12 +.0003 + .101=

.07 + .64 + .002= 26 +1.4 + .003=

.77 + 2.7 + .1003= 74 +.87 + 2.3=

.6 + 5.29 + .0076= 1 +.0003 + .00501=

.085 + .7 + 2.03= 12.02 +.0009 + .444=

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5 + 8.1202 = 248/42 =

David is runs at Town Lake. He ran 1.5 miles on Monday, 2.75 miles on

Wednesday, and 3.8 miles on Friday. How many miles did he run during the

week?

13.09 + .00034 = 10,028-8,976 =

Maria needs to combine different chemicals for her nursing class. She

combines 3.002 ounces of saline and 2.101 ounces of medication. How many

total ounces did she combine?

1.001 + 3.12 =

Mark is adding the weight of different rocks in his geology class. The first

stone is 1.0229 ounces. The second stone is 11.0301 ounces. The final stone is

2.0011 ounces. What is the total weight of all the stones weighed?

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12.99 + 12.012 = 5.2 + 12.001 + 5.001 =

9 + 15.0202 + .09 = 13,598/ 57 =

Maria is calibrating her hard drive for work. One circuit measures 3.022 volts.

The other measures 2.0097 volts. What is the combined voltage between

them? =

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Video

difference

.004 - .0002 = 12 - 2.2 =

.1 - .0006 = 1.003 - .2 =

.111 - .00007 = 4.00003 - .0202 =

.3939 - .0444 = .767 - .00002 =

3.003 - .88999 = .945 - .909 =

7.348 - .00099 = .003 - .000999 =

.33 - .0099 = 5 - .00099 =

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5 - 4.00999 =

Lisa needs to travel 23.4 miles to get to Kyle, Texas. She has driven 13.9 miles

now. How many miles does she need to travel to get to Kyle?

3.9 - 1.009 = 19,487 / 37 =

Mike is in a welding class at ACC. He has 131.023 feet of wire for his welder.

He uses 11.0229 feet to build a table. How many feet of wire does he have

remaining? =

12.04 - 4.0009 =

Todd, Miles and Mary are working on a project for their chemistry class. They

start with 76.045 ounces of chlorine. They use 21.0034 ounces for their

project. How many ounces of chlorine remain? =

3.0213 - 2.999 = 390,774 - 89,999 =

5.002 - 2 =

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Video

Factor product

12 x .03= .001 x 3= .003 x 7=

(.002)3= (.363)(4)= .025(9)=

.9(.03)= (.33)03= .003(.03)=

3.33 x .03= .99 x .36= .0055 x 7.1=

(.2323)3= (.77)(1.04)= .088(.99)=

(.023)(.013)= (.0901)(.34)=

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Video

10 x .03= .003 x 10=

(.002)(100)= (.025)(100)=

10 x .0002= .3 x 100=

(.0066)(1000)= (.392)(1000)=

10,000 x .492= .391 x 10,000=

100,000 x .009= 1.12 x 100,000=

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5.089 X 4 =

Mike used 331kilowatt hours of electricity for the month. The charge is .023

per kilowatt hour. What is his monthly bill?

Jill makes $15.45 per hour. She works for 9.75 hours today. How much did she

make today?

Carmen buys 24 gallons of gas for her truck. The charge on the billboard is

$3.849 per gallon. How much does she pay for her fill-up?

.089 X .002 = 12 - .0027 =

5.1 X .002 = 13.4 X .008 =

4.09 X 3 = 39,487 / 457 =

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Video

Dividend divisor quotient

Numerator denominator

.25

5=

.055

10=

.16

4=

.0488

16=

10.048 ÷ 4= 3.069 ÷ 9=.

. 09336 ÷ 3= 76.002 ÷ 2=

10.053

12=

30.024

16=

.00044

22=

49.007

7=

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Video

. 5 ÷ .5= . 6 ÷ .2=

. 8 ÷ .2= . 4 ÷ .2=

. 05 ÷ .5= . 06 ÷ .2=

. 08 ÷ .2= . 04 ÷ .2=

. 5 ÷ .05= . 6 ÷ .02=

.8 ÷ .02= . 4 ÷ .02=

. 5 ÷ .005= . 6 ÷ .002=

. 8 ÷ 00.2= . 4 ÷ .002=

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5 / .002 = 35,900 + 99,234 =

Dave drove to Dallas for a job interview. He drove a total of 188.25 miles in 5.5

hours. How many miles per hour did he drive?

Carla is mixing chemicals in the lab. She mixes 45.003 liters of chlorine with

.33 liters or H2O. What is the combined amount?

4.02 ÷ .022 = 900,356 - 47,977 =

Angela, a nurse, has 153.3 ounces of solution to administer to a patient. The

doctor insisted she give 36.3 ounces per day. How many days of solution does

she have?

2.524 / 5 = 19000 x 1300 =

1.334 ÷ .46 = 975,000 / 150 =

.9 ÷ 360 = 1.004 - .00089 =

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5.32 / .007 = 45(.0046) =

57.8

.68= 12 - .0397 =

558.6 / .06 = 10,022 - 969 =

Liz has 28 fl oz of saline. She needs to fill vials with .4 oz. How many vials can

she fill? =

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Video

Common multiple denominator numerator

Fraction equivalent fractions

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0___________1

2___________1 0___________

1

2___________1

Where is 𝟏

𝟒 on the number line? Where is

𝟏

𝟑 on the number line?

0___________1

2___________1 0___________

1

2___________1

Where is 𝟏

𝟓 on the number line? Where is

𝟐

𝟑 on the number line?

0___________1

2___________1 0___________

1

2___________1

Where is 𝟏

𝟖 on the number line? Where is

𝟒

𝟓 on the number line?

0___________1

2___________1 0___________

1

2___________1

Where is 𝟏

𝟏𝟐 on the number line? Where is

𝟖

𝟗 on the number line?

0___________1

2___________1 0___________

1

2___________1

Where is 𝟏𝟎

𝟏𝟏 on the number line? Where is

𝟑

𝟒 on the number line?

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Break into 8ths. Break into 5ths.

Break into 3rds. Break into 10ths.

Break into 6ths Break into 4ths

Break into 8ths Break into 7ths

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What fraction of the table is filled?

What fraction of the table is filled?

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Video

What is 6in of a foot?

What are 10 of a dozen?

What is the ratio of women in this class?

What is the ratio of men in this class?

What is the ratio of the weekend to the week?

What is the ratio of daughters you have?

What is the ratio of sons you have?

What is the ratio of people wearing white shirts today?

What is the ratio of people wearing a color other than white?

What is the ratio of hours you work this week compared to 40?

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Video

1

2= Proper - Why is this proper?

5

2 = Improper - Why is this improper?

32

3 = Mixed - What makes this mixed? Is it proper?

9

6 =

2

3 =

10

5 =

32

6 =

1

5=

7

7 =

42

6 =

5

27 =

13

5 =

38

6 =

5

14 =

10

45 =

5

2 = 6

7

14 =

200

2 =

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Video

15

5 =

10

8 =

26

8=

11

2 =

42

7 =

8

8 =

9

1 =

12

5 =

18

6 =

7

7 =

30

7 =

24

23 =

33

8 =

26

5 =

16

8 =

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Video

23

4= 3

5

9= 1

4

7=

67

8= 9

1

2= 5

1

3=

83

4= 10

1

3= 11

2

5=

25

6= 6

1

7= 4

5

12=

63

5= 5

4

6= 7

2

3=

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1

3=

9

1

5=

25

1

9=

36

2

4=

16

2

7=

35

4

5=

45

6

7=

49

9

11=

33

2

12=

24

4

9=

81

5

8=

64

3

7=

56

6

7=

28

3

10=

60

2

5=

65

3

8=

72

3

4=

36

4

5=

30

2

7=

21

3

8=

64

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Video

Simplify

How do you know when you cannot simplify anymore?

What are prime numbers? How do they apply here?

Does the amount change if the numbers change?

6

12=

4

12=

7

28=

3

9=

25

30=

32

36=

20

30=

21

24=

16

18=

20

50=

18

36=

70

200=

100

400=

54

81=

75

85=

45

70=

20

40=

42

56=

5

15=

48

64=

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Video

How do you find half?

Label the following fractions as more than, less than, or equal to one-half using

the following symbols: <, >, =.

2

3

1

2

5

15

1

2

10

20

1

2

2

11

1

2

7

14

1

2

10

13

1

2

21

50

1

2

8

15

1

2

2

4

1

2

17

30

1

2

3

4

1

2

4

9

1

2

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Video

What is a sum?

What are some other words that mean the same as sum?

Why do we add or subtract the parts first?

2

9 +

3

9 =

4

8 +

3

8 =

4

15 +

7

15 =

1

11 +

3

11 =

2

9 +

3

9 +

1

9 =

2

8 +

4

8 +

1

8 =

2

15 +

7

15 +

4

15 =

1

10 +

3

10 +

7

10 =

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9

20 +

3

20 +

7

20 = 3

3

10 + 2

1

10=

11

7 + 3

2

7= 6

6

24 + 3

1

24=

24

8 + 1

2

8= 4

2

11 + 3

4

11=

12

4 + 3

1

4= 4

5

15+ 7

3

15=

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Video

What does common mean?

What is a LCD? What is a GCD?

4

5+

1

4=

3

5+

2

15=

4

7+

5

14=

6

10+

5

20=

3

8+

3

4=

3

4+

5

8=

3

4+

5

6=

1

3+

2

5=

3

4+

4

7=

1

6+

1

7=

1

3+

1

7=

1

3+

1

8=

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1

6+

1

9=

1

4+

1

7=

1

6+

1

8=

43

5+ 6

3

4= 7

5

8+ 9

2

3=

85

9+ 3

2

3= 6

5

12+ 7

3

8=

63

4+ 4

3

5= 2

7

10+ 7

1

2=

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Video

What does the word difference mean?

5

9−

2

9=

5

8−

1

8=

7

12−

5

12=

15

16−

9

16=

3

4−

2

4=

3

5−

2

5=

14

17−

9

17= 7

8

9− 6

5

9=

93

5− 5

2

5= 13

9

10− 2

1

10=

158

18− 6

5

18= 15

9

11− 2

7

11=

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Video

3

4−

1

2=

1

2−

3

10=

5

6−

1

3=

5

8−

1

4=

5

6−

3

5=

5

9−

1

6=

7

8−

2

3=

4

5−

1

3=

3

4−

5

9=

7

24−

2

12=

3

4−

7

10=

4

8−

1

6=

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4

5−

3

4= 5

2

3− 3

3

5=

411

16− 2

3

8= 14

11

12− 7

5

8=

111

3− 5

1

8= 12

1

2− 8

4

9=

71

2− 3

2

5= 24

5

6− 21

4

5=

97

8− 2

1

24= 7

11

27− 4

2

9=

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Video

9 −3

8= 4 −

3

7=

12 − 83

7= 5 −

4

8=

12 −1

2= 18 −

7

10=

7 −1

3= 10 −

3

9=

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51

11− 2

10

11= 5

3

5− 2

4

5=

711

15− 2

13

15= 6

3

10− 3

9

10=

81

3− 4

5

9= 14

2

5− 6

11

12=

73

4− 1

9

10= 12

3

7− 7

4

5=

52

5− 3

7

8= 24

1

6− 21

4

5=

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At soccer practice, group A ran 68

100 yards. Group B ran

72

100 yards. How much

more did group B run than group A?

12 −1

2= 18 −

7

10= 5 −

4

8=

Kim parked at a timed parking space. She put in enough quarters for 3

4 of an

hour. She has been parked there for 1

4 of an hour. How much time does she

have left?

5

6 +

1

3 = 4

3

5+ 6

3

4= 7

5

8+ 9

2

3 =

72

3− 2

8

9= 19

1

2− 13

3

10= 18

4

9− 14

3

4=

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Video

What does the word product mean?

5

7 ×

2

9 =

2

3 ×

4

5 =

3

4 ×

5

8 =

1

8 ×

7

10 =

9

10 ×

1

4 =

4

7 ×

4

9 =

1

3 ×

1

5 =

5

6 ×

5

8 =

8

9 ×

2

9 =

3

8 ×

7

8 =

7

9 ×

2

5 =

1

6 ×

5

6 =

5

7 ×

1

3 ×

1

2=

2

5 ×

7

9 ×

1

3=

2

3 ×

1

3 ×

5

9=

3

5 ×

1

2 ×

3

4=

1

3 ×

4

5 ×

2

3=

1

3 ×

5

7 ×

2

3=

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Are you changing the amount of the fraction?

2

5×

3

4=

6

7×

5

12=

4

9×

3

8=

5

8×

7

10=

9

20×

5

6=

4

5×

1

6=

8

15×

5

12=

4

5×

15

16=

5

6×

9

10=

5

12×

9

10=

2

8×

5

10=

3

16×

8

9=

15

16×

12

25=

6

7×

5

24=

5

6×

12

25=

8

15×

9

32

5

36×

9

20=

15

16×

4

5=

4

9×

9

14=

8

15×

3

16=

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Video

:

13

7× 4 = 9 × 2

1

4= 2

2

3× 10 =

3 × 14

5= 2

8

15× 45 = 12 × 2

3

20=

5

9× 18 = 15 ×

2

3= 2

7

30× 35 =

16 × 15

24=

7

12× 36 = 2 ×

9

10=

115

16× 12 = 32 × 1

7

16= 2

11

40× 20 =

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24 ×7

8= 2

6

7(9) = 1

1

9(6) =

12

16(23) = 2

3

7(8) = 2

6

14⋅ 15 =

3

5⋅ 15 =

8

14⋅ 23 = 2

8

9⋅ 17 =

11

10(14) = 3

7

8(17) = 3

2

6(29) =

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Video

Invert Reciprocal quotient

Dividend divisor reciprocal

3

7÷

2

5=

7

15÷

4

5=

5

12÷

3

4=

21

25÷

7

10=

8

9÷

2

9=

11

16÷

5

8=

7

8÷

5

6=

8

9÷

5

12=

4

9÷

2

3=

1

12÷

7

9=

4

15÷

1

15=

49

50÷

7

10=

9

20÷

3

4=

17

48÷

1

24=

5

12÷

3

16=

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Video 1 Video 2

3

4÷ 2 =

2

3÷ 6 =

4

5÷ 4 =

2

3÷ 4 =

9

17÷ 3 =

1

2÷ 3 =

3

5÷ 15 =

1

4÷ 3 =

1

4÷ 2 =

12 ÷2

5= 6 ÷

1

2= 5 ÷

3

4=

9 ÷1

3= 45 ÷

9

10= 15 ÷

1

2=

21

3÷

1

4= 1

2

3÷

2

3= 1

1

2÷

3

4=

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41

3÷

2

9= 2

2

5÷ 3

1

2=

5

8÷ 1

1

4=

7

12÷ 2

1

2=

9

16÷ 3

3

4=

14

15÷ 1

1

6=

33

4÷ 4

1

2= 3

1

3÷ 3

1

2= 2

1

4÷ 4

2

3=

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During a culinary class at ACC, Stephanie has 10 cups of sugar. Her cookie

recipe calls for 11

4cups of sugar for one batch. What is the greatest batch of

cookies Stephanie can make with the sugar that she has?

In a survey conducted a local coffee shop in Austin, 7

8 of the people said that

buying products from local merchants is important. Of those, only 1

2buy

products from local merchants on a regular basis. What fraction of the people

surveyed buy products from local merchants regularly?

Paul planned to spend 31

2hours outside at Zilker Park. He has been outside for

13

4hours. How many more hours does he plan to spend at Zilker Park?

Kyra can work up to 20 hours per week at her part-time job tutoring with

ACC. She worked 51

4hours on Tuesday and 8

1

2hours on Wednesday. How

many more hours can she work this week?

Amy walked 1

4mile to HEB,

1

2a mile to her daughter’s school, and then

1

8mile to

the bus stop. How much did she walk in all?

58 | P a g e

An aquarium can hold 50 gallons of water. How many containers of water can

be filled from the tank if each container holds 11

3gallons?

Julian wants to share 51

2pounds of candy with three of his co-workers. What

is the weight of candy each person will get?

Jarred and Chelsea want to buy a condominium for $188,000. They plan to

make a down payment of 1

10the price of the condominium. How much is the

down payment?

Shawnese’s regular workweek is 40 hours. This week, she has already worked 4

5 of that time. How many hours has she worked this week?

At Juan in a Million Restaurant, the chef uses 1

3cup of queso on each serving of

enchiladas. How many servings can he make from 12 cups of queso?

Bryan drives 34

9miles to class and 7

5

6miles to get to work. How far does he

drive altogether?

59 | P a g e

Diane likes to talk on the phone. She spent 12

4 hour on the phone this

morning. Then, later that afternoon, she spends another 21

2 hours on the

phone. How much time time did she spend talking on the phone?

Jim spends 2

6 of his time studying math and

3

6of his time studying reading. How

much of his time spent studying does he spend on these two subjects?

Last week, Rosa’s basil plant grew 2

12 of an inch and this week it grew

5

12 of an

inch. How much has it grown in the last two weeks?

Before Judy started taking classes and working two jobs, she weighed 145

pounds. As a result of the stress of working and taking classes, Judy has lost

93

4pounds. How much does Judy weigh now?

From a piece of fabric 5 ft. long, Frances cut 21

2ft. long. How much fabric does

she have left?

60 | P a g e

From a piece of wood 335

8long, Sam cut a piece that was 18

2

4long in his

woodwork class. How long was the remaining piece?

Lisa bought 23

4pounds of sugar. If she used 1

1

10pounds baking cookies for her

math class, how much sugar does Lisa have left?

In Brianna’s class, 1

3of the students have a sister. Of those students who have a

sister, 1

2of them have a brother. How many students have a brother and a

sister in Brianna’s class?

Justin operates an orange juice stand. On Monday, he used 𝟑

𝟒 of a bag of

oranges. On Tuesday, he used 𝟓

𝟖 as many oranges as on Monday. How many

bags of oranges did Justin use on Tuesday?

A food truck in Austin uses 𝟏

𝟐 a pound of cheese a day. They use

𝟑

𝟒 as much

lettuce as cheese. How much lettuce does the food truck use every day?

61 | P a g e

Of the students in the Crockett High School band, 𝟏

𝟖 play a brass instrument. Of

the students who play a brass instrument, 𝟏

𝟑 play the trumpet. What fraction of

the students in the band plays the trumpet?

One cubic foot of water weighs 621

2 pounds. How much does 1

1

4cubic feet of

water weigh?

Rosalinda collected 21

9 pounds of newspaper for Austin’s recycling drive. Alec

collected42

4times as much newspaper as Rosalinda. How many pounds of

newspaper did Alec collect?

Andrea is working on a project for her design class. She cuts a piece of ribbon

that is 23

4 yards long into 3 equal pieces. What is the length of each piece?

62 | P a g e

Video

63 | P a g e

A percent divides a whole into (how many)______ equal parts?

A quarter is ____ percent of a dollar.

If I have 30% of 100 dollars, I have _____ dollars.

If a store sells every jacket in stock, _____% of the jackets were sold.

Angela ate half of the crackers on her plate. She ate_____% of the crackers.

Bob scored 100% on his last quiz. If there were 10 questions in that quiz, he

answered _____ questions correctly.

64 | P a g e

Shade 100%

Shade 25%

Shade 75%

Shade 10%

Shade 33%

65 | P a g e

Video

3

4=

1

4=

4

8=

8

12=

1

2=

1

8=

5

12=

12

18=

3

12=

11

15=

5

4=

6

6=

66 | P a g e

Video

0.34 = 0.08 =

0.2= 0.624 =

0.7 = 0.5 =

0.08½ = 0.4=

0.007 = 0.25 =

0.6 = 0.029 =

0.0051 = 0.0003 =

0.045 = 0.01 =

67 | P a g e

Video

1

4=

2

4=

3

4=

4

4=

1

5=

2

5=

3

5=

4

5=

5

5=

1

8=

68 | P a g e

Video

20% = 40% = 60% =

80% = 100% = 23% =

82% = 92% = 21% =

35% = 112% = 72%

17% = 87% = 5% =

85% = .77% = 21% =

69 | P a g e

What is 1

2 of 100? What is

1

3of 90?

What is 1

4of 80? What is

1

5of 50?

What is 1

6of 30? What is

1

10of 20?

What is 3

5of 200? What is

5

8of 1000?

What is 5

6of 240? What is

3

7of 2100?

What is 12

13of 390? 25 is

1

2of what number?

70 | P a g e

10 is 1

3of what number? 15 is

3

4of what number?

50% of 68 = 33 ⅓% of 15 =

20% of 125= 16 ⅔% of 270=

12 ½% of 144 = 10 % of 5,540 =

33 ⅓% of 168 = 25% of 280 =

16 ⅔ % of 54 = 25% of 260 =

71 | P a g e

Video

The college application that Marcus filled out had 20 questions on it. 15% of

the questions were multiple-choice. How many questions were not multiple-

choice?

Fern took an early morning class at Eastview Campus during the spring. It met

25 times, and she attended 80% of the time. How many classes did she miss?

Cara’s night class had a substitute teacher 10% of the time and met 20 times.

How many times did the real teacher attend class?

Greg joined a weight loss club at school and lost 20% of his original weight of

225 pounds. What does he weigh now?

In last month’s budget, Darla set aside 121

2% for food. If her take-home pay is

$2,240 each month, how much did she spend on food?

Edwin made a down payment of 331

3 % on a house that cost $60,000. How

much was the down payment?

72 | P a g e

The student council has 120 members. If 65% of the members attended the

last meeting, how many members were at the meeting?

While working as a telemarketer, Bob earned 5% commission on sales. If his

sales totaled $32,000 how much was his commission?

Abby’s class met a total of 30 times. During this term, Abby was late 20% of

the time. How many days was she late?

Heidi’s college textbooks cost $240 before taxes. If sales tax is 8 .25%, how

much will she pay in taxes?

Alex and Beatrice agree to each pay fifty percent of the restaurant bill. If the

bill is $28.30, how much does each of them pay?

73 | P a g e

4 is what percent of 20? = 30 is what percent of 120? =

16 is what percent of 48? = 18 is what percent of 180? =

28 is what percent of 168? = 45 is what percent of 60? =

42 is what percent of 336?= 26 is what percent of 52? =

34 is what percent of 85? = 180 is what percent of 225?=

18 is what percent of 120? = 72 is what percent of 240? =

74 | P a g e

There are 30 members in a nature watch club. Only 18 of them came to their last meeting. What percent of the members attended?

Usually, Sophie makes $500 a week, but last week she worked overtime and made $100 more. By what percent did her paycheck increase?

The new cell phone Tory wants is $128. He has saved $96 so far. What percent has he saved?

Valerie gets 28 out of 35 problems correct on the end-of-term assessment. What percent of the problems did she answer correctly?

Tracey sets aside 48 hours a week for work. Twelve of those hours are time spent commuting to and from work. What percent of the time is Tracey commuting?

Summer lasts from June to August. What percent of a year is that?

Taylor has to write an essay that is 300 words long but has only written 114 words. What percent is complete?

75 | P a g e

Isis lost 20% of her body weight of 175 pounds. How much does she weigh

now?

Oscar sets aside 10 hours for studying each week. He spends 25% of that time on Algebra. How many of his study hours are left for other courses?

The college bookstore has a sale for 40% off all clothing. If a sweater originally cost $60, what is it’s price after the discount?

Alan buys an energy drink from the school cafeteria for $1.60. How much does he pay after being charged 8.25% sales tax?

76 | P a g e

Kaitlyn works at the college bookstore and gets an employee discount of 15%. She buys a new backpack priced at $60. How much does she pay after the discount?

Last fall, a total of 250 new students enrolled in classes. This fall, that number is expected to increase by 12%. How many new students are expected?

Lewis receives store credit for selling one of his used textbooks. He gets 30% of its original cost of $120. He uses this store credit towards the purchase of his biology book, which costs $116. How much does he have left to pay after the store credit is applied?

Martha uses her gasoline credit card to pump gas and saves 3% off the total cost. If the regular price for 12 gallons of gasoline is $40.80, how much does she pay?

77 | P a g e

A laptop computer that cost $580 last month is 15% off this month. How much does it cost now?

Samantha has a school loan of $2,500. The bank charges 1.25% interest each

month. Find the monthly interest on her balance.

A new business interviewed 1,500 people to fill their job openings. Of these,

4.2 were hired. How many people were hired?

A handcrafted leather bracelet costs $12.50. Using an 8% sales tax, what is the

price of the bracelet?

78 | P a g e

A new edition of a GED practice book costs $74.90. Tracey finds a used version

of the same book at 20% off. How much is the used version?

Of 290 students surveyed, 60% do not have health insurance. How many

students do not have health insurance?

The campus cafe sells about 216 cups of coffee each day. During finals week

that number increases by 75% How many cups of coffee do they sell during a

day of finals week?

79 | P a g e

Video

Phillip wants to buy a T.V. It cost $450, but is on sale for $350. What is the

percent saving?

Steve makes $500 a week. His boss increased his salary to $660 each week.

What is the percent change?

Silvia sells jewelry. She buys a silver necklace for $45 and sells it for $90. What

is the percent markup she charges?

80 | P a g e

Video

2% of what number is 10? = 5% of what number is 7? =

5% of what number is 15? = 10% of what number is 23? =

10% of what number is 9? = 14% of what number is 42? =

20% of what number is 4? = 25% of what number is 10? =

25% of what number is 18? = 28% of what number is 56? =

30% of what number is 60? = 40% of what number is 6? =

81 | P a g e

50% of what number is 37? = 60% of what number is 12? =

75% of what number is 120? = 95% of what number is 190 =

12 ½% of what number is 10? = 16 ⅔% of what number is 9? =

33 ⅓% of what number is 32? = 5½% of what number is 11? =

82 | P a g e

Abbey saved $50 on her textbooks by buying them used. $50 is 40% of the

market value for the new textbooks. How much would she have paid if she had

bought the books new?

Bailey scored a 90% on a quiz by answering 18 problems correctly. How many

total problems were there?

Cory had to pay a 25% initial payment when setting up his tuition payment

plan for school. He paid $283. How much was his total tuition?

Derrick spends 15% of his paycheck on food each month. How much did he

get paid if he spent $176.25 on food?

Elisa saves 5% for every purchase she spends on a credit card. If she saved

$7.50 on her last purchase, how much was the original price of the sale?

The price of an iPod was reduced by 40% when the newest model came out. If

the price is now 96, how much was it originally?

83 | P a g e

Gabby has an employee discount of 12%. If she saved $18 on her last

purchase, how much was the cost before her discount?

Homer has to finish reading a book by the end of the week. He has read 65%

so far, a total of 182 pages. How many pages are in the book?

Ivan has placed 42 feet of fencing along the backyard. He is 70% done. Once

the job is complete, how many feet of fencing will he have placed?

Joanne has completed 24% of her homework. If there are 12 questions done

so far, how many questions are there in the homework assignment? =

Carlos put gas in his car on the way to Eastview Campus. He paid with his

store credit card which saves him 5%. The receipt says he saved $2. How

much gas did he put in the car?

Erica is traveling to South Austin Campus. She has traveled 6.3 miles has

driven 35% of the way. What is the total distance she will travel?

84 | P a g e

16 is what percent of 50? What is 25% of 80?

12 is 30% of what number? Find 20% of 125.

What percent of 80 is 10? What is 75% of 300?

52 is what percent of 156? What is 16 ⅔% of 42?

Find 50% of 128. is 8% of what number?

11 is 44% of what number? What percent of 60 is 15?

85 | P a g e

4 is what percent of 80? 78,111 - 65,476 =

15% of 65 is what? 35

6+ 5

6

7=

8 is 4% of what number? 58,376 / 34 =

3 is what percent of 38? 4 - 2

3=

Darla’s tomato seedling was 6 inches tall last week. That is 75% of the height

it is now. How tall is it now?

4 is what percent of 80? 390,234 + 211,228 =

15% of 65 is what? 1004

7- 5

6

7=

8 is 4% of what number? 800 x 223 =

86 | P a g e

5 is what percent of 40? 4 + 65

9=

Gale would like to buy a house on the east side of Austin. She found a house.

She would need to put $11,000 dollars down on the mortgage. She has 35% of

it now. How much money does she need to save to be complete? =

87 | P a g e

Video

50 = 42 = 62 = 71 =

82 = 112 = 23 = 43 =

54 = 81 = 10 = 73 =

53 = 82 = 14 = 41 =

52 = 83 = 04 = 21 =

88 | P a g e

Video

Arithmetic expression strategy

3+4+2-3-1= (3+4)+(4-3)-1=

3+(10+2-3)-1= 3+4+2-(3-1)=

3+(4+2)-(3-1)= (3+4+2)-3-1=

3 (4)

2= (3)(

4

2 )(8) =

3(4)

(2)(3)= 4 + 2(3) – 4 =

4(3)-2(2) +2 = (3+2)(2) -4 =

89 | P a g e

Video

What is average or mean? How do you use it?

What is median? How do you use it? What is mode? How do you use it?

What is range? How do you use it?

Sample data: 12, 15, 14, 10, 12, 17, 14, 12, 10, 12, 17, 12, 10

Now compute the mean, mode, median and range for this data.

Sample data: 100, 90, 100, 80, 80, 90, 100, 100, 90, 70, 80, 100, 80, 100

Now compute the mean, mode, median and range for this data.

90 | P a g e

Video

1 Ton = ______ lb 1 lb = ______ ounces

1 year = ______ weeks 1 week = ______ days

1 day = ______ hours 1 hour = ______ minutes

1 mile = ______ feet 1 foot = ______ inches

1 kilometer= ______meters 1 meter = ______ centimeters

1 yard = ______ feet 1 mile = ______ feet

91 | P a g e

2 T=____lb 4 lb=____oz

3 yr=____wks 6 wks____days

12 days=_____hr 11 hrs_____min

2 miles=______ft 5 ft=_____in

3 km=_______m 5 m=_____cm

5 mi=_____yds 4 yds=______ft

92 | P a g e

4 days 20 hr 10 hr 56 min

+ 3 days 14 hr + 1 hr 37 min

3 ft 16 in 3 yds 2 ft

+ 2 ft 13 in + 1 yd 4 ft

1 T 1999 lb 15 oz 1 yr 18 hr

+ 14 oz + 364 days 5 hr

300 days 18 hr 8 km 165 m 76 cm

+ 400 days 30 hr + 3 km 775 m 97 cm

93 | P a g e

8 days 13 hr 10 hr 22 min

- 3 days 14 hr - 1 hr 37 min

1 km 1345 m 4 m

- 2234 m - 2 m 99 cm

1 T 1999 lb 10 oz 1 yr 1 hr

- 14 oz - 364 days 5 hr

300 days 18 hr 8 km 165 m 67 cm

- 100 days 30 hr - 3 km 775 m 97 cm

94 | P a g e

4 days 20 hr 10 hr 56 min

X 3 x 5

3 ft 16 in 3 yds 2 ft

X 4 x 6

1 T 1999 lb 15 oz 1 yr 18 hr

X 7 x 9

300 days 18 hr 8 km 165 m 76 cm

X 8 x 6

95 | P a g e

13 𝑑𝑎𝑦𝑠 12 ℎ𝑟𝑠

4

4 𝑦𝑑𝑠 2 𝑓𝑡

5

4 𝑘𝑚 1500 𝑚

2

5 𝑦𝑟 234 𝑑𝑎𝑦𝑠 10 ℎ𝑟 52 𝑚𝑖𝑛

6

4 𝑘𝑚 1356 𝑚 65 𝑐𝑚

3

1 𝑐𝑒𝑛𝑡𝑢𝑟𝑦 4 𝑑𝑒𝑐𝑎𝑑𝑒𝑠 54 𝑦𝑟𝑠

2

8 𝑑𝑎𝑦 5 ℎ

4

7 𝑦𝑟 5 𝑚𝑜 50 𝑤𝑘 6 𝑑 10 ℎ𝑟 33 min 10 𝑠𝑒𝑐

6

96 | P a g e

Video

What is perimeter? When do you use it? What shapes can you use perimeter with?

P= P= P=

P= P=

P

P=

97 | P a g e

Gene wants to put a fence around her garden. The length is 12 feet and the

width is 10 feet. How many feet of fence does she need to buy? Gene goes to

the hardware store and the fence is $1.54 a foot. How much will the total cost

be?

Kylie has a window that is 6 feet in height and 3 feet wide. What is the

perimeter? Kylie has 13 identical windows in her home. She wants to add

weather stripping to all the windows. If the cost is .54cents per foot, what will

the total cost be?

98 | P a g e

Video

What is area? When do you use it? What shapes can you use it with?

A= A= A=

A= A= A=

99 | P a g e

Gene wants to buy tile for the bathroom. The room’s length is 12 feet and the

width is 10 feet. How many squared feet of tile does she need to buy? If the tile

costs $1.25 a foot and the installation is .25 cents a foot, what will the total

cost be?

Kylie has a window that has three sides. The bottom is 18 in and the height is

20 in. What is the area of this window? She has 10 windows that are all the

same. What is the total are in feet? Kylie wants to add window film to the

windows to bring down her electric bill. The cost of the film is .60 cents a foot.

If she does all the windows, what will the total bill be?

100 | P a g e

Video

Use the data above to answer the following questions.

1. What is the lowest year of enrollment?

2. What is the difference between the highest and lowest enrolments?

3. What is the percentage of increase from 2011 to 2014?

4. What is the estimated average enrollment for the four years listed?

5. Based on the data, what do you think the enrollment will be for 2015

0 500 1000 1500 2000 2500

Number of Students

2014 2013 2012 2011

101 | P a g e

Use the data above to answer the following questions.

1. Based on the data, what is the average number of graduates?

2. True or false, the highest numbers of graduates are in 2011 and 2012.

3. Is the trend ascending or descending?

4. Why do you think the number of graduates is increasing?

5. What is your estimate for 2015?

0 100 200 300 400 500 600 700

Number of GED Graduates

2014 2013 2012 2011

102 | P a g e

Video

Use the data above to answer the following questions.

1. What is the largest piece of the budget? Estimate the percentage.

2. What is the smallest piece of the budget? Estimate the percentage.

3. True or false, food and rent take the largest portion of the total budget?

4. True or false, rent and gas have the same portion as food?

5. If the total budget is $1000, place a dollar amount on each piece of the

pie based on the size of the portion.

Budget

Rent

Food

Gas

Bills

Entertainment

103 | P a g e

My budget

Use the empty pie chart to show the portions of your bills compared to your

total budget. Use this space to do your calculations before you fill in the pie

chart.

104 | P a g e

Video

Use the data above to answer the following questions.

1. Based on the data, what are the average sales per month for each sales

person?

2. True or false, Hector has had the highest sales each month.

3. Who totaled the most sales for the five months? What is the difference

between the highest and lowest person for the five months together?

4. Based on the trends, who should have the highest amount of sales for

June? Why?

0

50

100

150

200

250

300

350

400

450

500

January Febuary March April May

Linda

Sammy

Hector

105 | P a g e

Now create your own line chart with the data provided by the instructor.

106 | P a g e

21

5+ 6

3

10= 7 - 4

7

9=

Usually, Nathan drives 3

5mile to pick up Jane. They then drive another

4

5mile to

class at ACC. Today Jane is sick, so Nathan drives 1 mile directly to class. How

much shorter is the direct route?

Carrie worked at ACC yesterday for 72

3hours yesterday and 6

3

5hours today.

How many hours did she work in the two days?

Charles has an annual salary of $39,000. If he receives a bonus of 1

20of his

annual salary, about what is his bonus?

34

7 x

2

5= 0.12 x 1.5 =

107 | P a g e

Marisa works at a plant store in Austin. Most of the plants grow at a rate of

51

2inches per week. At these rates, how many inches will most of the plants

grow in 21

2 weeks?

In his woodworking class at ACC, Joe is replacing 8 warped shelves in a

bookshelf. Each piece of wood is 151

2inches long. How much wood will he

need to replace all 8 shelves?

2.3004(.022)= .055/.5 =

A flight from Austin to El Paso took 24

5hours total. Because of delays, the

return flight took 31

8hours. How much longer did the return flight take?

Kim gets 10 vacation days a year. If she has already used, 41

4of a day, how

many more vacation days does she have left?

108 | P a g e

Write 33 ⅓ % as a fraction. = Find 4% of 450. =

Kathy has a stack of 50 books in her office. If each book is 13

4inches thick,

what is the height of the stack?

One cubic foot of water weighs 621

2 pounds. How much does 1

1

4cubic feet of

water weigh?

Rosalinda collected 21

9 pounds of newspaper for Austin’s recycling drive. Alec

collected42

4times as much newspaper as Rosalinda. How many pounds of

newspaper did Alec collect?

Write 3

25as a percent. = Write 55% as a fraction. =

109 | P a g e

Carlos has a board that is 12 feet long. He needs to cut it into pieces that

measure 3

4foot. How many pieces can he cut from the board?

Which of the following is the same as 16 ⅔% of 90? =

a. 90 ÷4

b. 90 ÷6

c. 90 ÷8

d. 90 ÷12

Jason uses 1

4 pound of chicken making the lunch special for ACC’s culinary arts

program. How many lunch specials can he make from 12 pounds of chicken?

Jim works for ACC fixing computers. On average, he can make a repair in 3

4of

an hour. How many repairs can he make in a 71

2hour workday?

Find 12.5% of 240. =

Jana needs 21

2yards of material to make a dress for her daughter’s birthday

party at Amy’s Ice Cream. How many dresses can she make from 101

2yards of

material?

110 | P a g e

Round 3.895 to the nearest hundredth. =

Find 2.48÷4 to the nearest tenth. =

Write 0.245 as a percent. =

Write 32% as a decimal. =

Conrad knows that the average lifespan of a dog is about 12 years. If his dog is

3 years old. What percent of its life has it lived? What fraction of time does the

dog have left to live?

April works at a supermarket where she gets 10% off anything in the store. If

she buys a $38 shirt and pays with a $50 dollar bill, what will her change be?

Belinda has saved $54. This is 20% of what she needs to buy the cheapest

robotic vacuum cleaner she can find. How much is the robotic vacuum

cleaner?

111 | P a g e

6. 3 9 0 7

8 4 7 1

5 5 8 4

9 0 8 4

9 3 4 8

7. Eight tenths Three tenths

Five tenths Nine tenths

Tw enty-four hundredths Thirteen hundredths

Forty-f ive hundredths Eighty-seven hundredths

Thirty-f ive thousandths Ninety-eight thousandths

Forty-f ive ten-thousandths One thousand, three hundred tw enty two ten-thousandths

Three thousand, tw o hundred f if ty-five hundred -thousandths

Tw o thousand, tw o hundred thirty-eight hundred thousandths

8.

.8

.15

1.03

10.32

10.512

.317

.007

99.00004

10. 5.0232 23.032 .01

.011 .01 .0002

3.03321 .8 .52

1.01 .002 .03

11. 4

5

1

2

1

5

3

10

2

25

1

20

11

50

7

20

3

1000

1

40

1

250

6

125

3

500

1

250

1

500

21

500 2

1

5 8

2

5

12. .8 .375

. 62

3 . 41

2

3

.55 .625

.425 .75

.6 .28

.7 .125

112 | P a g e

13. .04 .99 .12

.51 .76 .22

.22 .17 .51

.11 .303 .33

.707 .3 .99

14. .004, .04, .0404, .4

.003, .03, .303, .33

.02, .027, .27, .2727

.005, .5, .55, .555

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122 | P a g e

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124 | P a g e

Glossary

A Abbreviate

To use a short form of a word, often followed by a period, in order to save space.

Abbreviation

A shortened form of a word or phrase.

Absolute Value

The distance between a number and zero: it is always a positive number.

Acute Angle

An angle with a measure greater than 0 and less than 9.

additive identity

The number zero is called the additive identity because the sum of zero and any number is that

number.

additive inverse

The additive inverse of any number x is the number that gives zero when added to x. The additive

inverse of 5 is -5.

adjacent angles

Two angles that share both a side and a vertex.

angle

The union of two rays with a common endpoint, called the vertex.

arc

A portion of the circumference of a circle.

area

The number of square units that covers a shape or figure.

associative property of addition

(a + b) + c = a + (b + c)

associative property of multiplication

(a x b) x c = a x (b x c)

average

A number that represents the characteristics of a data set.

axis of symmetry

A line that passes through a figure in such a way that the part of the figure on one side of the line is

a mirror reflection of the part on the other side of the line.

B base

The bottom of a plane figure or three-dimensional figure.

Bisect

To divide into two congruent parts.

125 | P a g e

Box and whisker plot

A type of data plot that displays the quartiles and range of a data set.

C Cartesian coordinates

A system in which points on a plane are identified by an ordered pair of numbers, representing the

distances to two or three perpendicular axes.

central angle

An angle that has its vertex at the center of a circle.

chord

A line segment that connects two points on a curve.

circle

The set of points in a plane that are a fixed distance from a given point, called the center.

circumference

The distance around a circle.

coefficient

A constant that multiplies a variable.

collinear

Points are collinear if they lie on the same line.

combination

A selection in which order is not important.

common factor

A factor of two or more numbers.

common multiple

A multiple of two or more numbers.

commutative property of addition

a + b = b + a.

commutative property of multiplication

a*b = b*a.

complementary angles

Two angles whose sum is 90 degrees.

composite number

A natural number that is not prime.

cone

A three-dimensional figure with one vertex and a circular base.

congruent

Figures or angles that have the same size and shape.

constant

A value that does not change.

126 | P a g e

coordinate plane

The plane determined by a horizontal number line, called the x-axis, and a vertical number line,

called the y-axis, intersecting at a point called the origin. Each point in the coordinate plane can be

specified by an ordered pair of numbers.

coplanar

Points that lie within the same plane.

counting numbers

The natural numbers, or the numbers used to count.

counting principle

If a first event has n outcomes and a second event has m outcomes, then the first event followed by

the second event has n times m outcomes.

cross product

A product found by multiplying the numerator of one fraction by the denominator of another

fraction and the denominator of the first fraction by the numerator of the second.

cube

A solid figure with six square faces.

cylinder

A three-dimensional figure having two parallel bases that are congruent circles.

D data

Information that is gathered.

decimal number

The numbers in the base 10 number system, having one or more places to the right of a decimal

point.

degree

A unit of measure of an angle.

denominator

The bottom part of a fraction.

dependent events

Two events in which the outcome of the second is influenced by the outcome of the first.

diagonal

The line segment connecting two nonadjacent vertices in a polygon.

diameter

The line segment joining two points on a circle and passing through the center of the circle.

difference

The result of subtracting two numbers.

digit

The ten symbols, 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. The number 215 has three digits: 2, 1, and 5.

distributive property

a(b + c) = ab + ac

dividend

In a / b = c, a is the dividend.

127 | P a g e

divisor

In a / b = c, b is the divisor.

E ellipse

The set of all points in a plane such that the sum of the distances to two fixed points is a constant.

equation

A mathematical statement that says that two expressions have the same value; any number

sentence with an =.

equilateral triangle

A triangle that has three equal sides.

equivalent equations

Two equations whose solutions are the same.

equivalent fractions

Fractions that reduce to the same number.

error of measurement

The difference between an approximate measurement and the actual measure taken.

evaluate

To substitute number values into an expression.

even number

A natural number that is divisible by 2.

event

In probability, a set of outcomes.

exponent

A number that indicates the operation of repeated multiplication.

equivalent fractions

Fractions that reduce to the same number.

F

factor

One of two or more expressions that are multiplied together to get a product.

factoring

To break a number into its factors.

face

A flat surface of a three-dimensional figure.

formula

A equation that states a rule or a fact.

fraction

A number used to name a part of a group or a whole. The number below the bar is the denominator,

and the number above the bar is the numerator.

128 | P a g e

frequency

The number of times a particular item appears in a data set.

frequency table

A data listing which also lists the frequencies of the data.

G

graph

A type of drawing used to represent data.

greatest common factor (GCF)

The largest number that divides two or more numbers evenly.

H

horizontal

A line with zero slope.

hypotenuse

The side opposite the right angle in a right triangle.

I

identity property of addition

The sum of any number and 0 is that number.

identity property of multiplication

The product of 1 and any number is that number.

improper fraction

A fraction with a numerator that is greater than the denominator.

independent events

Two events in which the outcome of the second is not affected by the outcome of the first.

inequality

A mathematical expression which shows that two quantities are not equal.

infinity

A limitless quantity.

inscribed angle

An angle placed inside a circle with its vertex on the circle and whose sides contain chords of the

circle.

inscribed polygon

A polygon placed inside a circle so that each vertex of the polygon touches the circle.

integers

The set of numbers containing zero, the natural numbers, and all the negatives of the natural

numbers.

129 | P a g e

intercept

The x-intercept of a line or curve is the point where it crosses the x-axis, and the y- intercept of a

line or curve is the point where it crosses the y-axis.

intercepted arc

The arc of a circle within an inscribed angle.

interpolation

A method for estimating values that lie between two known values.

intersecting lines

Lines that have one and only one point in common.

inverse

Opposite. -5 is the additive inverse of 5, because their sum is zero. 1/3 is the multiplicative inverse

of 3, because their product is 1.

inverse operations

Two operations that have the opposite effect, such as addition and subtraction.

irrational number

A number that cannot be expressed as the ratio of two integers.

isosceles triangle

A triangle with at least two equal sides.

L

least common denominator

The smallest multiple of the denominators of two or more fractions.

least common multiple

The smallest nonzero number that is a multiple of two or more numbers.

like fractions

Fractions that have the same denominator.

line

A straight set of points that extends into infinity in both directions.

line of symmetry

Line that divides a geometric figure into two congruent portions.

line segment

Two points on a line, and all the points between those two points.

locus

A path of points.

logic

The study of sound reasoning.

lowest terms

Simplest form; when the GCF of the numerator and the denominator of a fraction is 1.

130 | P a g e

M

mean

In a data set, the sum of all the data points, divided by the number of data points; average.

median

The middle number in a data set when the data are put in order; a type of average.

midpoint

A point on a line segment that divides the segment into two congruent segments.

mixed number

A number written as a whole number and a fraction.

mode

A type of average; the number (or numbers) that occurs most frequently in a set of data.

multiple

A multiple of a number is the product of that number and any other whole number. Zero is a

multiple of every number.

multiplicative identity

The number 1 is the multiplicative identity because multiplying 1 times any number gives that

number.

multiplicative inverse

The reciprocal of a number.

mutually exclusive events

Two or more events that cannot occur at the same time.

N

mutually exclusive events

Two or more events that cannot occur at the same time.

normal

Perpendicular.

number line

A line on which every point represents a real number.

numerator

The top part of a fraction.

O

obtuse angle

An angle whose measure is greater than 90 degrees.

obtuse triangle

A triangle with an obtuse angle.

octagon

A polygon with 8 sides.

131 | P a g e

odd number

A whole number that is not divisible by 2.

operation

Addition, subtraction, multiplication, and division are the basic arithmetic operations.

opposites

Two numbers that lie the same distance from 0 on the number line but in opposite directions.

ordered pair

Set of two numbers in which the order has an agreed-upon meaning, such as the Cartesian

coordinates (x, y), where the first coordinate represents the horizontal position, and the second

coordinate represents the vertical position.

origin

The point (0, 0) on a coordinate plane, where the x-axis and the y-axis intersect.

outcome

In probability, a possible result of an experiment.

P

parallel

Two lines are parallel if they are in the same plane and never intersect.

parallelogram

A quadrilateral with opposite sides parallel.

pentagon

A five-sided polygon.

percent

A fraction, or ratio, in which the denominator is assumed to be 100. The symbol % is used for

percent.

perimeter

The sum of the lengths of the sides of a polygon.

permutation

A way to arrange things in which order is important.

perpendicular

Two lines are perpendicular if the angle between them is 90 degrees.

pi

The ratio of the circumference of a circle to its diameter.

plane

A flat surface that stretches into infinity.

point

A location in a plane or in space, having no dimensions.

polygon

A closed plane figure made up of several line segments that are joined together.

polyhedron

A three-dimensional solid that is bounded by plane polygons.

132 | P a g e

positive number

A real number greater than zero.

power

A number that indicates the operation of repeated multiplication.

prime number

A number whose only factors are itself and 1.

probability

For an experiment, the total number of successful events divided by the total number of possible

events.

product

The result of two numbers being multiplied together.

proper fraction

A fraction whose numerator is less than its denominator.

proportion

An equation of fractions in the form:

a/b = c/d

protractor

A device for measuring angles.

pyramid

A three-dimensional figure that has a polygon for its base and whose faces are triangles having a

common vertex.

Pythagorean Theorem The theorem that relates the three sides of a right triangle:

Q

quadrant

One of the quarters of the plane of the Cartesian coordinate system

quadrilateral

A polygon with 4 sides.

quotient

The answer to a division problem.

R

radius

The distance from the center to a point on a circle; the line segment from the center to a point on a

circle.

range

In statistics, the difference between the largest and the smallest numbers in a data set.

133 | P a g e

rate

A ratio that compares different kinds of units.

ratio

A pair of numbers that compares different types of units.

rational number

A number that can be expressed as the ratio of two integers.

ray

part of a line, with one endpoint, and extending to infinity in one direction.

real numbers

The combined set of rational numbers and irrational numbers.

reciprocal

The number which, when multiplied times a particular fraction, gives a result of 1.

rectangle

A quadrilateral with four 90-degree angles.

reflection

A transformation resulting from a flip.

regular polygon

A polygon in which all the angles are equal and all of the sides are equal.

repeating decimal

A decimal in which the digits endlessly repeat a pattern.

rhombus

A parallelogram with four equal sides.

right angle

An angle whose measure is 90 degrees.

right triangle

A triangle that contains a right angle.

root

The root of an equation is the same as the solution to the equation.

rotation

A transformation in which a figure is rotated through a given angle, about a point.

S

sample space

For an experiment, the sample space includes all the possible outcomes.

Scale drawing

A drawing that is a reduction or enlargement of the original.

scalene triangle

A triangle with three unequal sides.

scattergram

A graph with points plotted on a coordinate plane.

134 | P a g e

scientific notation

A method for writing extremely large or small numbers compactly in which the number is shown as

the product of two factors.

set

A well-defined group of objects.

similar

Two polygons are similar if their corresponding sides are proportional.

simplifying

Reducing to lowest terms.

skew lines

Lines that are not in the same plane and that do not intersect.

slope

The steepness of a line expressed as a ratio, using any two points on the line.

solution

The value of a variable that makes an equation true.

sphere

A three-dimensional figure with all points in space a fixed distance from a given point, called the

center.

square

A quadrilateral with four equal sides and four 90 degree angles.

square root

The square root of x is the number that, when multiplied by itself, gives the number, x.

statistics

The science of collecting, organizing, and analyzing data.

stem and leaf plot

A technique for organizing data for comparison.

straight angle

An angle that measures 180 degrees.

supplementary angles

Two angles are supplementary if their sum is 180 degrees.

surface area

For a three-dimensional figure, the sum of the areas of all the faces.

T

terminating decimal

A fraction whose decimal representation contains a finite number of digits.

translation

A transformation, or change in position, resulting from a slide with no turn.

transformation

A change in the position, shape, or size of a geometric figure.

transversal

A line that intersects two other lines.

135 | P a g e

trapezoid

A quadrilateral that has exactly two sides parallel.

tree diagram

A diagram that shows outcomes of an experiment.

triangle

A three-sided polygon.

U

unit price

Price per unit of measure.

V

variable

A letter used to represent a number value in an expression or an equation.

vertex

The point on an angle where the two sides intersect.

vertical angles

A pair of opposite angles that is formed by intersecting lines.

volume

A measurement of space, or capacity.

W

whole numbers

The set of numbers that includes zero and all of the natural numbers.

X

x-axis

The horizontal axis in a Cartesian coordinate plane.

x-intercept

The value of x at the point where a line or curve crosses the x-axis.

Y

y-axis

The vertical axis in a Cartesian coordinate system.

y-intercept

The value of y at the point where a curve crosses the y-axis.

136 | P a g e

Z

zero

The additive identity; the number that, when added to another number n, gives n.

zero property of multiplication

The product of zero and any number is zero.