lesson 71 parallelograms name - yolalearningtops.yolasite.com/resources/crs1_lessons071-080.pdf ·...

Saxon Math Course 1 L71-281 Adaptations Lesson 71

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Parallelograms (page 368)

• A parallelogram has two pairs of opposite, parallel sides.

• The opposite angles of a parallelogram have equal measures.

• The adjacent angles of a parallelogram are supplementary (add to 180°).

• A parallelogram can be cut in half and rearranged to form a rectangle:

• You know how to find the area of a rectangle, so you can use this methodto find the area of a parallelogram.

• Imagine cutting the parallelogram on the dashed line.

• Move the part on the left under the part on the right.

• To get the area, multiply the base times the height.

• Do not be fooled by the slanted side.

Example: Find the area of this parallelogram.

A = bh A = (6)(5) A = 30 sq. cm

• When the angles of a parallelogram change the area changes. The perimeter does not change.

Practice Set (page 371)

Refer to parallelogram QRST to answer questions a–d.

a. Which angle is opposite ∠Q? ∠

b. Which angle is opposite ∠T? ∠

c. Name two angles that are supplements of ∠T? ∠ and ∠

d. If the measure of ∠R is 100°, what is the measure of ∠Q?

Teacher Notes:• Review “Geometric Formulas” on

page 29 in the Student Reference Guide.

• The activity in the Student Edition is optional.

A = bh A = (3)(3) A = 9 sq. cm


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Written Practice (page 372)

Find the perimeter and area of each parallelogram:

e. f.

perimeter area perimeter area

g. Here is the same parallelogram in two different positions.The area is the same in both drawings.

A = bh so h = A

__ b

What is the height in the figure to the right? 12 cm × 6 cm = 72 cm2

9 cm × h = 72 cm2

1. LCM of 6 and 10 2. Mt. Everest 29,035 ft =

sea level 0 ft =

Dead Sea –1371 ft

3. 105 minutes = hours minutes

time start 1:15 p.m.

Count forward hours.

Count forward minutes.

6. 3 __

4 ÷

3 __

8

___ ×

___ =

7. 4 1

__ 2

÷ 6

___ ×

___ =

8. 6 =

3 3

__ 4

=

___

+ 2 1 __

2 =

___

9. 5 1 __

8

– 3 1 __

8

Practice Set (continued) (page 371)

4. 2

__ 3

∙ 3 __

8 = 5. 1

1 __

4 ∙ 2

2 __

3

___ ×

___ =


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10.

11. (3.5)2 = 12. 15 ) _______

$75.00

13. (1 + 0.6) ÷ (1 – 0.6) =

15. name of point (0, 0) on coordinate plane

17. 1.2f = 120 18. 120

____ f = 1.2

19. 64

____ 224

= ∙ ∙ ∙ ∙ ∙ ____________________________ ∙ ∙ ∙ ∙ ∙ =

20. perimeter

each side

area

Written Practice (continued) (page 372)

5 1

__ 4

=

___

– 1 7 __

8 =

___

14. $4.50

a. tax

b. total

c. change

16. • Always begin at the origin.

• Next, move on the x-axis.

• Last, move on the y-axis.

) _____

210 ) _____

210 ) _____

210 ) _____

210 ) _____

210 ) _____

640

) _____

210 ) _____

210 ) _____

210 ) _____

210 ) _____

210 ) _____

224

c.

a.

b.

1.0+ 0.6

1.0– 0.6

f = f =

b.

d. ( , )

a.

c. ( , )


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21. not shaded

23. How many centimeters long is your little finger?

24.

32°

25. 20% =

is

__ of

___

___

26. Name this geometric solid. 27. perimeter

each side

so, perimeter of triangle

28. area of your state

A square inches

B square yards

C square miles

29. a. perimeter b. A = bh

30. In this figure ∠BMD is a right angle.

Name two angles that are

a. supplementary. supplementary = 180°

b. complementary. complementary = 90°


22. I multiplied the r by to find the diameter.

Then I m the diameter by .

a.

b.

a. ∠ and ∠

b. ∠ and ∠


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Fractions Chart Multiplying Three Fractions (page 375)

• To use the S.O.S. method in the Fractions Chart:

Step 1. Write the problem in the correct shape.

Step 2. Perform the operation.

Step 3. Simplify the answer.

• To multiply three or more fractions, cancel vertically and diagonally but never horizontally.


a. Fill in the fractions chart for this lesson.

b. Describe the three steps for adding fractions.

1. Write the f so that the d are the same.

2. Add the n but not the d .

3. Reduce and/or c the answer if possible.

Write fractions

with common

d .

Write numbers in f form.

Find the r

of the divisor, then cancel.

R fractions. C improper fractions.

Add or subtract the

n .


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1. average 4.2004.200

4.200

2. tablespoons

____________ cups

4 __

1 _ 4

? __

1 3. 130°

0º–110º

==

4. 5. 1 m = cm

6. Write in cents.

nickel

______ dollar

___ =

7. n – 1

__ 2 =

3 __

5

3 __

5 =

___

– 1 __

2 =

___

8. 1 – w = 7 ___

12

1 7 ___

12

– 1 7 ___

12

9. w + 2 1

__ 2 = 3

1 __

3

3 1 __

3 =

___

+ 2 1 __

2 =

___

10. 1 – w = 0.23

1.23– 0.23

c. Describe the steps for dividing fractions.

1. Write any mixed numbers in f form.

2. Find the r of the divisor.

3. C .

4. M the fractions.

5. S the answer if possible.

Practice Set (continued) (page 376)

d. 2 __

3 ∙

4 __

5 ∙

3 __

8 =

Cancel.

e. 2 1

__ 2 × 1

1 ___

10 × 4

___ ∙

___ ∙

___ =

b. a. c. c

n = w =

w =w =


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11. (6 × 10) + ( 4 × 1 ___

10 ) + ( 3 ×

1 ____

100 )

14. Which of these figures is not a parallelogram?

15. perimeter in.

a. each side

b. area

16. Figure ABCD is a rectangle.

a. complementary = 90°

b. supplementary = 180°

17.

2 sandwiches 1 green salad 1 small juice 2 medium juices

18. 0 0.07

$20.00 $20.00


Menu

Grilled Chicken Sandwich $3.49 Juice: Small $0.89

Green Salad $3.29 Medium $1.09

Pasta Salad $2.89 Large $1.29

12. closest to 1

A –1 B 0.1 C 10

13. Largest prime number less than 100.

19. • List the items for an order.

• Then find the total not including tax.

.

a. ∠

b. ∠

a.

b.


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22. a. K

b. F

• Always begin at the origin.



24. Draw a pair of parallel lines perpendicular to the parallel lines below.

Is the quadrilateral a rectangle?

25. 1 __

2 ∙

5 __

6 ∙

3 __

5 = 26. 3 × 1

1 __

2 × 2

2 __

3

___ ∙

___ ∙

___ =

27. 3

__ 4

÷ 2

___ ∙

___ =

28. 1 1

__ 2 ÷ 1

2 __

3

___ ∙

___ =

29. (0.12)(0.24) =

0.12 0.24

30. 0.6 ÷ 0.25 =

) _______

00000


23. a. (3, –4)

b. (–3, 0)

20. A = l × w

l = 2.5 w = 0.4

2.5

0.4

21. 72

____ 120

= ∙ ∙ ∙ ∙ ________________ ∙ ∙ ∙ ∙ =

) ___

00 ) ___

00 ) ___

00 ) ___

00 ) ___

72

) _____

000 ) _____

000 ) _____

000 ) _____

000 ) _____

120

a. ( , ) b. ( , )

a. point

b. point

A =

Use work area.


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Exponents Writing Decimal Numbers asFractions, Part 2 (page 380)

• The exponent shows how many times the base number ismultiplied by itself.

The exponent 2 is read “squared.”

The exponent 3 is read “cubed.”

Examples: 52 = 5 × 5 = 25(5 squared)

34 = 3 × 3 × 3 × 3 = 81(three to the fourth power)

25 = 2 × 2 × 2 × 2 × 2 = 32(two to the fifth power)

• To write decimal numbers as fractions or mixed numbers:

The denominator (10 or 100 or 1000…) is indicated by the number of decimal places in thedecimal number.

The numerator is the digits to the right of the decimal point.

Examples: 0.5 = 5 ___

10 =

1 __

2

3.75 = 3 75

____ 100

= 3 3 __

4


Find the value of each expression:

a. 104 = , b. 23 + 24 = c. 22 ∙ 52 =

d. Write the prime factorization of 72 using exponents.

72 = ∙ ∙ ∙ ∙ = ∙

Write each decimal number as a fraction or mixed number. Reduce.

e. 12.5 = 12 5 ___

10 = f. 1.25 = = g. 0.125 = =

h. 0.05 = = i. 0.24 = = j. 10.2 = =

Teacher Notes:• Introduce Hint #57, “Prime

Factorization of Powers of Ten.”

• Review “Exponents” on page 8 in the Student Reference Guide.


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1. 102 98.6 = d

102.0× 198.6

2. – 42 = d

180× 142

3. average pages to finish in 3 days

3p =

4. mixed number

2.5 =

5. reduced fraction

0.35 =

6. total plus tax

$12.60× $12.60

$12.60× $12.60

7. 3 __

4 × 2 × 1

1 __

3

___ ∙

___ ∙

___ =

8. (100 – 102) ÷ 52

÷ =

9. 3 =

2 1 __

3 =

00 ___

00

+ 1 3

__ 4 =

00 ___

00

10. 5 1 __

6 =

00 ___

00

– 3 1 __

2 =

00 ___

00



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11. 3 __

4 ÷ 1

1 __

2

___ ∙

___ =

12. 7 ÷ 0.4 =

13. a. 52 25 b. 0.3 0.125

14. a. C = π d

b. radiusdiameter

_____

15. 25m = 0.175 16. 1.2 + y + 4.25 = 7

1.200× 4.250

7.000× 7.000

17. ten-thousands place

123,456.78

18. least to greatest

1,

1 __

2 ,

1 ___

10 ,

1 __

4 ,

0

00

___ 20

00

___ 20

00

___ 20

19. Use exponents.

200 = ∙ ∙ ∙ ∙

20. a. 20% of $18.00

20% =

isof

_____ ______

18.00

b. $18.00× $18.00


0.30.125

a.

b.

a.

b.

m = y =

, , , ,

∙

a.

b.


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21. 22. Find the area. Then take 1 _ 2 of it.

23. 24. 22 + 23

________ 2 = 25. Before we multiply

fractions, we write any

m numbers

as i fractions.




a. H

b. L

27. a. (–4, 3)

b. (3, 0)

29. See the Student Reference Guide.


28. s = 9

30.

a. What is the measure of ∠X?

b. What is the measure of ∠Y?

Use work area.

a. ( , )

b. ( , )

a. point

b. point

d. b.

c. a.

b. a.

s2 =


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Writing Fractions as Decimal Numbers

Writing Ratios as Decimal Numbers (page 385)

• To write a fraction as a decimal:

Divide the numerator by the denominator.

Keep any whole number.

Examples: 3 _ 4 0.75

4 ) _____

3.00

2 2 _ 5 0.4

5 ) ____

2.0 2.4

• Ratios (such as probability) are often written as fractions, so they can be converted to decimals in the same way as any fraction.


You may use a calculator to convert these fractions to decimals:

a. 3

__ 4

= .

b. 4 1

__ 5

= .

c. 1 __

8 =

.

d. 7 ___

20 =

. e. 3

3 ___

10 =

. f.

7 ___

25 =

.

g. 11

___ 16

= .

h. 31

___ 32

= .

i. 3 24

___ 64

= .

j. In a bag are three red marbles and two blue marbles. If Chad pulls one marble from the bag, whatis the probability that the marble will be blue? Express the probability ratio as a fraction and as a decimal number.

blue

total

_____ fraction decimal

Teacher Note:• Instruct students on calculator

usage. See page 386 in theStudent Edition.


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1. (43) – ( ) = 2. in.

___ mi

1 ___

3 __

? 3. 2

3 __

4 =

4. a. sample space

b. Write the probability as a fraction and a decimal.

greater than 1

_____________ total numbers

___

5. reduced fraction

0.24 =

6. – 400 = d

ydft

1 ___

300 ____

?

7. A = bh b = 12 h = 8 8. 32 3 + 3

9. 1

__ 2 =

___

2 __

3 =

___

+ 1 __

6 =

___

10. 3 1 __

4 =

___

– 1 7 __

8 =

___


A =

.

a. { , , , , } b. . b.


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11. 5 __

8 ∙

3 __

5 ∙

4 __

5 = 12. 3

1 __

3 × 3

___ ∙

___ =

13. 3

__ 4 ÷ 1

1 __

2

___ ∙

___ =

14. (4 + 3.2) – 0.01 =

4.2 3.2

4.2 0.01

15. Complete the triangular prism. 16. 12g =

golf balls

$

12

___ 1

__ ?

17. 81

38

50× 50

18. average

424635

57

19. LCM of 6, 8, and 12 20. 24 + c + 96 = 150

24 96

150 906


Use work area.

c =


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21. 40

___ 96

= ∙ ∙ ∙ ________________ ∙ ∙ ∙ ∙ ∙ 22. perimeter 40 cm

each side

23. mountain bikes

all cyclists

___

25. 3

__ 4 26.

27. 28.

29. Name a pair of parallel segments that are not

___ AB and

___ DC .

30. 60% =

is

of

___ ____

300


24. All f sides of a square are the same

l . Some rectangles are longer than they

are w , so not all the s are the

same l .

a.

b.

and

a.

b.

a.

b.

a. ( , )

b. ( , )

Use work area.


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Teacher Note:• Review “Fraction Decimal

Percent” on page 13 in the Student Reference Guide.

Writing Fractions and Decimals as Percents, Part 1 (page 390)

• Percent means “per hundred.”

Examples: 23

____ 100

= 23% 3 ___

10 =

30 _____

100 = 30%

15

___ 30

= 1

__ 2 =

50 ____

100 = 50%

• To change a decimal to a percent, shift the decimal point two places to the right.

Examples: 0.08 = 8% 0.40 = 40%


Write each fraction as a percent:

a. 31

____ 100

= b. 1 ____

100 = c.

1 ___

10 = ____

100 =

d. 3 ___

50 = ____

100 = e.

7 ___

25 =

____

100 = f.

2 __

5 = ____

100 =

g. Twelve of the 30 students earned a B on the test. What percent of the students earned a B?

12 ___

30 = ___

10 =

____

100 =

h. Jorge correctly answered 18 of the 20 questions on the test. What percent of the questions did he answer correctly?

18 ___

20 = ___

10 = ____

100 =

Write each decimal number as a percent:shift

i. 0.25 = j. 0.3 = k. 0.05 =

l. 1.0 = m. 0.7 = n. 0.15 =


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Round 94¢ to $ and $6.35 to $ .

Add the items to get $ . Tax is 8¢ per

dollar, so the tax is about ¢. This is

close to my answer.

4. $4.000$4.000

$4.000

4.00

4.08


1. reciprocal

2 3 __

5 = __

5

2. time start

Count forward hours.

Count forward minutes.

3. 1 pound = 16 ounces

oz

___ $z

_____ 4.00

1

__ ?

5. part 50%

part

whole 100%

6. Connect the correct corners.

7. 3 __

4 = 8.

3 ___

20 =

9. Write 12% as a reduced fraction and a decimal.

10. 7 ___

10 =

n ____

100

a. .

b.

a.

b.

____

100

. n =


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11. 5 – m = 3 1 __

8

5 1 __

x

3 1 __

8

12. 1 – w = 0.95

1.00 0.95

13. m + 1 2

__ 3

= 3 1 __

6

3 1

__ 6 =

___

1 2

__ 3 =

___

14. ( 1 __ 2

+ 1

__ 3

) – 1 __

6 =

1

__ 2

=

___

1 __

3 =

___

15. 3 1 __

2 × 1

1 __

3 × 1

1 __

3

___ ∙

___ ∙

___ =

16. (0.43)(2.6)

0.43 2.6

17. 0.26 ÷ 5 Add zeros.

) _________

0000000

18. 17

___ 20

= ____ 100

= %

19. Round to the nearest foot. 20. 4.870.195

21. 18

___ 30

= ∙ ∙ ___________ ∙ ∙ =

) _____

000 ) _____

000 )

_____ 000 )

_____ 000

) _____

180 ) _____

300


m = w =

m =


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22. GCF of 18 and 30

1 , , , , , 18

23. product of 2 numbers is 1

A equal B reciprocals

C opposites D prime

24. A q is a four-sided

p , and every r

has four s .

25. b = 8 h = 6

bh

___ 2 =

26. Use exponents.

28. a. perimeter

b. area

29. a. perimeter

b. A = bh

30. Connect the endpoints to form a quadrilateral.

Is it a rectangle?

Use work area.

.




(3, 1), (3, –1), (–1, 1), (–1, –1)

Use work area.

a.

b.

a.

b. Use work area.


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Comparing Fractionsby Converting toDecimal Form (page 395)

• To compare two fractions:

1. Cross-multiply.

2. Compare the numbers above the fractions.

18 > 12 6 < 16

Examples: 2 __

3

4 __

9

2 __

8

2 __

3

• Convert to decimals if the problem is mixed (fraction and decimal).

Example: 0.7 3

__ 4

0.7 0.75


Compare by cross-multiplying.

24

a. 3 ___

20

1 __

8 b.

3 __

8

2 __

5 c.

15 ___

25

3 __

5

Convert; then compare.

d. 0.7 4

__ 5

e. 2 __

5 0.5 f.

3 __

8 0.325

5 ) ____

4.0 5 ) ____

2.0 8 ) ________

3. 0 0 0

Teacher Note:• Review Hint #47, “Comparing

Fractions.”

<


1. 102 23

( )( ) = 2. halfway: Add; then divide by 2.

4.5 6.7


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3. 13 × = y

humandog

7 __

1

? ___

4. 2 __

5

1 __

4

5. shaded

6. circumference of a juice glass

A centimeters

B meters

C kilometers

7. a. 2 1

__ 2 =

b. 3.75 =

8. a. 0.04 = ____

100 =

b. 0.04 =

9. Answer with a mixed number.

halfofeach

200

18

_____ =

10. 6 1 __

3 =

00 ___

00

3 1 __

4 =

00 ___

00

+ 2 1 __

2 =

00 ___

00

11. 4 __

5 =

? ____

100 12. ( 2

1 __

2 ) ( 3

1 __

3 ) ( 1

1 __

5 )

___ ∙ ___ ∙ ___ =

{


a. .

b.

a.

b.

b. .

c.

a.


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13. 5 ÷ 2 1 __

2

___ ∙

___ =

14. 6.7 + 0.48 + n = 8

6.70× 0.48

8.48× 0.48

15. 12 – d = 4.75

12.75× 4.75

16. 0.35× 0.45

17. shift

102

4.3 ÷ =

18. median First, put the numbers in order.

0.3, 0.25, 0.313, 0.2, 0.27

19. 3926 5184

5000× 5000

20. prime numbers between 40 and 50

21. 12

___ 25

= ____

100 = 22. perimeter


n =

d =

, ,


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23. complementary = 90° 24. millimeters

25. two congruent triangles

a. A = bh

b. area of one of the triangles

26.

bottom layer

all layers

27.




30. Draw a fourth line that intersects but is NOT

perpendicular to the parallel lines. Is the

quadrilateral a rectangle?


A (1, 2)

B (–3, –2)

C (1, –2)

28. a. perpendicular to ___

AC

b. right angle

29. b = 12 h = 9

bh

___ 2

=

a.

b. cubes

a.

b. ∠

Use work area.


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Finding Unstated Informationin Fraction Problems (page 399)

• Work through the Practice Set.


3

__ 8

of the 40 little engines could.

parts that could total parts

parts that could not total parts

The face of a spinner is divided into 12 equal sectors. part red 1 _ 4

part not red

whole 1

1

__ 4

of 12 =

The probability of spinning red on one spin is 1 _ 4 .

g. How many sectors are red?

h. How many sectors are not red?

i. What is the probability of spinning not red in one spin?

j. What is the sum of the probabilities of spinning red and not red?

How are the events related? The events are c .

Teacher Note:• Review Hint #35, “Fraction of a

Group, Part 2.”

3 __

8

5 __

8

a. Into how many parts was the group divided?

c. How many parts could climb the hill?

e. How many parts could not climb the hill?

b. How many engines were in each part?

d. How many engines could climb the hill?

f. How many engines could not climb the hill?


1. 1 __

6 of 114

is

__ of

1 __

6

___

2. A desk might weigh about 24 pounds.

is

__ of

1 __

6

___


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3. hitstimes

___ = 4. 3

__ 5

of 30 students are boys

5. shaded 6. 3.6 =

7. 3.6 + a = 4.15

4.15 3.60

8. 2 __

5 x = 1

9.

There is a g chance that it

will rain because % is greater

than %.

10. 3

__ 5

= ____

100 = %

11. Water freezes at °F.

0° = –3° =

12. a. 20 7 ___

20

b. 32 23

part 60%partwhole 100%

a.

b.

a.

b.

c.

d.

a.

b. .

c.

a = x =

Use work area.

a.

b.

0.35


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13. 1 __

2 =

___

+ 2

__ 3

=

___

14. 3 1 __

5 =

___

– 1 3

__ 5

=

___

15. 1

__ 2

=

___

3 __

4 =

___

+ 7

__ 8

=

___

16. 3 × 1 1

__ 3

___ ∙

___ =

17. 3 ÷ 1 1

__ 3

___ ∙

___ =

18. 1 1 __

3 ÷ 3

___ ∙

___ =

19. perimeter

20. area

21. Use exponents.

) ______

1000 )

______ 1000

) ______

1000 )

______ 1000

) ______

1000 )

______ 1000

22. a. 40% =

is

__ of

___ ____

$80

b. $80 $80

b.

a.

∙


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23. a. $38.80 $38.80

b. $38.80 $38.80

24. A polygon is a straight-sided closed figure.

Is every quadrilateral a polygon?

25. time start 12:00 p.m.

Count back hours.

Count back minutes.

26. What percent appears to be shaded?

A 20% B 40%

C 60% D 80%

27. W(2, 3), X(1, 0), Y(–3, 0), Z(–2, 3)




28. a. parallel to ____

WX

b. parallel to ___

XY

30. a. What shape?


29. 210

____ 350

= ∙ ∙ ∙ _____________ ∙ ∙ ∙ =

) _____

210 ) _____

350 )

_____ 210 )

_____ 350

) _____

210 ) _____

350 )

_____ 210 )

_____ 350

b. Round the circumference to the nearest ten miles.

b.

a.

a.

b.

a. b. Use work area.


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Capacity (page 404)

• Measuring liquids:

U.S. Customary System: ounces, cups, pints, quarts, gallons Metric system: milliliters, liters

• One liter is a little more than one quart.


a. What fraction of a gallon is a quart?

gallon

quarts

___

b. A 2-liter bottle has a capacity of how many milliliters? mL

L

mL

1 ___

2 __

?

c. A half gallon of orange juice will fill how many 8-ounce cups? cups

d. The entire contents of a full 2-liter bottle are poured into an empty half-gallon carton. Will the half-gallon container overflow? Why or why not?

The half-gallon c will o because 2 liters is a little m than

half a gallon.

Teacher Notes:• Introduce Hint #58, “Measuring

Liquids and Capacities of Containers.”

• Refer students to “Liquids” and “Equivalence Table for Units” onpage 1 in the Student Reference Guide.

• Post reference chart, “Liquids.”Liquids

U.S. Customary System Metric System

1 gallon = 4 quarts

1 quart = 2 pints

1 pint = 2 cups

1 cup = 8 ounces

1 liter = 1000 milliliters

Equivalence Table for Units of Liquid Measure

Half&Half

Milk


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1. ( ) – ( ) = 2. cm

mm 1 ___

___

?

3. Go down the 3s and 4s columns. 4. 4 __

5 of the 60 lights were on.

5. not prime, not composite 6. 4 __

5 m = 1

7. 4 __

5 + w = 1

1

4 __

5

4 __

5

8. 4

__ 5

÷ x = 1

9. y – 4 __

5 = 1

1 4 __

5

4 __

5

10. shaded


m =

x =w =

y =

a.

b. .

c.

a.

b.

c.

d.


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11. 1.15 = 12. a. 3 __

5

0.35

b. √_____

100 14 + 23

13. 5

__ 6

=

___

1

__ 2

=

___

14. 4 1

__ 4

=

___

– 3 1 __

3 =

___

15. 1

__ 2

=

___

2 __

3 =

___

+ 5

__ 6

=

___

16. 1 1

__ 2 × 2

2 __

3

___ ∙

___ =

17. 1 1

__ 2 ÷ 2

2 __

3

___ ∙

___ =

18. 2 2

__ 3 ÷ 1

1 __

2

___ ∙

___ =

19. 20. “The opposite sides of a rectangle are parallel.” True or false?


a.

b.

a.

b.


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21. average

33 52

22. ) ______

22.00

23. ft.

in.

1 ___

2 1 _ 2 ___

? 24. 0.1

25. Draw a quadrilateral that is NOT a rectangle.

See the Student Reference Guide.

26.

27. (5, 3), (5, –1), (–1, –1)

29. A liter is like a:

A pint B quart C 1 __

2 gallon D gallon

30. one pint = ounces


28. 3 teaspoons = 1 tablespoon16 tablespoons = 1 cup

2 cups = 1 pint2 pints = 1 quart

4 quarts = 1 gallon

.

a.

b. ( , )

Use work area. ∙ ∙


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Area of a Triangle (page 408)

• Notice that the area of any triangle is:

1 __

2 the area of a parallelogram with the same base and height

• So the formula for the area of a triangle is:

A = 1

__ 2

bh or A = bh

___ 2

• The height must be perpendicular to the base.

• Area must be expressed in square units (16 cm2).


Find the area of each triangle:

a. b.

c. d.

e. If the height of the triangle in c is doubled to 30 mm, would the area double?

1 __

2 (56)(30) = ÷ 2 = 420

Teacher Notes:• Review “Geometric Formulas” on

page 29 in the Student Reference Guide.

• The activity in the Student Edition is optional.


1. Divide the p by 2 and

s the length from the quotient.

2. 2 liters = 2 quarts + 3.6 ounces

1 liter 1 quart

A = 1 __

2 (8 cm)(4 cm)

A = 16 cm2

Use work area.


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3. 38 33

4. See the Student Reference Guide.

5. 90% =

a. isof

10

___ 03

___ 30

b. birchall others

___ 30

6. a. 18

___ 24

=

b.

7. A = 1 __

2 bh

8. 103

___ 102

_____

9. 6.42 + 12.7 + 8 =

6.426.42

× 6.42

10. 1.2(0.12) =

1.2

11. 64 ÷ 0.08 = 12. 3 1

__ 3 ×

1 __

5 × 3 __

4

____ ∙

____ ∙

____ =

a.

b.

a.

b.

a.

b.

c.


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13. 2 1 __

2 ÷ 3

____ ∙

____ =

14. 10 – q = 9.87

10.00× 19.87

15. 24m = 0.288 16. n – 2 3 __

4 = 3

1 __

3

3 1

__ 3

= 00

___ 00

+ 2 3

__ 4

= 00

___ 00

17. w + 1 __

4 =

5 __

6

5 __

6 =

___

1 __

4 =

___

18. perimeter

each side

area

19. (9 × 10) + (6 × 1) + ( 3 × 1 ____

100 ) 20. circumference

21. closest to zero

A –2 B 0.2

C 1 D 1 __

2

22. 6.7 7.3

500× 500

Round 6.7 to and 7.3 to .

Then m .

m = n =

.

q =


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23. 34 = 3 ∙ 3 ∙ 3 ∙ 3 = 24. halfway

0.2 0.3

25. 26. only one pair of parallel sides

27. (–5, 5), (1, 5), (3, 1), (–3, 1) 28. a. area of square 100 cm2

each side

b. perimeter of square

29. a. each side of hexagon

b. perimeter of hexagon

30. 32

___ 48

= ∙ ∙ ∙ ∙ _____________ ∙ ∙ ∙ ∙ =

) ___

32 ) ___

32 ) ___

32 ) ___

32 ) ___

32

) ___

32 ) ___

32 ) ___

32 ) ___

32 ) ___

48


a.

b.

a.

b.


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Using a Constant Factor to Solve Ratio Problems (page 413)

• Ratio can be used to express an actual count.

• Ratios and actual counts are related by a constant factor. Multiply the terms of a ratio by the constant factor to find the actual count.

• A ratio box can help to sort the numbers out.

• To find the constant factor ask: What did they multiply by to get the actual count? That number is your constant factor.

You will multiply the other ratio term by the same thing.

Example: To make green paint, the ratio of blue paint to yellow paint is 3 to 2. For 6 ounces of yellow paint, how much blue paint is needed? Draw a ratio box.

A ratio term and an actual count are given for yellow paint. What number times 2 (ratio term) equals 6 (actual count)? 33 is the constant factor.Multiply the ratio term for blue paint by the constant factor. 3 × 3 = 99 ounces of blue paint are needed.


Draw a ratio box and use a constant factor to illustrate and solve these ratio problems.

a. The ratio of boys to girls in the cafeteria was 6 to 5.

If there were 60 girls, how many boys were there?

b. The ratio of ants to flies at the picnic was 8 to 3. If there

were 24 flies, how many ants were there?

Blue Paint

Yellow Paint

Ratio Actual Count

3

2 6

Blue Paint

Yellow Paint

Ratio

3 × constant factor

2 × constant factor

Actual Count

6

?


1. mean range

) ______

0000

964968

75

96 75

2. 2 1

__ 2 = 2.5

mi

___ ft

1 ___

2.5 ___

?

Use work area.


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3. 12p =

players

_______ teams

168

____ ? __

1

4. a. perimeter

b. A = bh

5. a. perimeter

b. A = 1 __

2 bh

6. one pair of parallel sides

7. See the Student Reference Guide. 8. 4

__ 5

of 30 present

___ 5

of 30 absent

is

__ of

___

___ 30

9. 10. a. 19

___ 20

= ____

100 =

b. 0.6 =

11. square

_______ sides

1 ___ 12. a.

3 __

4

0.5

b. 3 qt 1 gal

a.

b.

a.

b.

a.

b.

b. .

a.

b. a.

b.


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13. 4.4 = 14. 8 ) ________

1. 0 0 0

15. 5 __

6 =

___

+ 1 __

2 =

___

16. 5

__ 8 =

___

– 1

__ 4 =

___

17. 2 1 __

2 × 1

1 __

3 ×

3 __

5

___ ∙

___ ∙

___ =

18. 4 – a = 2.6

4.6+ 2.6

19. 3n = 1 1

__ 2

20. 5x = 0.36

21. 0.9y = 63 22. 0.4287

.

a =

n = x =

y =


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23. Frosted Rice 24. Coco Flakes

sugar

______ cereal

____

100

? ___

50

25. How many f grams of sugar

does have than Coco Flakes?

Answer:

26. one quart = cups

27. (3, 0), (3, 3), (0, 3) 28. complement = 90°

A

B

C

29. b = 6 h = 8

A = 1 __

2 bh


30. Connect the endpoints. Is the quadrilateral a parallelogram?

Use work area.

a. ( , )

b.

A = Use work area.

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