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Chapter 1 Multiply and Divide Decimals

Page 24 Chapter 1 Are You Ready?

1. 300 3. 672 5. 2,820 7. $92 9. 774 mi 11. 34 13. 41

Pages 27–29 Lesson 1-1A

1. 6 × 4 = 24 3. 60 × 30 = 1,800 5. 14 × 3 = 427. about $8 9. 10 × 3 = 30

1111 Sample answer: Round 17.5 to 20, and round

8.4 to 8. 20 × 8 = 160 13. 30 × 80 = 2,400 15. 40 × 5 = 200 17. 70 × 2 =

140 19. about 90 21. His estimate is not reasonable. He rounded $15.75 to $20. If he rounded $15.75 to $16, the estimate would be $48 for the three books. 23. no; 70 25. yes

2727 More; her wage and hours worked were

rounded up, so the actual total is less than the estimate.

29. 35 × 8 = 280; 40 × 8 = 320; Rounding to the ones gives an estimate closer to the actual product. 31. 59 × 6 = 354; 60 × 6 = 360; Rounding to the ones gives an estimate closer to the actual product. 33. about 10 yards 35. no; 90.8 × 3.1 ≈ 90 × 3 ≈ 270 37. about $12 39. B 41. yes; 4 × $3.69 ≈ 4 × $4 = $16 43. G

Pages 34–35 Lesson 1-1C

1. 16.2 3. 1.56 5. 0.45 7. 1.17

99 Multiply 12 times $4.89, 17 times $4.72, and 15

times $5.09. Add the three products to fi nd that they spent $215.27 for gas. 11. 8.5 13. 3.6 15. 19.2 17. 1.5 19. 0.084 21. 1.485 23. 8,850 m; 8.85 rounds to 9 and 9 × 1,000 = 9,000

2525 134.6°F; 1,346 × 10 = 13,460. Since 13.46 has 2

decimal places, 13.46 × 10 = 134.60. 27. Sample answer: I bought three ice cream cones for $1.59 each. How much money did I spend? 3 × 1.59 = $4.77 29. The product of 123 × 47 is 5,781. The product of 123 × 0.47 is 57.81, which is one-hundredth the size of the whole number product. The second factor is one-hundredth the size of the whole number factor. 31. 12.12 33. H

Pages 39–41 Lesson 1-1E

1. 0.3 3. 29.87127

55 Sample answer: Multiply 52 × 21 to get 1,092.

Two decimal places in the fi rst factor and one decimal place in the second factor produce three decimal places in the product. 0.52 × 2.1 = 1.092

7. 3.645 9. 0.0848 11. 0.28 13. 1.48 15. 7.154 17. 0.186 19. 166.992 21. 0.0224

2323 Estimate.

46.93 × 1.8 ≈ 45 × 2 = 90

46.93 2 decimal places× 1.8 1 decimal place 37544+ 4693

84.474 3 decimal placesSo, the giraffe could run 84.474 feet in 1.8 seconds. Since 84.474 ≈ 90, the answer is reasonable.25. 75.2452 27. 20.48512 29. 2.0646 31. 6.5745 33. 30.39 in2; Since 3.1 × 6.9 = 21.39 and 3(6.1 - 3.1) = 9, the area of the fi gure is 21.39 + 9 or 30.39 in2.

3535 $5.76; Each price is about $1. He bought about

6 pounds of fruit. 6 × 1 = 6 ≈ $5.76 37. Sample answer: If a = 1.5 and b = 0.2, then ab = 0.3, which is less than 1; if a = 1.5 and b = 0.8, then ab = 1.2, which is not less than 1. 39. Sample answer: 0.1 × 0.6 41. always; 0.3 × 0.5 = 0.15; 0.75 × 0.6 = 0.45 43. 0.75 45. 2.7348 47. D 49. 12.15 51. 134.4 53a. Sample answer: about 75,000 mi 53b. Sample answer: about 1,000 mi 55. 65 57. 400

Pages 43–46 Lesson 1-2A Sample answers given.1. 25 ÷ 5 = 5 3. 1,000 ÷ 40 = 25

55 Sample answer: Divide 3 by 1. She can make

about 3 smoothies.7. 54 ÷ 9 = 6 9. 46 ÷ 23 = 2 11. 120 ÷ 20 = 6 13. about $10; $38.04 ÷ 4 ≈ $40 ÷ 4 = $10 15. no; 3 17. no; 4 19a. 5; 100 × 5 = 500 19b. 10

2121 Sample answer: Each cow produces about

6 gallons of milk per day. The answer is reasonable because 54 is close to 53 pounds, and 54 divided by 9 is 6.23. about $22 25. about $100 27. 300 ÷ 50 = 6; 6.42 29. 2,000 ÷ 25 = 80; 74.65

3131 Her answer is reasonable because $474.72 is

close to $480, and $480 divided by the 12 months in a year is $40. 33. Sample answer: Mrs. Fisher bought 2.75 lb of apples. The apples cost $1.79 per pound. About how much did she pay for the apples? about $6 35. Sample answer: 160.23 ÷ 6.54 37. A 39. I 41a. 93.6 lb 41b. 438.178 lb 41c. 241.198 lb 43. 320 45. 2,500

Pages 52–53 Lesson 1-2C 1. 0.9 3. 1.4 5. 0.6 7. 0.49 9. 13.1

R01_R39_EM_SelAns_895129.indd R1R01_R39_EM_SelAns_895129.indd R1 1/14/10 2:31 PM1/14/10 2:31 PM

R2 Selected Answers and Solutions

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-10 18

-15 35

-35 013. 1.0 15. 0.6 17. 1.2 19. 10.9 21. $770.56

2323 22.8 ft; Sample answer: area = length × width,

so to fi nd the width, divide the area by the length. 752.4 ÷ 33 = 22.8, so the deck is 22.8 feet wide.25. 1.42 thousand yards; 4.26 ÷ 3 = 1.42 27. 422; 0.422; 42.2; 0.0422; 4.22; 0.00422; Sample answer: You can fi rst mentally divide 96 by 3, which is 32. Since 0.0096 has four decimal places, place four decimal places in the quotient, 32. So, 0.0096 ÷ 3 = 0.0032. 29. Less than; the fi rst number in the dividend, 2, is less than the divisor, 3. 31. 62.46 33. B 35. Sample answer: 100 37. 13.68 39. 2.592


1. 12.3 3. 1.5

55 Move both decimal points four places to the

right after annexing three zeros to the dividend. Then divide. 2500.0024. � �� 0.6000.

-48 120

-120 00

00 07. 0.8025 9. 3 blankets 11. 0.2 13. 2.3 15. 0.0492 17. 0.4 19. 420 21. 0.605 23. 20 steps 25. 4.9 times; 6.64 ÷ 1.35 = 4.9 27. 29.4 29. 15.1 31. 5.8 33. 6.8

3535 a. To fi nd how many more chose silver than

red, divide 0.2 by 0.09. 0.0220.09 � �� 0.20 -18 20 -18 0 Respondents chose silver 2.2 times more than they chose red. 35b. To fi nd how many more chose silver or black than red, add the amount of silver and black to get 0.34. Then divide by the number who chose red, 0.09, to get 3.8. Respondents chose silver or black 3.8 times more than they chose red. 39. 24 41. Sample answer: If a < 1 and b < 1, then a ÷ b < 1. If a = 0.08 and b = 0.2, then a ÷ b = 0.4, which is less than 1. If a = 0.8 and b = 0.02, then a ÷ b = 40, which is not less than 1. 43. Sample answer: How many times more people live in India

than in Indonesia? Round to the nearest tenth. 4.8 45. I 47. $2; Because $11.18 is close to 10, and 10 is a multiple of 5, the estimate $10 ÷ 5 = $2 is reasonable. 49. 102.465 51. 91.64


1. 83 3. 15

55 6 × 6 × 6 × 6; 1,296; Multiply 6 together

4 times to equal 1,296. 7. 10 × 10 × 10 × 10 × 10 × 10; 1,000,000 9. 1.4 × 1.4; 1.96 11. 100 × 100 × 100; 1,000,000 13. 13 15. 56 17. 122 19. 153

2121 27 is multiplied together 4 times. 27 is the base

and 4 will be the exponent; 274 23. 9 × 9 × 9; 729 25. 2 × 2 × 2 × 2 × 2; 32 27. 50 × 50 × 50; 125,000 29. 0 × 0 × 0 × 0 × 0 × 0; 0 31. 0.5 × 0.5 × 0.5; 0.125 33. 1,000 × 1,000; 1,000,000

3535 0.5 × 0.5 × 0.5 × 0.5; 0.0625; Multiply 0.5

together four times to equal 0.0625.37. 3.2 × 3.2 × 3.2; 32.768 39. 6.5 × 6.5; 42.25 41. Sample answer: 502 43. Sample answer: Exponential form is a short way to write repeated multiplication of a common factor such as 5 × 5 × 5 × 5 = 54. 45. 145 47. 10 49. 11 51. 90 ft by 90 ft

Pages 68–69 Lesson 1-3B

1. 6.7 3. 8,950 5. 0.045 7. 0.0032 9. 655 11. 34.8

1313 Since there are three zeros in 1,000, annex

zeros to 0.5 to rewrite it as 0.5000, and then move the decimal point three places to the right; 0.5 × 1,000 = 500.15. 95,300 17. 28,600,000 19. 0.003 21. 0.87 23. 3.46 25. 0.002 27. 0.00045

2929 Sample answer: First, fi nd the amount of

decrease: 6,500 × 0.01 = 65. Then, subtract the amount of decrease from the original number of tickets sold: 6,500 - 65 = 6,435. There were 6,435 tickets sold during the second week. 31. Dwayne moved the decimal point the wrong direction; 0.60 × 1,000 = 600. 33. Multiply 3 by the number. Move the decimal point of the product one place to the left; 7.5. 35. B 37. 8 × 8 × 8; 512 39. 1 × 1 × 1 × 1 × 1 × 1 × 1 × 1 × 1 × 1; 1


1. 2.68 3. 0.00052 5. 6,254

77 Sample answer: 1,400 Aby cats is 0.01 times the

number of Labrador retriever dogs. To fi nd the number of dogs, divide the number of Aby cats by 0.01; 1,400 ÷ 0.01. Since there are two numbers to the right of the decimal point in 0.01, move the decimal point in 1,400 two places to the right; 1,400 ÷ 0.01 = 140,000. There are 140,000 registered Labrador retriever dogs. 9. 7.28 11. 0.295 13. 0.00082 15. 64,650 17. 8,160 19. 49.1 21. 18.5 weeks

2323 25 bags; 2.5 ÷ 0.1 = 25; The 2.5 pounds of

candies will be divided into bags, each holding





0.1 pound of candies; 2.5 ÷ 0.1 = 25. Keisha can fi ll 25 party favor bags.25. 420 27. 150 29. The divisor 0.0001 has 4 decimal places, so move the decimal point of 0.01 four places to the right: 0.01 ÷ 0.0001 = 100. 31a. 10; decimal point moved 1 place to the right 31b. 100; decimal point moved 2 places to the right 31c. 0.001; decimal point moved 3 places to the left 33. C 35. F 37. 41,217 39. 114 41. 0.45

Pages 74–75 Lesson 1-3D PSI

1. Sample answer: Checking on an answer for the distance to a planet; the distance is so large, an exact answer is not needed. 3. $100 is enough5. 270 ft 7a. 2009 7b. 2010

99 Two numbers that multiply to give 48 are 6

and 8, but they are only two digits apart. John needs a number smaller than 6 and another larger than 8, and they need to be even in order to give an even product. Four times twelve is 48 and 4 and 12 are eight digits apart. 11. 5 magnets and 7 keychains

Pages 78–81 Chapter Study Guide and Review

1. Compatible numbers 3. left 5. 95,210 7. Powers 9. Sample answer: 360 11. Sample answer: 4,500 13. Sample answer: 14 15. Sample answer: 180 mi 17. 29.85 19. 229.71 21. 765.7 23. 1.394 25. 0.78 27. 0.204 29. 0.1 31. 73.08 ft2 33. Sample answer: 2 35. Sample answer: 4 37. Sample answer: 10 39. Sample answer: 8 41. 0.882 43. 3.9 45. 0.34 47. 39.05 49. $17.89 51. 1.8 53. 14.7 55. 0.62 57. 5.4 59. 112 61. 5 × 5 × 5 × 5; 625 63. 81 65. 186,000 67. 10.6 69. about 4.5 ft; 5.75 × 0.8 is about 6 × 0.8 or 4.8, which is closest to 4.5

Chapter 2 Multiply and Divide Fractions


1. 12 3. 6 5. about 6 gallons 7. 1 1 _ 2 9. 4 11

_ 21

11. 6 7 _ 8 in.


1. Sample answer: 1 _ 8 × 16 = 2 3. Sample answer:

2 _

5 × 25 = 10 5. Sample answer: 0 × 1 = 0

7. Sample answer: 7 × 4 = 28

99 Sample answer: Area = length × width, and

9 3 _ 4 feet is close to 10 feet. The area is about

10 ft × 4 ft or about 40 ft2.

11. Sample answer: 1 _ 4 × 20 = 5

13. Sample answer: 1 _

3 of 42 = 14 15. Sample answer: 1 _

7 × 21 = 3,

3 × 5 = 15 17. Sample answer: 2 _ 3 × 9 = 6

19. 1 × 0 = 0 21. 4 × 3 = 12

2323 Sample answer: Use compatible numbers to

fi nd a multiple of 4 close to 11.1 _

4 × 11 ≈ 1 _

4 × 12

≈ 3

So, Cyrus should order 3 pizzas.

25. Sample answer: 6 × 8 = 48 ft2

2727 30 days; 3 _

10 × 90 ≈ 3 _

10 × 100; 1 _

10 × 100 = 10;

3 × 10 = 3029. Multiply 8 1 _

2 by any fraction between 1 _

2 and 3 _

5

because 5 is about 3 _ 5 of 8 1 _

2 . 31. Sample answer:

Estimation helps determine the reasonableness of answers. 33a. 44 feet 33b. 121 ft2

33c. 30 ft2 35. C

Pages 100–101 Lesson 2-1D

1. 8 3. 3 _ 2 or 1 1 _

2 5. 8 _

5 or 1 3 _

5

77 Sample answer: 2 _ 5 of the measurement of the

male frog is 2 _ 5 of 6 inches. Multiply

2 _

5 × 6 _

1 to get

12 _

5 or 2 2 _

5 inches.

9. 4 11. 2 13. 2 15. 22 _

5 or 4 2 _

5 17. 7 _

5 or 1 2 _

5 19. 25

_ 2

or 12 1 _ 2 21. 146 days

2323 neither; Sample answer: Find 2 _ 3 of Mrs. Thorne’s

36 students and 4 _ 5 of Mrs. Lombardo’s 30 students

and compare the results; 2 _ 3 × 36 = 24 students and

4 _ 5 × 30 = 24 students. The number of students

who watched the show is the same in both classes.

25. Sample answer: He multiplied by 8 _ 8 instead of

multiplying by 8 _ 1 . He should have gotten 24

_ 4 or 6 as

his answer. 27. Sample answer: Write 6 over 1. Multiply 6 times 3. Multiply 1 times 7. You now

have 18 _

7 or 2 4 _

7 . 29. 6 31. B


1. $21

? $9

$3 $3 $3

3. 15 min 45 min ?

5. 28 fl owers 7. Sample answer: 4 quarters, 2 dimes, and 5 pennies 9. 6 people 11. $29.25

1313 Sample answer: Make a diagram using the

given information.

165 mi

= 3 h

55 mi



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= 2 h

60 mi

Altogether, it took Jeffrey 5 hours to make the trip to his sister’s.


1. 1 _ 16

3. 8 5. 1 _ 4

77 Sample answer: Juanita spent 1 _ 2 of 3 _

4 of her

allowance on earphones. Multiply to fi nd 1 _ 2 of

3 _

4 ; 1 _

2 × 3 _

4 = 3 _

8 . She spent 3 _

8 of her allowance on new

earphones.

9. 3 _ 32

11. 6 _ 35

1313 2 _ 3 × 4 = 2 _

3 × 4 _

1 = 8 _

3 or 2 2 _

3

15. 4 1 _ 8 17. 3 _

7 19. 1 _

3 21. Nyemi: 138; Luke: 69;

Natalie: 23 23. $462 25. 1 _ 24

27. 3 _ 16

29a. 15 3 _ 4 min

29b. 42 min; If 1 _ 5 of the time is spent on instruction,

then 4 _ 5 of the 7 _

8 -hr class is not. So, 4 _

5 ×

7 _

8 = 7 _

10 . 7 _

10 ×

60 min = 42 min 31. 1 _ 2 c; 3 _

4 ×

2 _

3 =

3 × 2 _

4 × 3 =

1 _

2

3333 3 _ 10

; If the homerooms share a bulletin board,

then they each have 1 _ 2 of the board. Since

Homeroom 101 uses 3 _ 5 of their half, they use

3 _ 5 ×

1 _

2 or 3 _

10 of the whole board.

35a. true 35b. false; 4 9 _ 10

× 9 _

10 = 4 41

_ 100

35c. true

37. The fraction a _ b × b _ c × c _

d × d _ e can be simplifi ed

before multiplying by crossing out the factors that appear in both a numerator and a denominator. The factors that can be crossed out are b, c, and d. Thus, the only factors remaining are a in the numerator and e in the denominator, or a _ e .

39. C 41. H 43. 30 minutes 45. 40 _

3 or 13 1 _

3

47. 120 in2 49. Sample answer: 2 _ 3 × 18 = 12

51. 6 lb


1. 1 3 _ 16

3. 4 9 _ 10

5. 9

77 Sample answer: Multiply the amount of fl our

for one batch of waffl es by 1 1 _ 2 to fi nd how much

fl our Chun needs for his larger batch.

2 1 _ 4 cups × 1 1 _

2 = 9 _

4 × 3 _

2

= 27 _

8

= 3 3 _ 8

Chun needs 3 3 _ 8 cups of flour to make the waffle

recipe.

9. 2 1 _ 8 11. 1 1 _

2 13. 17

_ 20

15. 10 2 _ 15

17. 12 3 _ 4 19. 19 1 _

2

2121 Sample answer: Use the distance formula,

distance = rate × time, and the given information to answer the question.

d = r × t

= 3 7 _ 10

× 2 1 _ 2

= 37 _

10 × 5 _

2

= 37 _

4

= 9 1 _ 4

The distance the carp travels is 9 1 _ 4 miles.

23. 3 _ 5

2525 1 _ 7 × 5 5 _

6 × 1 1 _

4 =

1 _

7 × 35

_ 6 × 5 _

4 Write the mixed numbers

as improper fractions. 5

= 1 _

7 × 35

_ 6 × 5 _

4 Divide 7 and 35 by

their GCF, 7. 1

= 25

_ 24

Multiply the numerators and multiply the denominators.

= 1 1 _ 24

Simplify.

27a. about 69 27 _

40 million mi 27b. about 139 7 _

20

million mi 27c. about 487 29 _

40 million mi 27d. about

882 11 _

20 million mi 29. 2 1 _

3

3131 bc = 3 1 _ 2 × 1 3 _

4 Substitute.

= 7 _

2 ×

7 _

4 Write the mixed numbers as

improper fractions.

= 49

_ 8 Multiply the numerators and

multiply the denominators. = 6 1 _

8 Simplify.

33. Sample answer: 1 1 _ 5 × 1 1 _

2 = 1 4 _

5 35. B; The

product must be greater than 2 _ 3 and less than 2 1 _

2 .

37. D 39. 15 _

28 41. 3 _

20 43. 28 45. 15 47. 38

_ 2 or 19 1 _

2


1. 3 _ 2 3. 5 _

2 5. 6 7. 2 1 _

2

99 110 horses; Sample answer: Divide the total

amount of hay on hand by the amount each horse needs per day to find the number of horses that can

be fed each day. The expression is 44 bales divided

by 2 _ 5 bale for each horse.

44 _

1 ÷

2 _

5 =

44 _

1 ×

5 _

2 Multiply by the reciprocal of 2 _ 5 .

22

= 44

_ 1 ×

5 _

2 Divide 44 and 2 by their GCF, 2.

1

= 220


multiply the denominators. = 110 Simplify.

11. 10 13. 9 _ 7 15. 1 17. 3 1 _

3 19. 14 21. 6 23. 4 1 _

2





2525 Sample answer: To cut the large 8-foot board

into pieces that are 5 _ 6 foot each, use division.

8 ÷ 5 _ 6 =

8 _

1 ×

6 _


= 48


multiply the denominators. = 9 3 _

5 Simplify.

There will be 9 whole pieces to use for the steps

with 3 _ 5 foot left over.

29. Sample answer: Multiplication is repeated addition. Multiplication and division are inverse operations. Multiplication is commutative and associative; division is not. 31. I 33. 5 1 _

24 35. 23 1 _

3


1. 1 _ 2 3. 1 _

24 5. 9 _

10

77 Sample answer: Area = base × height, so

base = area ÷ height. Divide the area by one

measurement to find the other. 3 _ 4 ÷ 1 =

3 _

4 foot

9. 3 _ 4 11. 1 _

12 13. 7 _

24 15. 1 _

24 17. 2 _

5 19. 5 _

12

2121 2 T-shirts; Sample answer: Use the table to fi nd

the amount of orange dye available, then divide

that amount by the 3 _ 8 cup needed for each shirt.

3 _ 4 cup of orange dye ÷ 3 _

8 cup for each shirt

3 _ 4 ÷

3 _

8 =

3 _

4 ×

8 _


= 24

_ 12

or 2 Simplify.

23. 8 _ 9 25. 4 _

3 or 1 1 _

3 27. Sample answer: 1 _

2 ÷ 3 _

5

29a. c _ b ; When the numerators are the same, the

quotient is a fraction of the denominators. 29b. a _

c ; When the denominators are the same, the

quotient is a fraction of the numerators. 31. D33. Yes; the shelf can hold 24 ÷ 3 _

8 or 64 cases.

35. 24 1 _ 2 37. 4


1. 7 3. 6

55 Sample answer: Divide the dough Jay has,

10 1 _ 2 inches, by the amount needed for each slice,

3 _ 8 inch.

10 1 _ 2 ÷

3 _

8 =

21 _

2 ÷

3 _

8

Write the mixed numbers as improper fractions.

= 21

_ 2 ×

8 _


7 4

= 21

_ 2 ×

8 _

3

Divide 21 and 3 by their GCF, 3. Divide 2 and 8 by their GCF, 2.

1 1

= 28

_ 1 or 28 slices Simplify.

7. 5 _ 12

9. 2 2 _ 3 11. 39 13. 4 1 _

26

1515 3 3 _ 4 ÷ 5 5 _

8 =

15 _

4 ÷

45 _

8

Write the mixed numbers as improper fractions.

= 15

_ 4 ×

8 _


1 2

= 15

_ 4 ×

8 _

45 Divide 15 and 45 by their GCF, 15.

Divide 4 and 8 by their GCF, 4.1 3

= 2 _

3 Simplify.

17. 2 2 _ 5 19. 13 1 _

2 ÷ 2 1 _

4 ; 6 photos

2121 Sample answer: The distance around the

kitchen, 24 2 _ 3 feet, needs to be divided by the amount

of border in each strip, 1 3 _ 4 feet.

24 2 _ 3 ÷ 1 3 _

4 =

74 _

3 ÷

7 _

4 Write the mixed numbers as

improper fractions.=

74 _

3 ×

4 _


= 296

_ 21

or 14 2 _ 21

Multiply and simplify.

They will need to have 15 strips and there will be some left over.23. Sample answer: 8 2 _

3 ÷ 3 1 _

4 25. less than;

Sample answer: Since 3 5 _ 8 > 2 2 _

5 , the quotient of

5 1 _ 6 ÷ 3 5 _

8 < 5 1 _

6 ÷ 2 2 _

5 . The expression 5 1 _

6 ÷ 3 5 _

8

represents 5 1 _ 6 being divided into a greater number

of parts than the expression 5 1 _ 6 ÷ 2 2 _

5 . If 5 1 _

6 is

divided into a greater number of parts, each part

will be smaller. 27. D 29. 1 _ 2 qt 31. 800 mi

33. 54 35. 15


1. false; 21 3. true 5. false; Sample answer: 6 _ 7

7. true 9. Sample answer: 1 _ 6 × 12 = 2 11. Sample

answer: 1 _ 2 × 1 =

1 _

2 13. Sample answer: 300 sq. ft

15. 8 17. 10 19. $8.75 21. 1 _ 12

23. 5 _ 12

25. 1 _ 3

27. 6 2 _ 3 29. 1 7 _

12 31. 8 9 _

20 33. 12 5 _

6 sq. ft 35. 12

37. 6 39. 27 bags 41. 1 _ 6 43. 2 1 _

2 45. 1 _

2 47. 1 9 _

28

49. 1 2 _ 5 gallons

Chapter 3 Ratios and RatesPage 146 Chapter 3 Are You Ready?

1. 29 3. 6 5. $32 7. 2 _ 3 9. 3 _

5 11. 13

_ 25


1. 3 _ 4 ; For every 3 pens, there are 4 pencils. 3. 3 _

2 ; For

every 3 action thrillers showing, there are 2 romantic comedies showing. 5. 12 in the fi rst

group and 16 in the second group 7. 2 _ 1 ; For every

2 fl utes, there is 1 drum.

99 2 _ 5 ; 6 _

15 ÷

3 _

3 = 2 _

5 ; For every 2 boys, there are 5 girls

in the class.



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5 ; For every 3 ruby rings on sale, there are

5 emerald rings on sale. 13. 5 _ 12

, 5 to 12, or 5:12;

Every 5 out of 12 books Salvador read was a

mystery. 15. 1 _ 5 , 1 to 5, or 1:5; One out of every fi ve

articles of clothing Ramona packed was a pair of jeans. 17. 24, 40

1919 a. 5 _ 16

; The Rangers have made 5 Stanley Cup

fi nal appearances for every 16 appearances made by the Canadiens.

19b. 23 _

17 ; The Maple Leafs have made 23 Stanley

Cup appearances to every 17 Bruins’ appearances.

21. 21, 24 23. 1 _ 3 ; 1:3; or 1 to 3 25. 15

27. Sample answer:

29. If the fraction is in simplest form, the GCF of the numerator and denominator is 1, and the ratio is simplifi ed. 31. G 33. D


1. 11 points

_ 1 quarter

3. $3 _

1 case 5. $8

77 Divide the numerator and denominator by 8 to

make the denominator 1; 40.8 gallons

_ 8 containers

÷ 8 _ 8 =

5.1 gal _

1 container

9. 60 words _

1 min 11. $0.50

_ 1 bottle

13. 340 trees; Multiply

17 by 20. 15. Mr. Brown’s homeroom sold 3 subscriptions per student while Mrs. Garcia’s homeroom sold 3.5 subscriptions per student. So, Mrs. Garcia’s homeroom sold more subscriptions. 17. Divide the time by the number of laps. Evans drove the fastest at 2.3 seconds per lap. 19a. California: 223 people/sq mi; Florida: 278.3 people/sq mi; Iowa: 53.1 people/sq mi; New Jersey: 996.3 people/sq mi; Wyoming: 5.3 people/sq mi 19b. The higher the population density, the more people in a smaller space, if the population was distributed evenly across the state.

19c. Population Density

Peop

le p

er S

quar

e M

ile

State

Calif

orni

aFl

orid

a

Iow

a

Wyo

min

g

New

Jers

ey

0

200

400

600

800

1000

2121 a. The unit rate, miles in one hour, is 2,144

_ 8 , or

268 _

1 , or 268 miles per hour.

21b. To fi nd the time, divide the distance by the rate; 560 ÷ 268 ≈ 2.09. It would take a little over two hours to travel from Columbus to New York City.

23. 32 tickets 25. B 27. $14 per CD


1. $28 3. 15 tsp 5. 8 pounds

77

AmericanDollars

270 27 9

Mexican Pesos

3,000 300 100

÷10

÷10

÷3

÷3

He will have $9 left.9. 3 balls 11. 285 mi 13. If 20 lb ≈ 9 kg, then 60 lb is about 27 kg. Since half of 60 is 30, a 30 lb dog weighs half of 27 kg or 27 ÷ 2, which is 13.5 kg.

1515 a. People Served 24

Liters of Soda 4

Pints of Sherbet 2

Cups of Ice 6

15b.

Number of

People

Litersof

Soda

Pintsof

Sherbet

Cups of Ice

Steps

24 4 2 6 Original amounts

12 2 1 3 To find the ingredients for 12 people, divide each item by 2.

36 6 3 9 To find the ingredients for 36 people, multiply each item by 3.

18 3 1.5 4.5 To find the ingredients for 18 people, divide each item by 2.

2 L soda, 1 pt sherbet, 3 c ice; 6 L soda, 3 pt sherbet, 9 c ice 15c. 3 L soda, 1.5 pt sherbet, 4.5 c ice; Since 18 is half of 36, half the recipe that serves 36 people will serve 18 people. 6 L ÷ 2 = 3 L, 3 pt ÷ 2 = 1.5 pt, and 9 c ÷ 2 = 4.5 c.17. No; if 5 girls and 5 boys are added, there would be 15 girls and 13 boys in the class. Using the ratio table below, you can see that there should be 12 boys for 15 girls.

Number of Girls 10 5 15

Number of Boys 8 4 12





19. C 21. G 23. 11 parts

_ 1h

25. 3 _ 5 ; For every 3 soccer

balls there are 5 footballs.

Pages 170–171 Lesson 3-2C PSI

1. Sample answer: Use this strategy when the change between events is the same.

33 The pattern in this exercise is the step number

multiplied by 5. So, step number 7 multiplied by 5 equals 35. 5. 60 mph 7. 1, 5, 10, 10, 5, 1 9. 25 11. 2 adults, 2 senior citizens 13. Sample answer: Suppose the doctor says you should walk every day, starting with 1 block. After every 2 days, increase the amount by 2 blocks. How many blocks would you be walking after 2 weeks? First fi nd the number of 2-day periods in 2 weeks. There are 7 increases. You start with 1 and each increase is 2, so 1 + 7(2) = 1 + 14 = 15 blocks.


1. no; Since the unit rates, $8 _

1 wk and

$7.43 _

1 wk , are not

the same, the rates are not equivalent.

33 yes; Since 3 h · 3 _

$12 · 3 = 9 h

_ $36

, the fractions are

equivalent; 3 h _

$12 = 9 h

_ $36

. Also, the ratios both

simplify to equal 1 _ 4 , so they are equivalent to each

other.

5. no; Micah’s unit rate is 25 push-ups

__ 1 min

and Eduardo’s

unit rate is 26 push-ups

__ 1 min

. 7. no; Since the unit rates,

4 points _

1 game and

6 points _

1 game , are not the same, the rates are

not equivalent.

99 First fi nd the unit rate for each.

$3 _

6 bagels =

3 ÷ 6 _

6 ÷ 6

= $0.50 _

1 bagel

So, the unit rate is $0.50

_ 1 bagel

.

$9 _

24 bagels =

9 ÷ 24 _

24 ÷ 24

= $0.38 _

1 bagel

So, the unit rate is $0.38

_ 1 bagel

.

Since the rates do not have the same unit rate, they are not equivalent.

11. yes; Since 15 computers · 3

__ 45 students · 3

= 45 computers

__ 135 students

, the

fractions are equivalent; 15 computers

__ 45 students

= 45 computers

__ 135 students

.

13. no; Since 16 students

_ 28 students

≠ 240 students

__ 560 students

, the ratios

are not equivalent.

1515 no; Kiera did 6 problems

_ 30 minutes

or 1 problem

_ 5 minutes

, and

Heath did 18 problems

__ 40 minutes

or 9 problems

_ 20 minutes

. Heath took

less time to do each problem. 17a. Super Saver: $0.21 per can; Shop Smart: $0.19 per can; Price Busters: $0.25 per can 17b. They should purchase the cans of lemonade from Shop Smart. At Shop Smart, the cost per can is the

cheapest. 19. Sample answers: 10 _

14 and 15

_ 21

21. $10 23. about 1,200 miles


1. 170 3. 90 cookies

55 120 gallons

_ 4 days

= �

_ 28 days

Write equivalent ratios.

= 120 × 7 _

4 × 7

Since 4 times 7 is 28, multiply 120 by 7.

= 840 _

28

A Clydesdale will drink 840 gallons of water in 28 days.7. $30 9. 2 min

1111 Sample answer: Since there were 20 students

who responded to the original survey and 3 of them favored science, set up equivalent ratios to fi nd the number who would favor science out of 400 students.

3 science _

20 students = �

__ 400 students

Write equivalent ratios.

= 3 × 20 _

20 × 20

Since 20 times 20 is 400, multiply 3 by 20.

= 60 _

400

Therefore, 60 students could be expected to favor science out of 400 students surveyed. 13. 28 DVDs 17. Elisa did not set up the equivalent ratios in the

correct order. She should have set it up as 1 _ 12

= x _ 276

.

There are 23 teachers at the preschool. 19. 15 people

21. C 23. 27 25. yes; Since the unit rates are the

same, 1 poster

_ 3 students

, the rates are equivalent;

12 posters

_ 36 students

= 21 posters

_ 63 students

. 27. $75 29. $2.40 per

hot dog 31. 2 _ 9 , 2 to 9, or 2:9; Every 2 out of 9 shoes

sold last week were running shoes.


1. false; division 3. true 5. false; ratio 7. true

9. false; 2:3 11. 3 _ 5 13. 6 _

7 15. 11

_ 20

17. 1 _ 3 , 1 to 3, or

1:3; One out of 3 DVDs Amos owns is an action

DVD. 19. 15.75 lb _

1 wk 21.

6 passengers __

1 car 23. $4 million

25. $6 27. $18 29. 2 31. no; 14 _

21 = 2 _

3 and 21

_ 34

= 21 _

34

33. yes; 3 _ 9 = 1 _

3 and 12

_ 36

= 1 _ 3 35. yes; 79.50

_ 3 = 26.50

_ 1

and 132.50

_ 5 = 26.50

_ 1 37. yes; 8 _

48 = 1 _

6 and 4 _

24 = 1 _

6

39. 1,000 words



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nsChapter 4 Fractions, Decimals,

and PercentsPage 198 Chapter 4 Are You Ready?

1. 4 3. 12 5. 3 7. $3 9. 18 11. 72 13. 120


1. 2 _ 5 3. 16

_ 25

5. 21 _

40 7. 2 3 _

4 9. 23 3 _

4 mpg 11. 7 _

10

1313 0.5 = 5 _ 10

Say five tenths.

= 1 _ 2

Simplify. Divide the numerator and denominator by the GCF, 5.

15. 21 _

100 17. 41

_ 50

19. 17 _

40 21. 1

_ 250

23. 17 _

20 mi

25. 12 1 _ 10

27. 17 3 _

100 29. 42 24

_ 25

31. 50 121 _

200

3333 Write each decimal in fraction form, 8 _

100 and 4 _

10 .

Write 4 _ 10

as 40 _

100 . Now you can pick any two fractions

that are between 8 _

100 and 40

_ 100

. Simplify the fractions

if necessary. Sample answer: 20 _

100 or 1 _

5 in. and 35

_ 100

or 7 _ 20

in.

35. Mei wrote the wrong place value in the denominator, so her fraction was incorrect;

4.28 = 4 28 _

100 or 4 7 _

25 . 37. Sample answer: Since

6 is in the hundredths place, write 0.36 as a

fraction with a denominator of 100. So, 0.36 = 36 _

100 .

Then simplify by using the GCF, 4: 36 _

100 = 9 _

25 .

Therefore, 0.36 = 9 _ 25

. 39. H 41. C


1. 0.9 3. 3.5 5. 0.36 7. 3.7 9. 4.225 11. 0.05

1313 77 _

200 = 77 × 5

_ 200 × 5

Rewrite the fraction to have a denominator of 1,000.

= 385 _

1,000 Multiply.

= 0.385 Read 0.385 as three hundred eighty-five thousandths.

15. 0.625 17. 0.5625 19. 6.0625 21. 12.5375 23. 5.8125 in.

2525 To change a mixed number, keep the whole

part as it is and change the fraction part to a fraction with a denominator of 10, 100, or 1,000. Mercury:

87 24 _

25 = 87

24 × 4 _

25 × 4

Rewrite the fraction to have a denominator of 100.

= 87 96 _

100 Multiply.

= 87.96 Read 87.96 as eighty-seven and ninety-six hundredths.

Venus:

224 7 _ 10

= 224.7 Read 224.7 as two hundred twenty-four and seven tenths.

Mars:

686 49 _

50 = 686

49 × 2 _

50 × 2 Rewrite the fraction to have a

denominator of 100. = 686 98

_ 100

Multiply.

= 686.98 Read 686.98 as six hundred eighty-six and ninety-eight hundredths.

27. 1 _ 4 , 0.25 29. Sample answer: 7 _

12 = 0.58

− 3 31. C

33. 0.333… or 0. −

3 35. 0.8181… or 0. −−

81


1. 3 _ 20

3. 33 _

100 5. 3 _

4 7. 23

_ 50

9. 7 _ 50

1111 Write the percent number as a fraction with a

denominator of 100 and then simplify the fraction if necessary.

2% = 2 _

100 Definition of percent

= 1 _ 50

Divide the numerator and denominator by the GCF, 2.

13. 1 _ 5 15. 43

_ 50

17. 1 _ 25

19. 18 _

25 21. 7 _

25 23. 27

_ 50

2525 Eighty-two percent of the students use the

Internet at home, so 100% - 82%, or 18%, use the Internet elsewhere.

18% = 18 _

100 Definition of percent

= 9 _ 50

Divide the numerator and denominator by the GCF, 2.


20 = 55

_ 100

or 55%, 3 _ 5 = 60

_ 100

or

60%, 7 _

10 = 70

_ 100

or 70% 29. Sample answer: I received

a 95% on my science test. What fraction of the

problems did I get correct? 19 _

20 31. H 33. 0.75

35. 73 _

100 37. 11 7 _

50

Pages 215–217 Chapter 4-2C

1. 25%

33 3 _ 20

= 3 × 5 _

20 × 5 = 15

_ 100

or 15%

5. 90% 7. 30% 9. 30% 11. 44% 13. 72%

1515 Two sections out of the 10 sections are shaded.

Write 2 out of 10 as a fraction, 2 _ 10

. Since 10 × 10 gives

a denominator of 100, multiply both the numerator

and denominator by 10 and write the fraction as 20 _

100 .

Write the fraction as a percent, 20%. 17. 70% 19. 90% 21. 70% 23. 36%

2525 From the tally marks, you know that 20 students

were surveyed, 16 did not prefer uniforms, and 4 students preferred uniforms. Write each preference as a fraction with a denominator of 100 and then write that fraction as a percent.

16 _

20 = 16 × 5

_ 20 × 5

= 80 _

100

= 80%

4 _ 20

= 4 × 5 _

20 × 5

= 20 _

100

= 20% The sum of the percents, 80% + 20%, is equal to 100%.

27. 8 _ 45

; The other numbers are equivalent to 9 _ 20

.





29. Rewrite the fraction with a denominator of 100. Write the new numerator as the percent with the

percent symbol. 31. D 33. 21 _

25 35. 2 _

25 37. 0.7


1. 0.27 3. 0.04 5. 0.18 7. 32% 9. 91% 11. 82% 13. 70%

1515 35% = 35 _

100

Rewrite as a fraction with a denominator of 100.

= 0.35 Write thirty-five hundredths as a decimal.17. 0.03 19. 0.01 21. 0.95 23. 0.96 25. 99% 27. 62% 29. 60% 31. 87%

3333 0.12 = 12 _

100 Write twelve hundredths as a fraction.

= 12% Write the fraction as a percent.

35. Sample answer: 0.6; 3 _ 5 ; 60% 37. Sample answer:

Niko scored a 92% on his math test. Express this

percent as a decimal. 39. 0.25 41. 18% 43. 19 _

50

45. 7 _ 20

47. 0.3


1. 3.25; 3 1 _ 4 3. 4.8; 4 4 _

5

55 0.15% = 0.00.15 Divide by 100 and remove the % symbol.

= 0.0015

= 15 _

10,000 Write as a fraction.

= 3 _

2,000

Simplify. Divide the numerator and denominator by the GCF, 5.

7. 0.009; 9 _

1,000 9. 0.15% 11. 275% 13. 325%

15. 3.5; 3 1 _ 2 17. 6 19. 0.006; 3

_ 500

21. 0.0055; 11 _

2,000

23. 0.001; 1 _

1,000 25. 850% 27. 264% 29. 0.9%

31. 0.34%

3333 In order to write 1.4 as a percent, multiply 1.4

by 100.

1.4 × 100 = 140 The large milk shake is 140% larger than the size of the medium milk shake. 35. 350% 37. 0.4%

39. 0.00125 41. 0.0012 43. 0.003; 3 _

1,000 ; 3 out of

every 1,000 people are Japanese.

4545 a. Looking at the table, you know that 0.05% of

the human body is magnesium.0.05% = 0.00.05 Divide by 100 and remove the % symbol. = 0.0005

45b. Change 1 _

400 to a percent by dividing;

1 _

400 = 0.0025. Change 0.0025 to 0.25%. Sulfur is

0.25% of the human body. 47. 30 mph 49. D 51. 0.37 53. 0.62 55. 78%


1. > 3. <

55 2 3 _ 10

� 2 7 _ 20

Rewrite 3 _ 10 as 6 _ 20 using the LCD.

2 6 _ 20

< 2 7 _ 20

Compare the numerators.

2 3 _ 10

< 2 7 _ 20

Rewrite in original form.

7. 1 _ 2 , 3 _

4 , 4 _

5 , 9 _

10 9. garbage odors 11. > 13. >

15. = 17. =

19. 5 _ 8 foot

28

48

68

0 1

21. 2 _ 9 , 11

_ 18

, 2 _ 3 , 5 _

6 23. 3 1 _

2 , 3 9 _

16 , 3 5 _

8 , 3 3 _

4

2525 The LCD of the fractions is 48. Rewrite each

fraction with a denominator of 48.

5 _ 6 = 40

_ 48

× 8

× 8

7 _ 8 = 42

_ 48

× 6

× 6

3 _ 16

= 9 _ 48

× 3

× 3

So, the bead that is 7 _ 8 inch long is the longest of the

three. 27. < 29. >

3131 To compare the distances, you need to rewrite

the improper fractions as mixed numbers: 12 _

5 = 2 2 _

5

and 9 _ 4 = 2 1 _

4 . Then rewrite the fractions using the

LCD. The least common denominator of 5, 3, and 4 is 60.

2 2 _ 5 = 2

2 × 12 _

5 × 12

= 2 24 _

60

2 1 _ 3 = 2

1 × 20 _

3 × 20

= 2 20 _

60

2 1 _ 4 = 2

1 × 15 _

4 × 15

= 2 15 _

60

Compare the mixed numbers: 2 15 _

60 < 2 20

_ 60

< 2 24 _

60 .

Since 2 15 _

60 is the least mixed number, it is closest to

2 miles. Dominic rode the closest to 2 miles.

33. Sample answer: 3 _ 8 , 2 _

3 , 5 _

6 35. Sample answer: In

the fraction 1 _ 6 , the numerator is much less than the

denominator, so it is very close to 0. In the fraction 7 _ 9 ,

the numerator is very close to the denominator, so it

is very close to 1. So, 1 _ 6 < 7 _

9 . 37. H 39. 0.2% 41. 89%


1. >

33 3 _ 5 � 0.04 Write the sentence.

0.6 > 0.04 Write 3 _ 5 as a decimal.

3 _ 5 > 0.04 Compare.

5. < 7. Cora 9. 3 _ 10

, 0.33, 1 _ 3 11. 0.39, 7 _

16 , 44% 13. >



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ns 1515 1 _ 4 � 0.4 Write the sentence.

0.25 < 0.40 Write the fraction as 0.25 and annex a zero to 0.4.

1 _ 4 < 0.4 Compare.

17. > 19. > 21. < 23. < 25. Save More

27. Tricia 29. 38%, 0.4, 5 _ 8

31. 1 _ 5 , 0.22, 22.2% 33. 135%, 1.4, 3 _

2

35. mean: 161 _

900 ; median: 0.18

3737 Change each response portion to a decimal

written to the nearest hundredth.

17% = 17 _

100 Rewrite as a fraction with a denominator of 100.

= 0.17 Write seventeen hundredths as a decimal. 11

_ 20

= 11 × 5 _

20 × 5 Rewrite with a denominator of 100.

= 55 _

100 Multiply.

= 0.55 Read 0.55 as fifty-five hundredths. 0.2 = 0.20 Annex a zero to the 0.2 to make it hundredths. 8% = 8

_ 100

Rewrite as a fraction with a denominator of 100.

= 0.08 Write eight hundredths as a decimal.0.08, 0.17, 0.20, 0.55 Order from least to greatest.8%, 17%, 0.2, 11

_ 20

Rewrite in original form.

39. Greatest to least; when fractions have the same numerator, the fraction with the larger denominator

will be the smaller fraction. 41. B 43a. 1 _ 8 , 3 _

16 , 11

_ 32

, 3 _ 4 ;

Sample answer: When placed on a number line, the fractions read from left to right. 43b. Write them with a denominator of 32. Then, compare the

numerator. 45. < 47. 36 _

100,000 = 9

_ 25,000



5 of $50 is $10

33 Estimate 47% of 118. 47% is close to 50%, which

is 1 _ 2 . 118 is close to 120.47% of 118 is close to 1 _

2 of 120,

or 60.


5 of 15 is 9 7. Sample answer:

1 _ 2 of $30 is $15 9. Sample answer:

1 _

2 of 60 is 30


3 of 150 is 50

1313 42% is close to 40% or 2 _ 5 . Round 16 to 15.

2 _

5 of 15 is 6.

So, 42% of 16 is 6.


3 of 300 is 200

17. Sample answer: 3 _ 4 of 44 is 33 19. Sample answer:

3 _ 4 of 20 yr is 15 yr

2121 Sample answer: 71 - 37 = 34 missed shots and

34 _

71 is about 35

_ 70

, or 1 _ 2 . Since 1 _

2 = 50%, he missed about

50% of his shots. 23. about 75% 25a. No; 40% is 2 _

5 . 2 _

5 of 15 is 6. He

needs 7 baskets to win a prize. 25b. 50% 27. 1 _ 5 %

of 20, 10% of 20, 20% of 20 29. B 31. G 33. 1 4 _ 25


1. 19.2 3. 16.5 5. 0.216 7. 11 9. $10.50 11. 115 13. 161 15. 138

1717 Find 0.9% of 1,000.

0.9% = 0.009 Write 0.9% as a decimal. 0.9% of 1,000 = 0.009 × 1,000 Write the multiplication

problem. = 919. 336 21. 0.45

2323 Find 20% of $42. 20% = 0.2 Write 20% as a decimal.20% of 42 = 0.2 × 42 Write the multiplication problem. = 8.4The amount off during this sale was $8.40.25. 95 27a.

Test NumberCorrect Score Total

Math 68 80% 85

Science 63 90% 70

27b. science 27c. 48 29. Yes; 16% of 40 is 6.4 and 40% of 16 is 6.4. 31. Sample answer: Any number that can be written as a fraction can be expressed as a decimal or a percent. 33. About 135 cars; round 28% to 0.3 and multiply by 450. 35. Sample

answer: $30 37. = 39. 3 1 _ 4 , 3 1 _

3 , 5 3 _

4 41. 8%

43. 252%

Pages 252–253 Lesson 4-4E PSI

1. Sample answer: when there is a way to solve the problem in which you can arrive at the answer by using simpler numbers 3. $5 5. 400 pieces 7. 6 mi

99 Sample answer: To fi nd the amount of tax,

multiply the tax rate times the cost of the item. 6.75% × $350 = 0.0675 × 350 Write 6.75% as a decimal.

= 23.63 Multiply.She will pay about $23.63 in tax.11. 4.5 times 13. 21 stickers


1. percent 3. decimal 5. 5% 7. 0.09 9. 287

11. 7 _ 20

13. 1 _ 8 15. 4 11

_ 20

17. savings: 2 _ 5 ; charity: 3 _

20 ;

shopping: 9 _ 20

19. 0.6 21. 4.125 23. 8.5625

25. photos: 0.48; songs: 0.12; movies: 0.4 27. 12 _

25

29. 87.5% 31. 19% 33. 4 _ 5 35. 0.02 37. 0.46

39. 3% 41. 29% 43. 0.3 45. 1.25; 1 1 _ 4 47. 0.005; 1

_ 200

49. 475% 51. 1.35; 1 7 _ 20

53. = 55. > 57. 5 _ 8 , 3 _

4 , 3 7 _

12 ,

3 5 _ 6 59. > 61. > 63. > 65. 2 _

5 , 0.42, 44%, 12

_ 25

67. Miguel 69. 15 71. 20 73. 100 75. Sample answer: 80 students 77. 48 79. 4.5 81. 264 83. California: 22,205.26 mi2; Kentucky: 19,800.41 mi2; Ohio: 12,102.75 mi2 85. 15 in.





Chapter 5 Algebraic Expressions Page 268 Chapter 5 Are You Ready?

1. 65 3. 28 5. 144 7. 128 9. 1,000,000 11. 5 _ 3 or 1 2 _

3

13. 3 _ 10

15. 2 19 _

28 17. 1 _

20


1. 7 3. 47 5. 29 7. 4 × $24 + 2 × $10; $116 9. 6 11. 13 13. 61 15. 199

1717 55 ÷ 11 + 7 × (2 + 14)

= 55 ÷ 11 + 7 × 16 Add 2 and 14.= 5 + 7 × 16 Divide 55 by 11.= 5 + 112 Multiply 7 by 16.= 117 Add 5 and 112.

19. 35 21. 99 23. 5 × $7 + 5 × $3 + 5 × $2; $60 25. 22 27. 38

2929 3 Large + 2 Small Verbal expression

3 × 10 + 2 × 5 Numerical expression = 30 + 10 Multiply. = 40 Add.3 × 10 + 2 × 5; 40 rolls 31a. (34 - 12) ÷ 2 + 731b. Sample answer:

34 - (12 ÷ 2) + 7 = 34 - 6 + 7= 28 + 7= 35

33. Sample answer: They prescribe the order to use to simplify expressions containing more than one operation. It ensures that there is only one correct answer. 35. G 37. Sample answer: He should have multiplied 5 and 3 before adding 3 and 9; 24.


1. 7 3. 5 5. 14 7. $8 9. 24 11. 6 13. 6 15. 12 17. 18 19. 1 21. 4

2323 2b + 7

= 2(7) + 7 Replace b with 7.= 14 + 7 Multiply 2 by 7.= 21 Add 14 and 7.

25. 18 27. $117 29. 180 31. 12 33. 72 35. 4837a. $14.50 37b. $43.50 39. 15 41. 29 43. 49

4545 They deduct 23% for taxes, so his take-home

pay is 77% of what he earns. (100% - 23% is 77%.)0.77(13.50h)

= 0.77(13.50 × 40) Replace h with 40.= 0.77(540) Multiply 13.50 by 40.= 415.8 Multiply 0.77 by 540.

His earnings will be $415.80 after taxes. 47. yes; 30 49. B 51. I 53. 9d and 2d are like terms. 55. 9k and 3k are like terms. 57. 4c and 3c are like terms. 59. 14x, 7x, and 3x are like terms.


1. m = money Elliot saved; 4m3. = the length of the box; − 4

5. d = cost of one drink; 3d + 3.507. a = the number of apples; 4a

99 t represents Tracey’s age. Less than means to

subtract. Therefore, t - 6 represents six years less than her age.11. p = the number of points the Panthers scored; 1 _

3 p

or p ÷ 3 13. j = the cost of James’s dinner; j - 5

1515 s represents the number of members in the

Senate. The number of representatives in the House of Representatives is defi ned by 4s + 35.17. Sample answer: She is indicating a number less than 5; 5 - n is the correct expression. 19. Sample answer: 7 more songs, 2 fewer songs, 4 times the songs, and half the number of songs. 21a.

Weeks Height (cm)

1 6

2 8

3 10

4 12

5 14

21b. Sample answer: 2w + 4 21c. 24 cm 23. 29 25. 2 × $28 + 3 × $4; $68

Pages 286–287 Lesson 5-1E PSI

1. Sample answer: Using the act it out strategy, it is easier to determine the reasonableness of an answer.

33

Team 1 Team 2 Team 3 Team 4

Student1

Student2

Student3

Student4

Student5

Student6

Student7

Student8

Student9

Student10

Nate

Nate will be on Team 3.5. 5 students 7. 6 9. about 5 times 11. 120 words


1. yes; Associative Property

33 72 - (63 - 8) (72 - 63) - 8 72 - (55) (9) - 8 17 ≠ 1 no; The fi rst expression is equal to 17 and the second is equal to 1. 5. no; The fi rst expression is equal to 16 and the second is equal to 4. 7. Sample answer: (12 + 24) + 6 and 12 + (24 + 6) 9. yes; Associative Property 11. no; The fi rst expression is equal to 11 and the second is equal to 21. 13. yes; Associative Property 15. no; The fi rst expression is equal to 9 and the



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nssecond is equal to 1. 17. no; The fi rst expression is

equal to 32, not 0. 19. (4 1 _ 2 + 5 1 _

2 ) + 6 = 16 in.

2121 75,000 · 5 and 5 · 75,000; Use the Commutative

Property that states the order of the numbers does not change the product when multiplying. So, 75,000 people times 5 days and 5 days times 75,000 people both have the same product. 23. y + 5 25. b + 4 27. 8n 29. 36w 31. 36k

3333 17 + x = 3 + 17 Write the original equation.

17 + x = 17 + 3 Commutative Property of Additionx = 3

35. 0 37. False; using the order of operations, (18 + 35) · 4 = 212 and 18 + 35 · 4 = 158. 39. Sample answer: For each operation the identity elements are numbers that combine with other numbers without changing the value of the other numbers. The additive identity is zero (0). The multiplicative identity is one (1). 41a. (2 × 7) × 6 and 2 × (7 × 6) 41b. $84; Sample answer: I knew that 6 × 7 = 42 and double 42 is 84. 43. Identity Property of Addition 45. Identity Property of Addition 47. Identity Property of Multiplication


1. 4(30) + 4(8) = 152 3. 11(20) + 11(7) = 297

5. 3x + 3 7. 4x + 24 9. 4(5) + 4 ( 1 _ 8 ) = 20 1 _

2

1111 7 × 3.8= 7 × (3 + 0.8) Write 3.8 as 3 + 0.8.= (7 × 3) + (3 × 0.8) Distributive Property

= 21 + 5.6 Multiply mentally within the parentheses.

= 26.6 Add.

1313 Distance is equal to rate multiplied by time.

Therefore, a coyote can run 43(6) miles in 6 hours and a rabbit can run 35(6) miles in 6 hours. The difference between the two distances can be written 43(6) - 35(6). Rewrite the expression using the Distributive Property: (43 - 35) × 6. Simplify within the parentheses: 8 × 6 equals 48. Therefore, a coyote can run 48 miles farther in 6 hours than a rabbit can. 15. 6x + 66 17. 4x + 8 19. 0.37; Sample answer: 0.1(3.7) = 0.1(3) + 0.1(0.7) = 0.3 + 0.07 = 0.37 21. Sample answer: The friend did not multiply 5 and 2. The expression 5(x + 2) = 5x + 10. 23. F25. 8 days 27. b = price of a book; b × 3 29. 4


1. true 3. false; equivalent 5. false; seven times x 7. 30 9. 7 11. 3 × 5 + 7; 22 motorcycles 13. 54 15. 26 17. 456 19. 144 tiles 21. c represents the cost of renting a video game; c + 3 23. m represents the amount of memory that is music;

m + 0.5 25. 25 s 27. no; The fi rst expression is

equal to 8 and the second is equal to 1 _ 8 . 29. no;

The fi rst expression is equal to 17, not 1. 31. 14 +

(16 + 11) and (14 + 16) + 11 33. 7 × 4 2 _ 7 = 7(4) +

7 ( 2 _ 7 ) = 28 + 2 = 30 35. 6 × 5.4 = 6(5) + 6(0.4) =

30 + 2.4 = 32.4 37. 4x + 12 39. 9x + 18 41. 4($9.50) + 4($5.50) = 4($15) = $60

Chapter 6 EquationsPage 312 Chapter 6 Are You Ready?

1. 13 _

24 3. 1 5 _

12 5. 1 5 _

8 c 7. 1 _

3 9. 11

_ 35

11. mowing the

lawn, 19 _

30 h


1. 8 3. 2 5. 12 7. 2 9. 34 11. 15 votes

1313 Valueof d 29 + d = 54 Are both

sides equal?

24 53 ≠ 54 No

25 54 = 54 Yes

26 55 ≠ 54 No

Therefore, 25 is the solution.15. 31 17. 7 19. 21 21. 13 23. 12 25. 5 27. 9 29. 18 31. 2 33. $10

3535 Sample answer:

Try 45. 700 - d = 665 700 - 45 � 665 655 ≠ 665Try 40. 700 - d = 665 700 - 40 � 665 660 ≠ 665Try 35. 700 - d = 665 700 - 35 � 665 665 = 665Therefore, there are 35 fewer students this year.37. Sample answer: m + 8 = 13 39. True; m + 8 is not equal to any specifi c value, so there are no restrictions placed upon the value of m. 41. Sample answer: Curtis has 12 more baseball cards than Juan. Curtis and Juan have a total of 30 baseball cards. Solve the equation a + 12 = 30 to fi nd the number of baseball cards that Juan has. 43. 7 45. 4 × 14 = 56; Each side is 14 units.

Pages 318–319 Lesson 6-1B PSI

1. Sample answer: Start with the answer that you found and then work forward to see if you arrive at the number you were given in the problem. 3. 6:55 a.m.

55 To use the work backward strategy, begin with the

fi nal answer and do the opposite of each operation

R01_R39_EM_SelAns_895129.indd R12R01_R39_EM_SelAns_895129.indd R12 1/19/10 8:46 AM1/19/10 8:46 AM




but in reverse order. 18 was the fi nal answer. Six had been added to it, so subtract 6 from 18 and get 12. The original value had been multiplied by 4, so divide 12 by 4 to fi nd the original value. It was 3. 7. 127 pictures 9. 17 rungs 11. 8 13. 37 spaces


1. 2

33 Solution:

c + 3 = 6 Write the equation. - 3 = - 3 Subtract 3 from each side.c = 3Check: c + 3 = 6 Write the equation.3 + 3 6 Replace c with 3. 6 = 6 The equation is true.5. x + 7 = 19; 12 m 7. 3 9. 7 11. 2 13. 5 15. 5

1717 The length of a Black Mamba plus 22 inches is

118 inches. Let � represent the length of a Black Mamba.� + 22 = 118 - 22 - 22

� = 96So, a Black Mamba is 96 inches. 19. 15.4 = x + 4.9; 10.5 ft 21. 0.3

2323 Solution:

7.8 = x + 1.5 Write the equation.- 1.5 = - 1.5 Subtract 1.5 from each side. 6.3 = xCheck:7.8 = x + 1.5 Write the equation.7.8 6.3 + 1.5 Replace x with 6.3.7.8 = 7.8 The equation is true.25. 1 _

2 27. Sample answers: 56 = 44 + x; 36 = 24 + m

29. Sample answer: Nicholas added $5 to his savings account. He now has $87. How much money did he originally have? 31. G 33a. 15 + b = 24; b = 9 33b. Sample answer: Wes could have had 3 land on the board for 3 points and 2 went through the hole for 6 points. 35. 8 37. 3

Pages 330–331 Chapter 6-1F

1. 14 3. 12 5. s - 20 = 45; 65 min 7. 6

99 Solution:

1 = g - 3 Write the equation.+ 3 = + 3 Add 3 to both sides. 4 = gCheck:1 = g - 3 Write the equation.1 4 - 3 Replace g with 4.1 = 1 The equation is true.11. 9 13. 15 = v - 12; 27 votes 15. 21 17. 3.4

19. 1 21. 10 _

9 or 1 1 _

9

2323 x represents the amount she gave the cashier.x - (24 + 13 + 16 + 3) = 4 x - 56 = 4 Add the amounts in the parentheses. + 56 = + 56 Add 56 to both sides. x = 60 Alejandra gave the cashier $60.25. Sample answer: I have d dollars. After paying my sister $32, I have $64 left. How much money did I have to start with? 27. H 29. 3:05 p.m.


1. 3 3. 2 5. 18x = 90; 5; To check, multiply 18 by 5. The result should be 90. 7. 4 9. 3

1111 Solution:

4g = 24 Write the original equation.4g

_ 4 = 24

_ 4 Divide both sides by 4.

g = 6Check: 4g = 24 Write the original equation. 4(6) 24 Replace g with 6. 24 = 24 The equation is true.13. 2 15. 4e = 58; $14.50 17. 2 19. 9 21. 1 _

2

2323 a. p = the number of points Blanda scored

each year.26p = 2,002 Write the original equation.26p

_ 26

= 2,002

_ 26

Divide both sides by 26.

p = 77 George Blanda averaged 77 points each year.23b. p = the number of points Johnson scored each year.16p = 1,736 Write the original equation.16p

_ 16

= 1,736

_ 16


p = 108.5Norm Johnson averaged 108.5 points each year.25. 4b = 7; The solution for the other equations is 4. 27. Sample answer: Jacob bought four T-shirts for $24 at a souvenir shop. How much did each T-shirt cost? 29. I 31. 5 33. 7 35. 500 min.


1. 60 3. 40

55 Solution:

5 = p _

4 Write the original equation.

5(4) = p _

4 (4) Multiply both sides by 4.

20 = pCheck:

5 = p _

4 Write the original equation.

5 20 _

4 Replace p with 20.

5 = 5 The equation is true.

7. h _ 6 = 12; 72 oz 9. 32 11. 36 13. 132 15. 36

17. 133 19. 100



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ns 2121 The number of dozens of cookies divided by

4 equals the number of dozens she cooked for the bake sale. Let x represent the total number of dozens of cookies she baked.

x _ 4 = 3

x _ 4 (4) = 3(4)

x = 12

So, she baked 12 dozen cookies in all.

23. r _ 4 = 16; 64 in.

2525 Solution:

4.7 = g _

3.2 Write the original equation.

4.7(3.2) = g _

3.2 (3.2) Multiply both sides by 3.2.

15.04 = gCheck:

4.7 = g _

3.2 Write the original equation.

4.7 � 15.04 _

3.2 Replace g with 15.04.

4.7 = 4.7 The equation is true.27. 10.08 29. 1.4 31a. 20 = 5x; 4 books

31b. x _ 5 = 7; 35 points 33. True; Sample answer:

Dividing by 3 is the same as multiplying by 1 _ 3 .

35. A 37. H 39. 10 41. a - 3 = 11; 14 yr

43. 21 45. $29


1. 4

33 Solution:

9k - 4 = 32 Write the original equation. + 4 = + 4 Add 4 to each side of the equation. 9k = 36 Simplify.

9k _ 9 =

36 _

9 Divide both sides by 9.

k = 4 Simplify.Check: 9k - 4 = 32 Write the original equation. 9(4) - 4 � 32 Substitute 4 for k. 36 - 4 = 32 Simplify. 32 = 32 This equation is true.5. 7 7. 18x - 9 = 171; 10 h 9. 8 11. 7 13. 515. 15x + 89 = 149; 4 wk 17. 3.1 19. 1.98 21. 4.2

2323 games + shoes = total cost

g represents the number of games, so $3.00g is the

cost of g games.3.00g + 3.50 = 15.50 Write the original equation. - 3.50 = - 3.50 Subtract 3.50 from each side. 3.00g = 12.00 Simplify.

3.00g

_ 3.00

= 12.00

_ 3.00

Divide each side by 3.00.

g = 4You can bowl 4 games.

2525 current temp + increase = new temp

h represents the number of hours, so 2.5h is the increase during those hours. 62.8 + 2.5x = 75.3 Write the original equation.- 62.8 = - 62.8 Subtract 62.8 from each side. 2.5x = 12.5 Simplify.

2.5x _ 2.5

= 12.5

_ 2.5


x = 5It will take 5 hours for the temperature to reach 75.3 degrees.27. 45 29a. Sample answer: Anita had $15 and spent all of it on 2 bracelets and a necklace. If the necklace was $7, how much were each of the bracelets?29b. $15

x x 7

29c. $4 29d. Only one number makes a true sentence when it replaces the variable. 31. Sample answer: Five more than three times a number is 29. 33. Addition; since the variable is being multiplied fi rst and added second, the opposite would be to undo addition and then undo multiplication. 35. 12 represents the cost per hour, x represents the unknown number of hours, 35 represents the fl at rate, and 95 represents the total spent. 37. C 39. add 8; divide by 3 41. 77 43. 45 45. 56 47. x - 3 = 14; x = 17 inches 49. 18 51. 31 53. 15


1. false; coeffi cient 3. true 5. false; multiplication 7. true 9. 7 11. 25 13. 30 15. 16 years old 17. 4:45 p.m. 19. 3 21. 12 23. 4 + x = 10; 6 ft 25. 19 27. 92 29. 8 31. 12 33. 3 35. 25t = 5; $0.20

37. 48 39. 60 41. s _ 3 = 15; 45 mph 43. 3 45. 2

47. 5

Chapter 7 Functions, Inequalities, and Integers


1. > 3. > 5. 300 > 206 7. 14 9. 25 11. 8 13. 5


1–4. y

x

123456789

1 2 3 4 5

5a. (0, 0), (1, 3), (2, 6), (3, 9)

5b. The points appear to fall on a line.





y

6 721 43 5

6789

12345

x

(3, 9)

(2, 6)

(1, 3)

(0, 0)

77 To graph (3, 0), start at the origin and move

3 units to the right. You do not need to move any units up or down. Draw a dot and label it M.

6–13. y

xO

123456789

1 2 3 4 5 6 7

Q

M

R

L

N

PA

B

1515 a. (5, 20), (5 1 _ 4 , 21) , (5 1 _

2 , 22) , (5 3 _

4 , 23)

15b. The points appear to fall on a line.

y

x

161718192021222324

5 6

(5, 20)(5 , 21)1

4

(5 , 22)12

(5 , 23)34

17. Sample answer: Laureen earned $7 an hour tutoring. Make a table showing the relationship between the number of hours she tutors and the amount of money she earns.

Hours AmountEarned ($)

1 7

2 14

3 21

19. Sample answer: The point (3, 2) is 3 units to the right of the origin on the x-axis and 2 units up the y-axis. The point (2, 3) is 2 units to the right on the x-axis and 3 units up the y-axis. 21. D

23. Total

Time (h)Number of Paintings

0 0

3 1

6 2

9 3


1. Input (x) x + 3 Output

0 0 + 3 3

2 2 + 3 5

4 4 + 3 7

3. Input (x) x - 1 Output

1 1 - 1 0

3 3 - 1 2

5 5 - 1 4

5. Pounds (x) 3x + 2 Cost ($)

2 3(2) + 2 8

3 3(3) + 2 11

4 3(4) + 2 14

y

x

3

6

9

12

1 2 3 4 5

15

(2 lb, $8)

(3 lb, $11)(4 lb, $14)

77 Insert the input into the function rule to

determine the output.

Input (x) 3x + 5 Output

0 3(0) + 5 5

3 3(3) + 5 14

9 3(9) + 5 32

9. Input (x) 2x + 4 Output

7 2(7) + 4 18

9 2(9) + 4 22

15 2(15) + 4 34



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ns 1111 Number of Guests (x) 30 ÷ x

Cupcakesper Guest

6 30 ÷ 6 5

10 30 ÷ 10 3

15 30 ÷ 15 2

y

xO

1

2

3

4

4 8 12 16 20

5

(15, 2)

(10, 3)

(6, 5)

13. Years (x) 223 million × $10 × x

1 $2,230,000,000

2 $4,460,000,000

3 $6,690,000,000

15. 4 17. B


1. multiply the position number by 2; 2n; 30 3. 2x + 1

55 Position Add 9 Value of Term

3 3 + 9 12

4 4 + 9 13

5 5 + 9 14

6 6 + 9 15

n n + 9 n + 9

Add 9 to the position number; n + 9;therefore, the twelfth term is 21.7. multiply the position number by 5; 5n; 60 9. Sample answer: This is a geometric sequence. Each term is found by multiplying the previous term by 3; 486, 1,458, 4,37411a. The amount increases by $8. 11b. 8x + 5 13. add 12; 52, 64 15. add 2.4; 11.1, 13.5

17. add 1 _ 2 ; 4 1 _

4 , 4 3 _

4 19. 11 1 _

2 21. 24 1 _

2

2323 arithmetic sequence; Each term is found by

adding 2 to previous term.; 10 + 2 = 12; 12 boxes25. arithmetic sequence; 4.75, 5.75 27. Sample

answer: 1, 2 1 _ 4 , 3 1 _

2 , 4 3 _

4 , ... 29. Sample answer: Both

are numerical patterns, but arithmetic sequences are additive and geometric sequences are multiplicative. 31. B 33. 4x + 1


4 4(4) + 2 18

5 4(5) + 2 22

6 4(6) + 2 26

36–39. y

x

2

4

6

8

1 2 3 4 5 6 7 8 9 10

10

1

3

5

7

9

(0, 4)

(0, 0)

(6, 2)

(7, 0)


1. y = 4x

3. y

xO

2

4

6

8

1 2 3

10

1

3

5

7

9

5. y

xO

2

4

6

8

1 3 5 7 9 102 4 6 8

10

1

3

5

7

9

7. y = 6x 9. y = 15x

1111 To graph the equation, make a table of values

using any three values for x, and calculate y. Then graph the line passing through the three ordered pairs.

x x + 4 y (x, y)

0 0 + 4 4 (0, 4)

3 3 + 4 7 (3, 7)

5 5 + 4 9 (5, 9)





y

x

2

4

6

8

1 3 5 7 9 102 4 6 8

10

1

3

5

7

9

13. y

x

2

4

6

8

1 3 5 7 9 102 4 6 8

10

1

3

5

7

9

15. y

x

2

4

6

8

1 3 5 7 9 102 4 6 8

10

1

3

5

7

9

17.

Tota

l Cha

rge

30

1 2 3

20

40

100

5060

Number of Classes

Health Club Costs

y

x

1919 a. Input (d) 1 2 3 4

Output (t) 5 10 15 20

19b. The equation for the money spent t on lunch for d days is y = 5x. 21a. y = x · x or y = x2

21b. y

xO

2

4

6

8

1 3 5 7 9 102 4 6 8

10

1

3

5

7

9

21c. No; the graph is curved; it does not form a line.

25. y = x _ 2 - 3 27. C 29. Sample answer: The

graph could represent the growth of a tree.

Pages 391–393 Chapter 7-1F

1a. t = 3n 1b. Number of Lunches, n

1 2 3

Total Cost ($), t 3 6 9

1c. y

xO

2

4

6

8

1 3 5 7 9 102 4 6 8

10

1

3

5

7

9

(1, 3)

(2, 6)

(3, 9)

1d. The graph is a line because each ticket costs $3.

33 a. Use v = 400d because 400 multiplied by the

number of days will give you the total amount of vegetation eaten.

3b. Number of Days, d 1 2 3

Pounds Eaten, v 400 800 1,200

3c. y

x

400

800

1200

1 2 3

200

600

1000

1400(3, 1,200)

(2, 800)

(1, 400)

Number of Days

Poun

ds E

aten

3d. The graph is a line because with each day, the amount of vegetation increases by 400.5a. Music Man: t = 45n; Road Tunes: t = 35n; where t represents the total cost and n represents the number of hours 5b. The Music Man; The Music Man charges more.

77 a. t = 3 + 1.75c; where t represents the total



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nsearned and c represents the number of chores

7b. Number of Chores Completed

1 2 3

Total Earned ($) 4.75 6.50 8.25

7c. y

x

2

4

6

8

1 2 3

1011

1

3

5

7

9

(1, 4.75)

(2, 6.5)

(3, 8.25)

Tota

l Ear

ned

($)

Number of Chores

Total Earned

7d. t = 3 + 1.75(5)

t = 3 + 8.75

t = $11.75

9. straight line; Sample answers: (0, 0), (1, 1), and (2, 2) 11. Sample answer: Cable Company A charges a $50 start-up fee and $60 a month. Cable Company B doesn’t charge a start-up fee, but charges $70 a month. You could use a graph to see how many months it would take before Company A would become cheaper. 13. c = 25 + 2m 15. p = 2m + 5s17.

Feet Yards

3 1

6 2

9 3

12 4

3n n ; 12 ft


1. 7 3. no 5. Friday and Saturday 7. 8 9. 0

1111 t - 7 < 10 Write the inequality. 28 - 7 < 10 Replace t with 28. 13 < 10 Simplify.Since 13 is not less than 10, 28 is not a solution.13. no

1515 Month Number

of Texts t > 55True or

False

January 56 56 > 55 True

February 57 57 > 55 True

March 55 55 > 55 False

April 51 51 > 55 False

She went over her limit of text messages in January and February.

17. true; 112 _

8 + 2 ≥ 15 + 4(2) - 7, so 16 ≥ 16 19. A

21a. h = 5w

21b. Weeks(w)

Hours (h)

1 5

2 10

3 15

21c. y

x

3

6

9

12

1 2 3 4 5

15

(1, 5)

(2, 10)

(3, 15)

Hour

sWeeks


1. Sample answer: when you are trying to fi nd the solution of an equation 3. 5 problems worth 2 points each and 2 problems worth 4 points each5. 8 quarters, 1 dime, 1 nickel, and 5 pennies 7. Sample answer: 7 and 13

99 Use the guess, check, and revise strategy for this

exercise. Remember to use the order of operations. 3 × 4 + 6 ÷ 1 = 18; (3 × 4) + (6 ÷ 1) = 12 + 6 = 18

11. 31 students;

40

? 9

3rd grading period

13. Sample answer: The sum of four coins is thirty-two cents. What are the coins? To solve this problem, choose any four coins and fi nd their sum. Then check to see if the sum is thirty-two. If not, choose another four coins and check the answer. Repeat this process. The answer is a quarter, a nickel, and two pennies.


1. � ≤ 90

3. 8 9 10 11 12765432

5. 8 9 10 11 12765432





7. p ≤ 35

99 s = the amount spent; s ≤ 50

11. f > 800

13. 7 8 9 10 11654310 2

15. 7 8 9 10 11654310 2

17. 7 8 9 10 11654310 2

19. s < 20

20 21 22 23 24191817161413 15

2121 a. Softball, drama, and band have more than

20 participants; basketball, softball, drama, and band have at least 20 participants; tennis, orchestra, and baseball have fewer than 19 participants.

21b. 12 > 6

23. Sample answer: 1 _ 5 , 1 _

4 , 1 _

3

0 45

35

25

15

13

14

15

25. n > 21

20 21 22

27. ham and turkey

Pages 409–411 Lesson 7-2F

1. h ≥ 19

18 1916 17 20 21 22

33 7x > 56 Write the inequality.

7x _ 7 >

56 _


x > 8 Simplify.

7 85 6 9 10 11

5. 2x ≤ 10; x ≤ 5 7. y ≤ 1

0 1-2 -1 2 3 4

9. w < 5 4 52 3 6 7 8

11. t ≤ 4 3 41 2 5 6 7

13. d ≤ 6 3 41 2 5 6 7

15. r > 72 71 7269 70 73 74 75

1717 The number of letters times $0.10 must be less

than or equal to $5.00. Let x = the number of

letters. The inequality is 0.10x ≤ 5.00.

0.10x ≤ 5.00 Write the inequality. 0.10x _ 0.10

≤ 5.00

_ 0.10


x ≤ 50 Simplify.

So, Bobby can have a maximum of 50 letters engraved.

1919 p - 7 _ 12

> 3 _ 10

Write the inequality.

+ 7 _ 12

+ 7 _ 12

Add 7 _ 12 to both sides._____________p > 53

_ 60

Simplify.

5060

5160

5260

5360

5460

5560

21. g > 9 8 96 7 10 11 12

23a. 14.50x ≤ 32.75 23b. 2 shirts 25. at least 86 27. A 29. F 31. 13 and 15 33. geometric; 1,536; 6,144

Pages 413–415 Lesson 7-2G

1. x > 8 8 96 7 10 11 12

33 6x + 4 ≥ 28 Write the inequality. - 4 - 4 Subtract 4 from each side. 6x ≥ 24 Simplify.

6x _ 6 ≥ 24

_ 6 Divide both sides by 6.

x ≥ 4 Simplify.

2 3 4 5 65. 12 + 9.5x ≤ 50; 4 hours 7. x ≥ 5

2 30 1 4 5 6

9. x < 6

6 74 5 8 9 10

11. x ≤ 3

1 2 3 4 5

1313 8x + 3 ≥ 43 Write the inequality. - 3 - 3 Subtract 3 from each side. 8x ≥ 40 Simplify.

8x _ 8 ≥ 40

_ 8 Divide each side by 8.

x ≥ 5 Simplify.The solution is x ≥ 5.

3 4 5 6 7

15. 50 + 45x ≤ 185; x ≤ 3; at most 3 hours 17. d < 6

6 74 5 8 9 10

19. b ≥ 3

2 30 1 4 5 6

2121 current weight + weight gained > 178 pounds

Let x be the number of months.



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nsThen 3x is the number of pounds gained each month. 163 + 3x > 178 Write the inequality.-163 -163 Subtract 163 from both sides. 3x > 15 Simplify.

3x _ 3 >

15 _


x > 5It will take him greater than 5 months.23. Sample answer: 2x + 2 ≥ 1625. x ≥ 3

2 30 1 4 5 627. 42529. f > 3

2 30 1 4 5 6

31. x ≥ 3 2 30 1 4 5 6

33. C and I or G and L


1. 15 3. 245.

5-5 -4 3 421-3 -2 -1 0

7. 5 9. 28 11. 45

1313 Spending money means a loss, so the integer

would be -25. 15. -217.

12-12 -8 84-4 0

19.

-10-12-14 -8 -6 4 6 8 102-4 -2 0

21. 12 14-12 -8 84-4 0

23. 18 25. 25

2727 ⎪-15⎥ + ⎪-6⎥ = 15 + ⎪-6⎥ Absolute value of -15 is 15.= 15 + 6 Absolute value of -6 is 6.= 21 Add.

29. 30 31. -3 33. 14

3535 The absolute value of -230°F is 230. The

absolute value of 70°F is 70. 70 < 230, so 70°F has the lower absolute value.37. Never; distance cannot be negative. 39. Absolute value is distance and distance cannot be negative. 41. F 43. x < -5

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


1. H 3. B 5. (0, -2); none 7. gym

9–11. y

xO

21

345

21 3 4 5-5-4-3-2-1-1-2-3-4-5

(-3, 3)

(2, 1)

(0, -1)

13. U 15. S 17. J

1919 The coordinates for point C are (5, 0). Since the

point lies on the x-axis, it is not in any of the quadrants. 21. (3, -5); IV 23. (5, 4); I

24–29.

O

21

345

21 3 4 5-5-4-3 -1-1-2-3-4-5

-2

(-1.5, 2.5)

(5, -2)

(1, 2)

(-4, -1)

(-2, -5)

(0, 0)

(-3, 4)

4 , -1 34

14

2 , -2 12

12

31–33. y

x

21

345

21 3 4 5-5-4-3 -1-1-2-3-4-5

(-1.5, 2.5)

-2

2 , -2 12

12

4 , -1 34

14

3535 The length of the base AB is 4 units. The length

of the height AC is 3 units. Use the formula to fi nd the area of the triangle.

A = 1 _ 2 bh Area of triangle

A = 1 _ 2 (4)(3) Replace b with 4 and h with 3.

A = 6 Multiply.

The area of the triangle is 6 square units.

x

y





37. Quadrants II and IV; Sample answer: In both Quadrants II and IV, the coordinates have different signs. 39. Sample answer: The fi rst coordinate tells the location of the point to the left or right of the y-axis and the second point tells the location of the point above or below the x-axis. The coordinates of a point defi ne its unique location. Any given point is defi ned by only one ordered pair. 41. G 43. -3


1. true 3. true 5. false; x > 7

6–8. y

xO

2

4

6

8

1 3 5 7 9 102 4 6 8

10

1

3

5

7

9

X (5, 0)

Y (4.75, 6)

Z(2, 8 )12

9. (11, 5), (12, 5.5), (11.5, 5.25), (12.5, 5.75); They appear to form a line.

y

xO

1

2

3

4

6

7

10 12 142 4 6 8

5(11, 5) (11.5, 5.25)

(12.5, 5.75)(12, 5.5)


1 3(1) + 1 4

3 3(3) + 1 10

7 3(7) + 1 22


5 2(5) + 4 14

6 2(6) + 4 16

7 2(7) + 4 18

15. 2x 17. Multiply each term by 8; 12,288, 93,304

19. y = 7x + 1 21. y = x - 12

23. y = 16x Batches ofPretzels (x) Butter (y)

1 16

2 32

3 48

25. no 27. 27 small cars 29. p ≤ 45

31. 108 9 11 12 13 14

33. x > 3

10 119876543210

35. 4g ≤ 12; g ≤ 3

37. x ≥ 8

10 119876543210

39. 65 7-7 -6 -5 -4 3 421-3 -2 -1 0

41. 6 43. 16 45. 21 47. 5 49. (-4, 3)50–53.

x

y

(-2, 4)

(-3, -2)

(4, 1)

(2, -1)

Chapter 8 Properties of Triangles and Quadrilaterals

Page 440 Are You Ready?

1. 46 3. 58 5. 19 7. 58 9. 181 11. yes


1. plane; plane JKL p

33 no; Line segment TV measures 8 millimeters and line segment RS measures 13 millimeters so the line segments are not congruent. 5. intersecting 7. intersecting 9. plane; plane RST

1111 line; � EF or � FE ; The fi gure shown is a line that continues in both directions so it must be a line. It can be labeled as either � EF or � FE . 13. line segment;

−−− LM or

−−− ML

15. no 17. yes 19. intersecting 21. parallel

2323 Sample answer: � AC is parallel to � DF because

the lines are the same distance apart and do not intersect. � AC and � BE are perpendicular because the lines intersect to make a right angle. 25. Intersecting; since they are lines, they extend forever. These lines eventually intersect. 27. Sample answer: Line segment

−− AB is represented

with the bar because it has two endpoints where



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nsline � �� AB continues in both directions without ending. 29. F 31. Sample answer: Both are similar in that they meet or cross at a point. The difference between the two is that perpendicular lines make a right angle where they meet or cross.


11 Using a protractor, the angle measures 137°.

Since this angle is between 90° and 180° it is an obtuse angle. 3. 180°; straight 5. 20°; acute 7. 163°; obtuse 9. 115°; obtuse

1111 Using a protractor, the angle of the roof

measures 120°. Since this angle is between 90° and 180° it is an obtuse angle.

1313 Using a protractor, the angle of the exit sign

measures 90°. Since this angle is exactly 90° it is a right angle. 15. 115° 17. 60° 21. ∠X and ∠Y have the same measure, but ∠X looks bigger because the rays are longer. 23. Sample answer: First, align the center of the protractor with the vertex of the angle. Next, make sure one side of the angle passes through zero on the protractor. Last, use the scale where the fi rst side of the angle crosses 0°. 25. obtuse 27. Sample answer: You can estimate using fraction circles to compare the angle to the fraction circles. If the angle is the same

as the 1 _ 4 fraction circle, it is a right angle. If it is less

than this fraction circle, it is an acute angle. Anything greater is an obtuse angle.29.

31.

33.

35.


1. supplementary 3. complementary

55 30° + x° = 180° - 30 = - 30

x° = 150°

So the value of x is 150. 7. 70 9. supplementary 11. complementary pp

1313 85° + 95° = 180°

Since the sum of their measures is 180°, the angles are supplementary. 15. 88 17. 155 19. 3521. Sample answer: If the measure of ∠1 is 50°,

what is the measure of ∠2? 23. 115° 25. vertical angles 27. vertical angles 29. Always; Sample answer: Vertical angles are congruent. 31. Never; Sample answer: Since an obtuse angle is greater than 90°, the sum of two obtuse angles must be greater than, not equal to, 180°. g

3333 a. 25; Since x° and 65° are complementary, their

sum will equal 90°. So, 90° - 65° = 25°. The value of x is 25. 33b. 60; Since y°, x°, 65°, and 30° are supplementary, their sum will equal 180°. y° + 25° + 65° + 30° = 180° y° + 120° = 180° - 120 = -120 y° = 60°The value of y is 60.33c. Two; Sample answer: The 65° angle and the angle labeled x° are complementary and the 30° angle and the angle labeled y° are complementary. 35a. Sample answer: an obtuse angle 35b. a right angle 35c. no, two acute angles will never add up to 180° because each acute angle, by defi nition, has a measure that is less than 90°. Two angles that are both less than 90° will never add up to 180°. 37. The measures of the two angles must be equal. If two angles are supplementary to the same angle, say x°, then each angle has a measure of (180 - x)° and thus have the same measure themselves. 39. 95 41. adjacent 43. neither 45. adjacent47. Sample answer:

21


1. obtuse 3. scalene

55 60 + 73 + x = 180 133 + x = 180 - 133 = - 133 x = 47So the value of x is 47. 7. 120 9. obtuse 11. acute

1313 The 96° angle is obtuse. This is an obtuse

triangle. 15. equilateral; also isosceles 17. 130 19. 63 21. 35

2323 29 + 62 + x = 180 91 + x = 180 - 91 = - 91 x = 89 So the measure of the third angle is 89°.25a. right triangle 25b. by the fl agpole 27. Sample answer: If you know the length of the sides of a triangle, you can determine if any lengths





are congruent to classify the triangle. If you know the angles of the triangle, since two angles are acute, you can use the third angle to classify the triangle. 29. F 31. B 33. Sample answer: The set of measures cannot form a triangle because 12 + 13 is less than 26 and the theorem states that the sum must be greater than the sum of both sides. 35. Sample answer: The set of measures cannot

form a triangle because 3 1 _ 2 + 4 1 _

4 is less than 8 3 _

4 and

the theorem states that the sum must be greater than the sum of both sides.


1. Sample answer: He drew a diagram to solve the problem because the diagram allowed him to visualize the garden and understand the information. 3. 5 ways 5. 450 ft2, 388 ft2, 388 ft2 7. 12 ways 9. 4.6 cm

4.6 cm4.6 cm

11. $76.95 1313 For each table, there would be a

balloon on each corner and one on each side. The table is square so there would be 4 balloons on the corners and 4 on the sides. Each table would have 8 balloons. If there are 4 tables with 8 balloons on each table, she would need 32 balloons.


1. quadrilateral 3. square 5. 97 q

77 The railing of the steps has opposite sides that

are parallel and congruent. The opposite angles are congruent so it must be a parallelogram. 9. square 11. trapezoid 13. trapezoid 15. 133 17. 117

1919 62 + 84 + 114 + ∠U = 360 260 + ∠U = 360 - 260 = - 260 ∠U = 10021. 134.5

2323 52 + 52 + 2x + 2x = 360 104 + 4x = 360 - 104 = - 104 4x = 256

4x _ 4 = 256

_ 4

x = 64

25. Sample answer: A book is shaped like a rectangle. It has four right angles. 27. Sample Answer: A trapezoid has bottom or base angles that are congruent. An isosceles trapezoid is an isosceles triangle whose top has been cut off parallel to its base.

29. Sample answer: The kite has two pairs of adjacent congruent sides. It also has one pair of opposite angles that are congruent. 31. sometimes 33. never 35. yes; sample answer:

37. C 39. G 41.

in.1 34in.1 3

4

in.1 34

43. 60 45. complementary 47. supplementary 49. 90°; right


11 The fi gure is a polygon because no sides cross,

it is a closed fi gure, and it has no curved sides. Since there are 8 sides connecting, it is called an octagon. 3. 1,620° 5. 135° 7. yes; pentagon 9. yes; pentagon 11. No; the fi gure is not closed.

1313 Draw all of the diagonals from one vertex as

shown and count the number of triangles formed.

Find the sum of the angle measures in the nonagon.7 × 180 = 1,260°So, the sum of the angle measures of a nonagon is 1,260°.

15. 3,600° 17. 140° 19. triangles and pentagons

2121 A decagon has 10 sides. Since it is a regular

decagon, each side is equal. To fi nd the perimeter, we can multiply 10 times the length of each side,



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ns3.2 centimeters. So the perimeter is 32 centimeters. 23. 1,080° 25a. octagon 25b. 1,080°

25c.

27. Sample answer:

29. Sample answer: A regular polygon has all sides and angles congruent. A polygon that is not regular has different side lengths, different angle measures, or both. To fi nd the interior angle measure of a regular polygon, subtract 2 from the number of sides, multiply the result by 180, then divide that number by the number of angles. 31. D 33. 2160 35. Sample answer: ∠4 = 124°; ∠5 = 108°; ∠6 = 128° 37. Sample answer: The sum of the exterior angles of all the triangles is 360°

Pages 483-485 Lesson 8-3D

1. congruent

33 The fi gures do not have the same size or shape

so they are neither congruent nor similar. 5. −−

ST 7. similar 9. similar 11. neither 13. similar

1515 Corresponding sides represent the same side of

similar fi gures. So, −−

DE corresponds to −−

KL .17. −−

LN 19. similar 21. not similar 23. not similar25. 132 ft; 112 ft

2727 Use equivalent ratios to solve this problem.

12 _

8 = 21

_ x

× 1.75

× 1.75 So the value of x is 14.29. Sample answer: Triangle JKL is similar to

triangle TUV.

Parallelogram DEFG is congruent to parallelogram QRST.

31. Sample answer: The fi gure will have exactly the

same size and shape. Corresponding angles will have the same measure and corresponding sides will have the same length. 33. H 35. 80 37. 47°


1. y

x

′ ′

′′

33 The fi gures do not have the same shape and

size. They are not congruent. W and Z were moved 4 units down and 5 units to the right, and X and Y were moved 3 units down and 5 units to the right.

5. y

x

′′

′

′

7. y

x

′

′

′

′

99 The fi gures do not have the same shape and

size. They are not congruent. A was moved 2 units down and 3 units to the right, but B was moved 2 units down and 4 units to the right. 11. (-1, 1), (-1, -6), (6, 1), (6, -6) 13. E(5, 4), F(7, 4), G(7, 0), H(5, 0) 15. M(-6, -2), N(-4, -2), O(-4, -4), P(-6, -4) 17. Sample answer: There are two main images, stars and triangles. Both are translated over different parts of the egg. These translations allow for the tessellations of both the stars and the triangles on the egg.

1919 J(-6, 9) y

x

′ ′

′ ′





21. Sample answer: Z(-1, -4)y

x′

′′

23. 6 possibilities; (1, -4), (2, -4), (3, -4), (-1, -4), (-2, -4), (-3, -4) 25. The triangle was translated 6 units left and 3 units down.; (-6, -3) 27. The triangle was translated 5 units left and 1 unit up.; (-5, 1) 29. Sample answer: First fi nd the new coordinates of rectangle Q′R′S′T′ by adding 7 to each x-coordinate and subtracting 4 from each y-coordinate. Then graph rectangle QRST and rectangle Q′R′S′T′ on the same coordinate plane.31. I 33. A′(-5, -2), B′(-4, 2), C′(0, 2), and D′(1, -2)


11 y

x

′

′

′

′

Q′(-2, -4), R′(4, -1), S′(-1, 0), T′(-3, -2)

3.

5. y

x′

′

′

R′(-3, -1), S′(-2, -3), T′(2, -3)

7. y

x′

′

′

′

W′(-4, -2), X′(1, -4), Y′(2, -2), Z′(-3, 0)

9. y

x′

′

′

X′(1, 0), Y′(2, -4), Z′(3, -1)

1111 y

x

′

′

′

′

P′(-3, -2), Q′(-3, 4), R′(-5, 6), S′(-5, 0)

13.

15.

17.

19. The fi gures do not have the same shape and size. They are not congruent. S was refl ected over the y-axis and the distance from the y-axis did not change, but the refl ection of T was 1 unit up from the original fi gure.

21. A and B, C and D 23. fi gure C

25a. Sample answer:

25b. Sample answer:



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ns25c. Sample answer:

27. neither 29. Sample answer: E, H, I31. Sample answer: When an image is refl ected over the x-axis, the y-coordinates of the vertices are opposites. When an image is refl ected over the y-axis, the x-coordinates of the vertices are opposites. 33. F 35. y

x

′

′

′

′

37. neither

Pages 504-506 Lesson 8-4D

1.

x

y

′′

′

A′(0, 0), B′(0, -3), C′(-3, 0)

3.

x

y

′ ′

′

A′(0, 0), B′(3, 0), C′(0, -3)

55 The sun can be rotated and still look like it

does in its original position so it has rotational symmetry. The sun matches itself at 45°, 90°, 135°, 180°, 225°, 270°, and 360°.

7.

x

y

′

′

′

A′(-4, -1), B′(0, 0), C′(-4, -4)

9.

x

y

′

′′

A′(-1, 4), B′(0, 0), C′(-4, 4)

1111

x

y

′

′

′′

M′(3, -4), N′(1, -3), P′(0, 0), Q′(3, -1)

13.

x

y

′

′

′

′

M′(3, -4), N′(1, -3), P′(0, 0), Q′(3, -1)

15. yes; 45°, 90°, 135°, 180°, 225°, 270°, 315°, and 360°

1717 The fi gure cannot be rotated and look like it

does in its original position. So it does not have rotational symmetry because the top arrow is different than the other arrows.

19. Sample answer:

21. No; Sample answer: if a fi gure has rotational symmetry, then it has at least one line of symmetry.

8 lines of 6 lines of 3 lines of symmetry symmetry symmetry





23. Sample answer: Both rotations give the same result. 25. (4, -3) 27. 75 29. 19


1. false; vertical angles 3. true 5. false; supplementary angles 7. false; rotational symmetry 9. line segment;

−−− MN or

−−− NM

11. parallel 13. 180°; straight 15. 90°; right 17. acute 19. scalene 21. 60 23. 39° 25. 6127. rhombus 29. parallelogram 31. yes; 11-sided polygon 33. 1,440° 35. similar

37. y

x

′ ′

′

R′(3, 2), S′(2, -2), T′(6, 2)

39. y

x′

′ ′

R′(-2, 5), S′(-3, 1), T′(1, 5)

41. y

x′

′

′

A′(1, 3), B′(-2, -2), C′(-4, 0)

43. y

x

′

′

′

L′(-2, 1), M′(1, -2), N′(-5, -4)

45.

x

y

′

′

′

A′(0, 0), B′(3, -1), C′(1, -4)

47.

x

y

′

′

′

A′(0, 0), B′(-1, -3), C′(-4, -1)

Chapter 9 Perimeter, Area, and Volume


1. 31.4 3. 50.24 5. 2 14 _

15 7. 2 3 _

4 9. $12.56

11. 103.5 in2


1. 12 units2 3. 77 m2 5. 325 yd2 7. 12 units2

99 A = bh Area of parallelogram

A = 8 · 9 Replace b with 8 and h with 9. A = 72 cm2 Multiply.11. 180 in2 13. 8 ft 15. 166 1 _

2 ft2 17. 227 ft2

1919 No;

A = bh Area of parallelogram20,000 = 250 · 70 Replace b with 250 and h with 70.20,000 ≠ 17,500 Multiply.Since 17,500 square feet is less than 20,000 square feet, the height cannot be 70 feet. It must be greater than 70 feet.

21. Sample answer:

10 in.

5 in. 50 in2

23. Sample answer:

28 ft

7 ft196 ft2

25. 5 in. 27. 17.5 in2 29. The rectangle; the area of the rectangle is 5y units2. The area of the parallelogram cannot be greater than 5y units2 since



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nsy is less than 5 and the height of the parallelogram is not greater than y. 31. D 33. D


1. 6 units2 3. 87.75 m2 5. 45 cm2 7. 7.5 units2 9. 198.4 cm2

1111 A = 1 _ 2 bh Area of triangle

A = 1 _ 2 (41 1 _

2 ) (36) Replace b with 41 1 _ 2 and h with 36.

A = 747 Multiply.The area of the triangle is 747 square feet. 13. 19 cm 15. 4,853.52 ft2

1717 a. A = 1 _ 2 bh Area of triangle

A = 1 _ 2 (5)(n) Replace b with 5 and h with n.

A = 5n _ 2 Multiply.

The expression is 5n _ 2 .

17b. y

xO

63

91215182124

3027

1 3 5 7 92 4 6 8 10

(2, 5)

(4, 10)

(6, 15)

(8, 20)

17c. The points appear to form a line.

19. The formula is 1 _ 2 bh, not bh.

100 = b · 20 _

2

b = 10 m21. Sample answer:

12 cm

4 cm

12 cm

8 cm

Area of fi rst triangle is 24 cm2; Area of second triangle is 48 cm2; 1:2

or 1 _ 2 .

23. 40 25. B 27. 20 m2 29. 38.76 cm2


1. 90.4 ft2 3. 112 m2 5. 161.5 ft2

77 A = 1 _ 2 h(b1 + b2) Area of trapezoid

A = 1 _ 2 (12)(5 + 23)

Replace h with 12, b1 with 5, and b2 with 23.

A = 1 _ 2 (12)(28) Add 5 and 23.

A = 168 Multiply.The area is 168 square yards.

9. 121 ft2 11. 470 1 _ 4 ft2 13. 81 tiles

15. 1,904 in2

17. 50 in2 8 in.

12 in.

5 in.

1919 a. You need to calculate the area of the

trapezoid and subtract the area of the building to fi nd the area of the lawn; 7,000 ft2.19b. 7,000 ÷ 2,000 = 3.5; So, they would need at least 4 bags of seed.

21. 100 cm2 23. Since 9 = 1 _ 2 (1)(b1 + b2), the

possible lengths have a sum of 18. 25. 11,000 cm2

27. G 29. 988 ft2 31. 21 m 33. 8 7 _ 12

ft 35. 13 yd

Pages 543–546 Chapter 9-2B

1. 1.5 m 3. 10 in. 5. 22 _

7 × 21 = 66 ft

77 C = πd Circumference of a circleC ≈ 3.14 · 13 Replace π with 3.14 and d with 13.C ≈ 40.8 Multiply.

The circumference of the circle is 40.8 centimeters rounded to the nearest tenth.

9. 22 _

7 × 14

_ 15

= 2 14 _

15 in. 11. 2.5 mm 13. 34 cm

15. 3.14 × 8 = 25.1 ft 17. 22 _

7 × 7 = 22 mi

19. 22 _

7 × 35 = 110 ft 21. 22

_ 7 × 42 = 132 mm

23. 37.7 cm

2525 First calculate the approximate circumference

of the tree, then divide that number by 6 feet to fi nd the number of people needed to reach around the base of the tree.

C = πd Circumference of a circleC ≈ 3.14 · 36 Replace π with 3.14 and d with 36.C ≈ 113.04 Multiply.Now divide the circumference, 113.04, by 6 feet, the distance each person can reach: 113.04 ÷ 6 = 18.84. Therefore, it would take 19 people to reach around the base of the tree.27a. 30 mm 27b. 31.4 mm 27c. 31.4159 mm 27d. Sample answer: The more decimal places of the estimate of π, the more precise the circumference.29. Greater than; Sample answer: Since the radius is 4 feet, the diameter is 8 feet. Since π is a little more than 3, the circumference will be a little more than 3 times 8, or 24 feet.

3131 no; Sample answer: The circumference of each

candle is about 12.6 inches. So, 12.6 × 8 or 100.8 inches of ribbon are needed to make all of the candles. Since 2 yards is equal to 72 inches, and 72 < 100.8, she does not have enough ribbon for all of the candles.33. 18 in. 35. 257 cm37. Sample answer:

7 in.





estimated circumference: 21 in.; using calculator: 22.0; The estimate is close to the more accurate value found on the calculator. 39. Sample answer: The circumference is about 3 times the measure of the diameter. 41. I 43. D 45. 12.74 in2 47. 375 in2

Pages 550–552 Chapter 9-2D

1. 3.14 × 5 × 5 = 78.5 cm2 3. 3.14 × 8 × 8 = 201.0 m2 5. 379.94 ft2 7. 3.14 × 6 × 6 = 113.0 cm2

99 Since the diameter is 11 feet, we know the

radius is 5.5 feet.A = πr2 Area of a circleA = 3.14 · 5.52 Replace π with 3.14 and r with 5.5.A = 94.985 Multiply.The area is 95.0 square feet rounded to the nearest tenth.11. 3.14 × 6.3 × 6.3 = 124.6 cm2 13. 1.2 in2 15. 207.6 ft2

1717 circle; You need to calculate the area of the

triangle and the area of the circle and compare them.


A = 1 _ 2 (100)(100) Replace b with 100 and h with 100.

A = 5,000 Multiply.The area of the triangle is 5,000 square feet.A = πr2 Area of a circleA = 3.14 · 502 Replace π with 3.14 and r with 50.A = 7,850 Multiply.The area of the circle is 7,850 square feet. Since 5,000 is less than 7,850, the area of the circle is greater.19a. 1,962.5 ft2 19b. 5,024 ft2 21. 62.8 m2 23. 103.4 cm2 25. D 27. A 29. 210 in2 31. 39.5 cm2


11 P = 2b + 2h Perimeter of a rectangle P = 2(18) + 2(5) Replace b with 18 and h with 5. P = 36 + 10 Multiply. P = 46 Add.The perimeter is 46 yards.3. 88 m

55 Add all of the distances around the composite

fi gure. P = 40 + 21 + 21 + 40 + 21 + 21 Sum of all sidesP = 164 yd Add. The perimeter is 164 yards.

7. 62.27 cm 9. 64 ft 11. 106 yd

1313 Adding ten meters to each end of the court

makes the new length 46 meters. Adding ten meters to each side of the court makes the new width 34 meters. The perimeter is then 46 + 34 + 46 + 34, or 160 meters.15. Sample answer: 111.4 cm

20 cm 20 cm

30 cm

17. Sample answer: Perimeter is the distance around the outside of a fi gure while area is the measure of the amount of space enclosed by the perimeter. 19. D

21. 22 _

7 × 7 _

11 × 7 _

11 = 1 3 _

11 in2 23. 22

_ 7 × 7 = 22 ft

25. 56 ft2


1. 112 m2 3. 145 m2 5. 189 ft2

77 The fi gure can be separated into a rectangle

and a trapezoid. Find the area of each and then add them together.

A = bh Area of parallelogramA = 8 · 4 Replace b with 8 and h with 4.A = 32 Multiply.The area of the rectangle is 32 square inches.

A = 1 _ 2 h(b1 + b2) Area of trapezoid

A = 1 _ 2 (4)(5.3 + 8)

Replace h with 4, b1 with 5.3, and b2 with 8.

A = 1 _ 2 (4)(13.3) Add 5.5 and 8.

A = 26.6 Multiply.The area of the trapezoid is 26.6 square inches. The area of the whole figure is 32 + 26.6, or 58.6 square inches. 9. 257 mm2 11. 66.2 yd2 13. about 592.8 ft2

1515 a. Find the area of the triangle.


A = 1 _ 2 (22.8)(12) Replace b with 22.8 and h with 12.

A = 136.8 Multiply.The area of the triangle is 136.8 square feet.Find the area of the rectangle.

A = bh Area of rectangleA = 22.8 · 14.5 Replace b with 22.8 and h with 14.5.A = 330.6 Multiply.Add both areas. 136.8 + 330.6 = 467.4 ft2

15b. 467.4 ÷ 350 ≈ 1.34; Since only whole gallons of paint can be purchased, you will need 2 gallons of paint. At $20 each, the cost will be 2 × $20, or $40. 17. Sample answer: Area of rectangle: 5 × 5 = 25. So, an approximate area is 25 × 2,400 or 60,000 mi2. 19. A 21a. 3,150 ft2 21b. $9,418.50 23. 30 ft 25. 69.4 cm2 27. 176.6 in2


1. Sample answer: By making a model, D.J. could fi rst see if he had enough chairs before setting them all up. 3. 3 or 4 blocks 5. 16 students 7. 3 hours

99 The price for adults is $40 per ticket and the price

for children is $30 per ticket. 2($40) + 3($30) = $170 11. 5 boys


1. 15 ft3 3. 4,986.875 in3 5. 20 in.



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V = bwh Volume of a rectangular prismV = (6)(6) (4 3 _

4 ) Replace b with 6, w with 6, and h with 4 3 _ 4 .

V = 171 Multiply.The volume is 171 cubic inches.9. 84 cm3 11. 6,664.77 m3 13. 2,702.5 in3 15. 17 m 17. 6 in. 19. 360 mi3 21. >

2323 a.

V = bwh Volume of a rectangular prism

V = (5)(4.5)(2.25) Replace b with 5, w with 4.5, and h with 2.25.

V = 50.625 Multiply.Currently, there are 50.625 cubic inches of sand in the container.23b. The volume of the container is 5 × 4.5 × 3, or 67.5 cubic inches. Therefore, 67.5 - 50.625, or 16.875, cubic inches of sand could be added before the container overfl ows.

23c. 50.625 of the total 67.5 cubic inches are fi lled

with sand. So, 50.625 _

67.5 = 0.75. After changing 0.75

to a percent, you know that 75% of the container is now fi lled with sand. 25a. 577.5 ft3 25b. 3-bedroom moving truck 25c. 641.25 ft3 27. She added the base, width, and height instead of multiplying them. V = bwh; V = 13.7 × 6.8 × 21.4 = 1,993.624 cm3 29. Each of the three dimensions being multiplied is expressed in a unit of measure. Just like the product 5 × 5 × 5 can be expressed using exponents as 53, feet × feet ×

feet can be expressed with exponents as feet3. 31. F 33. 1,500 mm2


1. 292 m2 3. 298 cm2 5. 256 in2 7. 384.62 cm2

99 S.A. = 2bh + 2bw + 2hw = 2(35.7)(15.1) + 2(35.7)(25.5) + 2(15.1)(25.5) = 1,078.14 + 1,820.7 + 770.1 = 3,668.94

After replacing b with 35.7, h with 15.1, and w with 25.5, the surface area is 3,668.94 square meters. 11. 390 in2 13. Yes; the approximate surface area of the rectangular prism is (2 × 13 × 6) + (2 × 13 × 8) + (2 × 6 × 8) or 460 ft2. 15. area; Sample answer: The length and width of the house will determine the land area needed to build the house; m2 or ft2

17. length; Sample answer: The height of a tree is also its length

1919 Package A

In the formula, use 14 for b, 12 for h, and 3 for w.

S.A. = 2bh + 2bw + 2hw = 2(14)(12) + 2(14)(3) + 2(12)(3)

= 336 + 84 + 72

= 492

Package BIn the formula, use 11 for b, 6 for h, and 8 for w.

S.A. = 2bh + 2bw + 2hw= 2(11)(6) + 2(11)(8) + 2(6)(8)

= 132 + 176 + 96

= 404

The surface area of Package A is 492 square inches, which is larger than the surface area of Package B, 404 square inches. Package A has a greater surface area.

Package A

V = bwh Volume of a rectangular prism= (14)(3)(12) Replace b with 14, w with 3, and h with 12.= (42)(12) Multiply.= 504 Multiply.

The volume of Package A is 504 cubic inches.

Package B

V = bwh Volume of a rectangular prism= (11)(8)(6) Replace b with 11, w with 8, and h with 6.= (88)(6) Multiply.= 528 Multiply.

The volume of Package B is 528 cubic inches. Package A has the greater surface area, but Package B has the greater volume. 21a. 48 in2; 144 in2 21b. 336 in2 23. B 25. 4:9, 4 to 9, or 4 _

9 27. 231 in3 29. 301.4 ft2


1. volume 3. perimeter 5. volume 7. 24 units2 9. 18.125 m2 11. 6 ft 13. 4.5 m2 15. 99 in2 17. 195 m2 19. 66.5 ft2 21. r = 29 cm 23. d = 18 ft 25. 53.4 cm 27. 125.6 ft 29. 3.14 × 12 × 12 ≈ 452.2 in2

31. 1 _ 2 × 3.14 × 30 × 30 ≈ 1,413 yd2 33. 40 cm

35. 437.5 mm2 37. 42 ft2 39. 33 cans 41. 96 yd3 43. 38 in. 45. 1,854,720 yd3 47. 208 cm2 49. 376 ft2

Chapter 10 Volume and Surface Area


1. 48 3. 80 5. 5 h 7. 11.3 in2


1. 45 ft3 3. 90 in3 5. 336 m3 7. 140.4 m3

99 V = Bh Volume of a prism

V = 1 _ 2 (5.7)(7.6)h Replace B with 1 _ 2 (5.7)(7.6).

V = 21.66h Multiply.V = 21.66(4.8) Replace h with 4.8.V = 103.968 Multiply.

The volume is about 104 cubic centimeters.11. 187 yd3

1313 To fi nd the height, substitute the given values

into the formula and then solve for h. V = Bh Volume of a prism





V = ( 1 _ 2 · b · h) · h Triangular base

108 = ( 1 _ 2 · 3 · 8) · h Replace V with 108, b with 3, and

h with 8. 108 = 12h Multiply.108

_ 12

= 12 · h _ 12


9 = h Simplify.The height of the prism is 9 inches.15. Sample answer: rectangular prism: length, 7; width, 5; height, 6; triangular prism: area of base, 35 sq. meters; height, 6 meters 17. Sample answer: Both three-dimensional shapes use the same formula to fi nd the volume. The difference is when you fi nd the B in the formula for triangular prisms,

you will use 1 _ 2 bh instead of base times height.

19. H 21. Cabinet A: 3,888 in3; Cabinet B: 4,760 in3; Tia should purchase cabinet B.


1. 196 ft3 3. 70 ft3

55 V = 1 _ 3 Bh Volume of a pyramid

V = 1 _ 3 (8 · 5)h Replace B with 8 · 5 since the

base is a rectangle. V = 1 _

3 (8 · 5)(10) Replace h with 10.

V = 133.3 Multiply.The volume is 133.3 cubic yards.7. 560 ft3 9. 284.7 cm3 11. 85,730,400 ft3 13. 1,805 m3

1515 To fi nd the height, substitute the given values

into the formula and then solve for h.

V = 1 _ 3 Bh Volume of a pyramid

504 = 1 _ 3 (14 · 12)h Replace V with 504 and B with 14 · 12.

504 = 56h Multiply.504

_ 56

= 56h _ 56


9 = h Simplify.The height is 9 inches.17. Sample answer: The base of the pyramid is a

triangle. He should have found V = 1 _ 3 ( 1 _

2 × 6 ×

7)10; 70 ft3

19. Sample answer: The formula for the volume of

a pyramid multiplies by 1 _ 3 . A prism is 3 times larger

than a pyramid. 21. F 23. F


1. 6,612.8 in3

33 V = πr2h Volume of a cylinder

V ≈ 3.14(2.5)2(6.2) Replace π with 3.14, r with 2.5, and h with 6.2.

V ≈ 121.675 Multiply.The volume is about 121.7 cubic yards rounded to the nearest tenth.5. 117.8 ft3 7. 1,921.7 m3

99 V = πr2h Volume of a cylinder

V ≈ 3.14 (6)2(5) Replace r with 6 and h with 5. V ≈ 565.2 Multiply.

The volume is about 565.2 cubic yards.

11. 95.5 in3 13. 150.7 cm3 15. 2,355,000 mm3 17. 2,256.9 cm3

1919 The formula calls for the radius, and since the

diameter is 6 cm, the radius is 3 cm.

V = πr2h Volume of a cylinder

226.2 ≈ 3.14(3)2h Replace V with 226.2, π with 3.14, and r with 3.

226.2 ≈ 28.26h Multiply.226.2

_ 28.26

≈ 28.26h _ 28.26

Divide both sides by 28.26.

8 ≈ h Simplify.21. Sample answer: radius, 4 ft; height, 4 ft

4 ft

4 ft

23. Sample answer: The formula V = πr2h uses πr2 to fi nd the area of the fi rst “layer” of the volume. By multiplying the area of the circle by the height of the cylinder, the volume of all of the “layers” is found. 25. G 27. 80 cm3 29. 208 yd3


1. 307.7 yd3

33 V = 1 _ 3 πr2h Volume of a cone

≈ 1 _ 3 · 3.14 · 72

· 13 Replace π with 3.14, r with 7, and h with 13.

≈ 666.726 Multiply.The volume of the cone is about 666.7 cubic inches rounded to the nearest tenth.5. 47.1 m3 7. 13.6 in3 9. 267.5 ft3 11. 77.3 yd3

1313 Since the diameter is 250 meters, use 125 meters

for the radius.V = 1 _

3 πr2h Volume of a cone

V ≈ 1 _ 3 · 3.14 · 1252 · 1,500 Replace r with 125 and

h with 1,500.V ≈ 24,531,250 Multiply.

The volume of the volcano is about 24,531,250 cubic meters. 15. 11.0 in.

17a.

Radius Height Volume (ft3)

4 6 100.5

5 6 157.0

6 6 226.1

Radius Height Volume

(ft3)

4 6 100.5

4 7 117.2

4 8 134.0



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Volu

me

(ft3 )

8758

116

29

1 2 3 4 5 6 7 8 9

145174203

Radius (ft)

x

y

Cone

17c.

Volu

me

(ft3 )

8758

116

29

1 2 3 4 5 6 7 8 9

145174203

Height (ft)

x

y

Cone

17d. Sample answer: Changing the radius impacts the volume more than changing the height. The volume increases more when you change the radius, because when you calculate the volume, you square the radius and not the height.19. Sample answer:

2 m

8 m

4 m

8 m

21. A 23. 3,014.4 mm3 25. 7,385.3 m3

Pages 618–619 Lesson 10-3A PSI

1. Sample answer: A three-dimensional object allows you to see all of the combined areas that make up the total surface area of the object.

33 You will make a diagram showing the wall

with the table against it. You will show the position of the balloons using a *. Counting the stars will tell you how many balloons are needed. Remember, there will only be one balloon on each corner.

wall

3 ft3 ft

8 ft

15 balloons are needed.5. mean 7. 11 9. Sample answer: 2 in. by 2 in. by 5 in.; 1 in. by 4 in. by 5 in.11a. 120 ft2 11b. 2 qt


1. 3,014.4 yd2 3. 301.4 in2

55 S.A. = 2πrh + 2πr2 Surface area of a cylinder

= 2(3.14)(6.4)(3) + Replace π with 3.14, 2(3.14)(6.4)2 r with 6.4, and h with 3.

= 120.576 + 257.2288 Multiply.= 377.8048 Add.

The surface area is 377.8 square yards.

77 The surface area formula uses radius, and

since the diameter is given as 1 inch, the radius is 1 _ 2

or 0.5 inch. Also, since the question only asks for the outside of the pipe, you do not need to calculate the ends. You only need the lateral surface area of the cylinder, so the formula is S.A. = 2πrh. S.A. = 2πrh Surface area of the outside of a cylinder

≈ 2(3.14)(0.5)(180) Replace π with 3.14, r with 0.5, and h with 180.

≈ 565.2 Multiply.The surface area of the outside of the pipe is 565.2 square inches; 565.2 in2.9a. rectangular prism: 328 in2; cylinder: 301.44 in2

9b. rectangular prism 11. Surface area describes the area of all the surfaces of a solid. Volume describes the capacity, or amount of space contained inside a solid. 13. D 15. 2 blocks by 2 blocks by 2 blocks; 4 blocks by 2 blocks by 1 block 17. 527.5 m3 19. 62.8 ft3


1. 450 in3 3. 326 m2

55 The top of the fi gure is a rectangular pyramid

and the bottom is a rectangular prism. To fi nd the volume of the whole fi gure, you will fi nd the volume of each piece and add them together.

V = 1 _ 3 Bh Volume of a pyramid

= 1 _ 3 (8 · 8)h

Replace B with 8 · 8 since the base is a rectangle.

= 1 _ 3 (8 · 8)(6) Replace h with 6.

= 128 Multiply.The volume of the top section is 128 cubic millimeters.V = Bh Volume of a rectangular prism

= 8 · 8 · 9 Replace B with 8 · 8 and h with 9.= 576 Multiply.

The volume of the bottom section is 576 cubic millimeters, so the volume of the whole figure is 704 cubic millimeters.7. 100 in3 9. 292 yd2

1111 You need to fi nd the surface area of the

television and the surface area of the sides of the





cylinder. The surface area of the bottom of the cylinder will be included in the surface area of the bottom of the television since both ends of the cylinder are the same. That eliminates the need for subtracting the overlapping part of the cylinder.

TelevisionIn the formula, use 35 for b, 20 for h, and 5 for w.S.A. = 2bh + 2bw + 2hw

= 2(35)(20) + 2(35)(5) + 2(20)(5)= (70)(20) + (70)(5) + (40)(5) Multiply.= 1400 + 350 + 200 Multiply.= 1,950 Add.

The surface area of the television is 1,950 cubic inches.

CylinderIn the formula, use 3.14 for π, 7.5 for r, and 3 for h.S.A. = 2πrh

≈ 2(3.14)(7.5)(3) ≈ 141.3 Multiply.

The surface area of the outside of the base is 141.3 square inches.Therefore, the total surface area is 2,091.3 square inches.15. C 17. 175.8 yd2 19. 376.8 m2 21. 527.5 m3


1. triangular prism 3. square 5. cone 7. multiplying 9. 168 m3 11. 80 ft3 13. 60 yd3 15. 310.9 cm3 17. 18.84 in3 19. 134.0 ft3 21. 4 windows 23. 339.1 yd2 25. 2,088 mm3

27. 4 quarts

Chapter 11 Analyze Data and Graphs

Page 642 Are You Ready?

1. June 3. May and June 5. 2 girls


1. 2 siblings 3. 7.24 km 5. $7

77 87 + 93 + 86 + 90 + 84 = 440, 440 ÷ 5 = 88;

The mean is 88%.

99 a. 15 + 20 + 10 + 12 + 20 + 16 + 80 + 18 + 25

= 216, 216 ÷ 9 = 24; The mean amount she earned is $24. 9b. $80 9c. 9c. Sample answer: This value that is considerably higher than all the other values causes the mean to be greater than all the values, except $25 and $80. Without the value, the mean would better represent the average of the data. 11a. 40; 40 11b. No; both means are equal. 13. Sample answer: pages read: 27, 38, 26, 39, 40 15. If the precipitation for the month of July is 3 inches, then the mean would decrease since this amount is smaller than the mean. If the precipitation for the month of July is 4 inches, then the mean would probably not be affected since the

original mean is about 4 inches. If the precipitation for the month of July is 5 inches, then the mean would increase since this amount is greater than the mean. 17. C 19. 80

Page 652–654 Lesson 11-1D

1. 17; 17; 103. mean: $15.98

median: $15.89mode: $19.99range: $8.04

5. 23; none; 29

77 Mean: 97 + 85 + 92 + 86

__ 4

= 360 _

4 or 90

Mode: There is no mode.

Median: 85, 86, 92, 97

{

86 + 92

_ 2 = 178

_ 2

= 89

9. mean: 45.6; median: 44; mode: 44; range: 12 11. mean: 10; median: 10; mode: 8; range: 9

1313 Mode; The mode of the temperatures in

Louisville is 70° and the mode for Lexington′s temperatures is 76°. Since 76° - 70° = 6°, the mode was used to make this claim.15a. Cranes: median: 40, mode: 31, range: 19; Panthers: median: 40, mode: 40, range: 615b. Sample answer: The Panthers had the better record. Even though the mean and median are the same, the Panthers’ mode is higher. 17a. True; the mode of the data set is 1. 17b. False; the median of the data is 2. 19a. 1 19b. Sample answer: The data have a small range and are all relatively close.21. $4.61 23. 46 min

Pages 659–660 Lesson 11-1F

11 The mean or mode best represent the data. The

mode is 45 and 60. The mean is 56.4. There are no extreme values. 3. Since there are repeated numbers, the mode, 47, best represents the data.

55 outlier: 2.43; without the outlier: mean: 7.2,

median: 7.3, mode: none; with the outlier: mean: 6.3, median: 6.19, mode: none; The mean best describes the data without the outlier. The median best describes the data with the outlier. 7a. 1,1487b. With the outlier, the mean is 303.75, the median is 28.5, there is no mode, and the range is 1,138. Without the outlier, the mean is 22.3, the median is 14, there is no mode, and the range is 33. 7c. With the outlier, the best measure is the median; without the outlier, the best measure is the median.9. Sample answer: 125, 32, and 19 11. C 13. I15. median: $17; mode: $18; range: $12



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1. The mode is Republican. It means that more U.S. presidents have been Republican than any other political party.

3a. Number of Letters Tally Frequency

3–4 35–6 97–8 39–10 2

3b. 4 _ 17

55 a. Sample answer:

Temperatures Tally Frequency

40–41 | 1

42–43 |||| ||| 8

44–45 |||| 4

46–47 |||| || 7

5b. Most of the temperatures were either between 42 and 43 or 46 and 47.

77 a. T-Shirts SoldT-Shirt Size Tally Frequency

S 9M 11L 6

XL 4

7b. The mode is medium. More T-shirts were soldin medium than any other size. 7c. 9 _

30 or 3 _

10

9a. Speed (miles per hour) Tally Frequency

20–29 230–39 740–49 450–59 3

9b. Most of the speeds are between 30 and 39 miles per hour. The mode is 30 miles per hour, although it cannot be determined from the frequency table. The range is 30 miles per hour, which also cannot be determined from the frequency table.

9c. The smaller the intervals, the less the frequencies. If the intervals were broader, the frequencies would decrease. The mode and range do not change because the individual data values do not change. 11. The mode of a set of data is determined by looking at individual data values. The mode cannot be determined from a frequency table. 13. D 15. There are no outliers, so the mean, 5, or median, 5.5, would be the measure of central tendency that best represents the data. 17. median: $5; mode: $5; range: $3


1. 36 3. $60.00 - $69.99

55 The bar that shows the greatest number of

cyclists is the interval from 60–64 with a frequency of 9.7. 16

9.

10–1

45–

90–

4

15–1

9

Number of States

Freq

uenc

y

4

6

2

8

0

10

Number of States Visited by Students in Marty’s Class

20–2

4

25–2

9

1111 6th grade; The 6th grade had around 18

students with sales of $400 - 599. The 7th grade had around 16 students with sales of $400 - 599. So the 6th grade had more students with sales in this interval. 13. 24 students15.

50–9

9

0–49

Num

ber o

f Bar

s

Calories

150–

199

100–

149

200–

249

250–

299

300–

349

350–

399

46

20

810

Calories of Various Types of Frozen Bars

17. Sample answer: Ages of students at summer camp: 3, 4, 5, 7, 7, 8, 8, 10, 10, 11, 13, 15, 15, 16 19. 40–45; all the other intervals represent 5 whole numbers 21. A 23. I 25. The median and mode best represent the data. The median and the mode are both 45. There are no extreme values. 27. median: 47 airplanes; mode: 55 airplanes


1. Do You Like Surprise Parties?

No Answer3%

Yes72%

No25%

33 42%; There is 11% of students who said they





have between 500–999 songs and 31% of students who said they have over 1,000 songs. So there are 11% + 31% or 42% of students who have 500 or more songs.5. Class President Ballots

Lacey25%

Troy25%

Melissa31%

Omar19%

77 oxygen; Oxygen makes up 64% of the elements

in the human body which is the greatest percent of all the elements. 9. Oxygen and carbon make up about 82% of the entire body.11. 18%

1313 135 students; Since 54% of the students that

were surveyed said they preferred apples as their favorite fruit, fi nd 54% of 250 students. 250 × 0.54 = 135 studentsSo, there would be 135 students who would prefer apples if there were 250 students surveyed.15. Sample answer: Mei did not represent 5% as a decimal correctly. It should be 0.05 × 40 = 2.; 2 people 17. A19.

80–89

70–79

60–69

50–59

4

6

2

0

8

Num

ber o

f Stu

dent

s

10

12

90–99

Percentage on Test

Test Scores


1. line plot; The line plot shows the greatest value as a numerical value rather than a bar. 3. line graph; A line graph shows the trend over time. g p

55 bar graph; The bar graph shows the maximum

speeds, not just the interval in which the data occurs in. 7. line graph; A line graph shows the trend over time. 9. bar graph; A bar graph allows for the prices to be compared.

11. Sample answer: bar graph;

18221826

1818

18101814

1830

Year

of

Inde

pend

ence

CountryArge

ntinaBolivi

aChile

Colombia

Equad

or

Mexico Peru

Venezu

ela

Independence of Latin AmericanCountries

1313 Sample answer:

7 8 9 10 11 15141312

Number of Neighbors

× ×

×

×

The line plot allows you to easily see how many countries have a given number of neighbors. The bar graph however allows you to see the number of neighbors each given country has.

15. False; counterexample: to compare the price of fi ve different cell phones, a line graph would not be appropriate because these data do not show change over a period of time 17. Sample answer: Circle graphs are best used for data showing a relationship of the parts to the whole. 19. F 21. 18%23.

411–460

361–410

311–360

240–310

2

3

1

0

4

Num

ber o

f Brid

ges

5

6

Length (ft)

Bridges


11 Graph B; From the length of the bars, it

appears that Cy Young had about 3 times as many wins as Jim Galvin. However, Jim Galvin had 365 wins and Cy Young had 511 wins. So, the conclusion is not valid. 3. Sample answer: The mean is 8,638 and the median is 8,941. Since the median is greater than the mean, use the median to emphasize the average length. 5. Sample answer: There are not equal intervals on the x-axis. 7. The median or the mode



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1111 A line graph would allow you to see the

dramatic increase from year to year.

475

01 2 3 4 5

500

525

550

Rent

($) 575

600

625

Year

Monthly Cost to Rent an Apartment

13. Sample answer: Outliers may distort measures of central tendency; data shown in graphs may be exaggerated or minimized by manipulating scales and intervals. 15a. 225 min 15b. Sample answer: The ratio of the area of the cell phones are not proportional to the number of minutes. 17. line graph; Sample answer: A line graph shows change over a period of time.


1. Add the number of students in math and the number of students in Spanish, then subtract the number of students who are in both. 3. 26 students 5. 6 owners 7. $235

99 6; 10; In order to fi nd the amount of students

that like just softball and just basketball, subtract the amount of students that liked both from the total amount of students that liked each sports. softball: 14 - 8 = 6; basketball: 18 - 8 = 10. So 6 students liked softball only and 10 students liked basketball only.11. 27 runs


1. false; mean 3. false; median 5. true 7. false; scale 9. 27 days 11. $55 13. 24; 23; 9 15. 42; 36; 46 17. 84; 82; 7 19. Sample answer: Since the set of data has no extreme values or numbers that are identical, the mean, 7.1, would best represent the data.21. mean: 9.6 in.; median: 10; mode: 9; range: 9; outlier: 3

Heights (in.) Tally Frequency

3 | 1

9 ||||⁄ | 6

10 |||| 4

11 | 1

12 ||| 3

23. 14 students

25. Favorite Movie Type

Action25%

Romance10%

Comedy40%Drama

25%

27. The section representing comedy is 4 times the size of the section representing westerns. 29. line graph 31. line plot 33. circle graph 35. Sample answer: The average used by Timea was the mean. This measure is greater than the price of most of the shoes because of the outlier, $105. So, it is misleading to use this measure for the price of shoes. 37. 5%

Chapter 12 ProbabilityPage 710 Are You Ready?

1. certain 3. impossible 5. 1 _ 2 7. 1 _

8 9. 1 11. 7 _

10


1. 1 _ 9 3. 2 _

9 5. 5 _

9 7. The complement of selecting a

“Go Back 1 Space” card is selecting any card other

than that card. Its probability is 3 _ 4 , 0.75, or 75%.

9. 0 or 0 _ 1 11. 3 _

4 13. 5 _

8

1515 There are 2 chances out of 10 to draw a 7 or 9.

So, the probability of selecting either of those

numbers is 2 _ 10

or 1 _ 5 .

17. 7 _ 10

19. 1 _ 2 21. 3 _

5

23. Picking a black jelly bean is impossible since the probability of picking a black jelly bean is 0%.25. Picking a purple, red, or yellow jelly bean is very likely to happen since the probability of picking a purple, red, or yellow jelly bean is 90%.p

2727 The complement of selecting a girl is selecting

a boy. The probability of the complement is 37 _

100 ,

0.37, or 37%. 29a. 9 outcomes 29b. 1 _

3 31. Sample answer: The





probability of an event occurring or its complement occurring is certain to happen. Therefore, the sum of these probabilities is 1. For example, if there is a 30% chance of rain, then the complement is a 70% chance of no rain. It is certain that one of these two events will occur. 33. G 35. D 37. 2 : 4 or 1 : 2 39. 1 : 5


1. Let R = Ramiro, G = Garth, and L = Lakita. The different ways are RGL, RLG, GRL, GLR, LRG, and LGR. So, there are 6 ways the three students can line up.

33 1 _ 16

; Sample answer: There is a 1 _ 4 chance she will

choose the waves screen saver and a 1 _ 4 chance she

will choose the family background photo. So, the

probability of selecting both of those is 1 _ 4 × 1 _

4 = 1 _

16 .

5. Let 1 = CD 1, 2 = CD 2, 3 = CD 3, and 4 = CD 4. The different ways are 1234; 1243; 1324; 1342; 1423; 1432; 2134; 2143; 2314; 2341; 2413; 2431; 3124; 3142; 3214; 3241; 3412; 3421; 4123; 4132; 4213; 4231; 4312; and 4321. So, Kame can listen to four CDs 24 ways.7. 8 possible combinations Book Gift Bag

The Poky Little Puppy yellow

The Poky Little Puppy green

The Tale of Peter Rabbit yellow

The Tale of Peter Rabbit green

Tootle yellow

Tootle green

Green Eggs and Ham yellow

Green Eggs and Ham green

9.

11.

13. 1 _ 8 ;



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; Sample answer: There are 12 possible

outcomes and there is only 1 correct answer for each question. There is only one chance of getting each question correct.17. 30 ways; Sample answer: By just choosing a three-student group, the order in which the names are drawn does not matter. When the order matters, the sample space is increased. A three-person group of Kayla, Jeremy, and Chi-Wei is the same as a three-person group of Jeremy, Chi-Wei, and Kayla. However, these two groupings would refl ect different orderings of captain, co-captain, and secretary. 19. Sample answer: The results when a number cube is rolled and a coin is tossed. 21. I 23. Sample answer: The tree diagram is showing all the possible outcomes of seeing 2 different movies at 3 different times.


1. 42 3. 12 5. 1 _ 64

7. 48 9. 20

1111 There are 3 possible outcomes to be captain

and 3 possible outcomes to be co-captain. So, 3 × 3 = 9 possible outcomes.

13. 50 15. 1 _ 9

1717 a.

17b. Sample answer: You can use the

Fundamental Counting Principle to fi nd the total number of outcomes by multiplying the number of bread choices (two) by the number of meat choices (fi ve). So, there are a total of 10 possible sandwiches.

17c. 1 _ 10

, 0.1, 10%; Sample answer: There are 2 × 5

or 10 different possible outcomes of sandwich choices. There is 1 possible outcome for a sandwich that includes white bread and ham. The probability

of randomly selecting this sandwich is 1 _ 10

.

19. Sample answer: William has 4 shirts that he can wear with a choice of 3 different pants. He has 12 different possible outfi ts. 21. Sample answer: You can use the Fundamental Counting Principle to calculate the total possibilities of a situation quicker

than having to draw a tree diagram to determine the probability. 23. G 25. 1227. Coin Spinner

Heads A

Heads B

Heads C

Heads D

Tails A

Tails B

Tails C

Tails D

29. 3 _ 7 31. 9 _

14 33. 4 _

7


1. 1 _ 10

33 1 _ 20

; There is only 1 orange color out of 8

possible colors and 2 As out of 5 possible letters. So, the probability of spinning an orange and

getting an A is 1 _ 8 × 2 _

5 = 2 _

40 or 1 _

20 .

5. 9 _ 10

, 0.09, 9% 7. 1 _ 4 9. 1 _

8

1111 3 _

100 ; There are 3 green tiles out of 10 so the

probability of selecting a green tile is 3 _ 10

. There is

1 blue tile out of 10 so the probability of selecting a

blue tile is 1 _ 10

. So, the probability of green and blue

is 1 _ 10

× 3 _ 10

= 3 _

100 .

13. 1 _ 25

1515 a. 1 _ 4 ; The probability of the DVD being comedy

is 12 _

24 or 1 _

2 and the probability of the DVD not being

comedy is 12 _

24 or 1 _

2 . So, 1 _

2 × 1 _

2 = 1 _

4 .

15b. 1 _ 18

; The probability of the DVD being drama

is 8 _ 24

or 1 _ 3 and the probability of the DVD being

action is 4 _ 24

or 1 _ 6 . So, 1 _

3 × 1 _

6 = 1 _

18 .

15c. 5 _ 36

; The probability of the DVD being comedy

or drama is 20 _

24 or 5 _

6 and the probability of the DVD

being action is 4 _ 24

or 1 _ 6 . So, 5 _

6 × 1 _

6 = 5 _

36 .

17. 2 _ 5 19. 1 _

20 21. 72 23. 1 _

12


1. 1 _ 6 3. 1 _

12 5. 1 _

45

77 independent; Sample answer: Spinning the

spinner will not affect the results of rolling a number cube.





9. 7 _ 34

11. 2 _ 17

13. 5 _ 18

15. independent; Sample answer: The fi rst roll will not affect the results of the second roll.

1717 dependent; Sample answer: The fi rst student

already picked a partner, which will affect the pick for the second student because there will be less students to choose from.

1919 3 _ 10

, 0.3, 30%; The probability of selecting a

girl is 3 _ 5 and then selecting a boy would be 1 _

2 . So,

the probability of selecting a girl then a boy is

3 _ 5 × 1 _

2 = 3 _

10 .

21a. 1 _ 6 21b. 1 _

12 23. 3 _

8 25. B 27. 5/68 29a. 1 _

5 ; 1 _

3

29b. 1 _ 15

29c.

31. 30 33. 120


1. 3 _ 25

, 0.12, or 12% 3. 3 _ 10

, 0.3, or 30% 5. 3 _ 5 , 0.6, or

60% 7. 180

99 40; There are 2 out of 25 students who

participate in gymnastics as shown in the table. If 500 students participated in sports, there would be 2 out of every 25 students who would participate

in gymnastics. So, 2 _ 25

× 500 = 40 students who

would participate in gymnastics.11a. about 60,000 11b. about 72,500 11c. about 7,200

1313 about 6 free throws; Jaden makes free throws

15% of the time, or 3 out of every 20 free throws. If he shot 40 free throws, you would expect him to

make about 3 _ 20

× 40 = 6 free throws.

15. about 100 times 17. Yes; Mitch can predict that

one out of four sixth-graders will attend the dance.

Since 1 _ 4 = 25

_ 100

, about 25 of the sixth-graders will

attend the dance. 19. 35 21. 15 _

77

23. 6 ways

Video 1, Video 2, Video 3Video 1, Video 3, Video 2Video 2, Video 1, Video 3Video 2, Video 3, Video 1Video 3, Video 1, Video 2Video 3, Video 2, Video 1

25. 7 _ 15

27. 1 _ 5


1. Sample answer: You are able to actually see the results of an activity rather than predict the results or use the theoretical results. The results may be different than the theoretical probability.3. 20 5. 6 ways 7. 2, 9, 9; 3, 8, 9; 4, 7, 9; 4, 8, 8; 5, 6, 9; 5, 7, 8; 6, 6, 8; 6, 7, 7

99 Sample answer: 2,000 pieces/day × 6 days/

week × 50 wk/yr × 5 yr, or about 3,000,000 pieces 11. 30


1. true 3. false; multiplication 5. false;

complement 7. false; outcome 9. 3 _ 4 11. 3 _

4

13. Color Style

black classic fit

black stretch

black bootcut

blue classic fit

blue stretch

blue bootcut

6 outcomes

15.

apple (A)tea (T)

peach (P)

juice (J)

Pie OutcomeBeverage

milk (M)

tea (T)

juice (J)

milk (M)

AM

AJ

ATPM

PJ

PT

cherry (C)

tea (T)

juice (J)

milk (M) CM

CJ

CT

17. 12 19. 1 _ 3 , 0.

− 3 , 33 1 _

3 % 21. 1 _

6 23. 3 _

13

25. 60 students 27. 4


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