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Selected Answers and Solutions
Chapter 1 Multiply and Divide
Decimals
Page 24
1. 300
13. 41
Chapter 1
3. 672
Pages 27–29
Are You Ready?
5. 2,820
7. $92
9. 774 mi
11. 34
Lesson 1-1A
1. 6 × 4 = 24 3. 60 × 30 = 1,800 5. 14 × 3 = 42
7. about $8 9. 10 × 3 = 30
11 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
27 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
9 Multiply 12 times $4.89, 17 times $4.72, and 15
times $5.09. Add the three products to find 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
25 134.6°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
5 Sample answer: Multiply 52 × 21 to get 1,092.
Two decimal places in the first factor and one
decimal place in the second factor produce three
decimal places in the product. 0.52 × 2.1 = 1.092
For Homework Help, go to Hotmath.com
7. 3.645 9. 0.0848 11. 0.28 13. 1.48 15. 7.154
17. 0.186 19. 166.992 21. 0.0224
23 Estimate.
46.93 × 1.8 ≈ 45 × 2 = 90
46.93
2 decimal places
×
1.8
1 decimal place
37544
+ 4693
84.474
3 decimal places
So, 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 figure is 21.39 + 9 or 30.39 in2.
35 $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
5 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
21 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
31 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
1. 0.9
Lesson 1-2C
3. 1.4
5. 0.6
7. 0.49
9. 13.1
Selected Answers and Solutions
R1
Selected Answers and Solutions
23.7
5 118.5
-10
18
-15
35
-35
0
13. 1.0 15. 0.6 17. 1.2 19. 10.9 21. $770.56
23 22.8 ft; Sample answer: area = length × width,
so to find 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 first 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 first 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
11
Pages 58–60
Lesson 1-2E
1. 12.3 3. 1.5
5 Move both decimal points four places to the
right after annexing three zeros to the dividend.
Then divide.
250
0.0024. 0.6000.
-48
120
-120
00
00
0
7. 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
35 a. To find how many more chose silver than
red, divide 0.2 by 0.09.
0.022
0.09 0.20
-18
20
-18
0
Respondents chose silver 2.2 times more than they
chose red.
35b. To find 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
R2 Selected Answers and Solutions
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
Pages 63–65
83
Lesson 1-3A
15
1.
3.
5 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
21 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
35 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
13 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
29 Sample answer: First, find 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
Pages 72–73
Lesson 1-3C
1. 2.68 3. 0.00052 5. 6,254
7 Sample answer: 1,400 Aby cats is 0.01 times the
number of Labrador retriever dogs. To find 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
23 25 bags; 2.5 ÷ 0.1 = 25; The 2.5 pounds of
candies will be divided into bags, each holding
Pages 74–75
Lesson 1-3D
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
Page 88
Chapter 2
23 Sample answer: Use compatible numbers to
find a multiple of 4 close to 11.
_1 × 11 ≈ _1 × 12
4
4
≈3
So, Cyrus should order 3 pizzas.
25. Sample answer: 6 × 8 = 48 ft2
3
1
_
× 100; _
× 100 = 10;
27 30 days; 10 × 90 ≈ _
10
10
3 × 10 = 30
3
1
1
29. Multiply 8_
by any fraction between _
and _
2
2
5
3
1
because 5 is about _
of 8_
. 31. Sample answer:
5
2
Estimation helps determine the reasonableness of
answers. 33a. 44 feet 33b. 121 ft2
33c. 30 ft2 35. C
Pages 100–101
Lesson 2-1D
3
8
3
1
1. 8 3. _ or 1_
5. _ or 1_
2
5
2
5
_2
7 Sample answer: 5 of the measurement of the
2
6
2
male frog is _
of 6 inches. Multiply _ × _
to get
5
5
1
12
2
_ or 2_ inches.
5
5
25
22
7
2
2
9. 4 11. 2 13. 2 15. _ or 4_
17. _ or 1_
19. _
5
5
2
5
5
1
or 12_
21. 146 days
2
_2
23 neither; Sample answer: Find 3 of Mrs. Thorne’s
4
36 students and _
of Mrs. Lombardo’s 30 students
5
2
and compare the results; _
× 36 = 24 students and
_4 × 30 = 24 students. The3 number of students
5
who watched the show is the same in both classes.
8
25. Sample answer: He multiplied by _
instead of
8
8
24
_
multiplying by . He should have gotten _
or 6 as
1
4
his answer. 27. Sample answer: Write 6 over 1.
Multiply 6 times 3. Multiply 1 times 7. You now
18
4
have _
or 2_
. 29. 6 31. B
7
Are You Ready?
1
11
1. 12 3. 6 5. about 6 gallons 7. 1_
9. 4_
2
21
7
11. 6_ in.
Pages 102–103
7
Lesson 2-1E
1. $21
8
Pages 93–95
21. 4 × 3 = 12
3
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 enough
5. 270 ft 7a. 2009 7b. 2010
9 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
19. 1 × 0 = 0
Selected Answers and Solutions
0.1 pound of candies; 2.5 ÷ 0.1 = 25. Keisha can fill
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
$3
?
$3
$3
$9
Lesson 2-1B
1
1. Sample answer: _
× 16 = 2 3. Sample answer:
8
3. 15 min
45 min
?
_2 × 25 = 10 5. Sample answer: 0 × 1 = 0
5
7. Sample answer: 7 × 4 = 28
9 Sample answer: Area = length × width, and
3
feet is close to 10 feet. The area is about
9_
4
10 ft × 4 ft or about 40 ft2.
1
× 20 = 5
11. Sample answer: _
4
13. Sample answer:
5. 28 flowers 7. Sample answer: 4 quarters,
2 dimes, and 5 pennies 9. 6 people 11. $29.25
13 Sample answer: Make a diagram using the
given information.
165 mi
_1 of 42 = 14 15. Sample answer: _1 × 21 = 3,
3
7
2
3 × 5 = 15 17. Sample answer: _
×9=6
3
For Homework Help, go to Hotmath.com
=3h
55 mi
Selected Answers and Solutions
R3
Selected Answers and Solutions
1
9. 2_
285 - 165 or 120 mi
=2h
60 mi
Altogether, it took Jeffrey 5 hours to make the trip
to his sister’s.
Pages 107–110
10
4 2
4
8
8
earphones.
9. _
3
6
11. _
32
35
8
2
2 _
_2
× 4 =_
or 2_
13 3 × 4 = _
3
3
3
1
3
1
1
_
_
_
15. 4
17.
19.
21. Nyemi: 138; Luke: 69;
7
3
8
3
1
3
Natalie: 23 23. $462 25. _ 27. _ 29a. 15_
min
24
16
4
1
_
29b. 42 min; If of the time is spent on instruction,
5
4
7
4 _
7 _
_
_
then of the -hr class is not. So, _
×7 =_
. 7 ×
5
8
5
8 10 10
1
3 _
3×2 _
60 min = 42 min 31. _ c; _
× 2 =_
=1
2
4
3
2
4×3
3
_
33 10 ; If the homerooms share a bulletin board,
1
then they each have _
of the board. Since
2
3
Homeroom 101 uses _ of their half, they use
5
3
_3 × _1 or _
of the whole board.
5
10
2
9
9
41
35a. true 35b. false; 4_
×_
= 4_
35c. true
10
100
10
a
b
c
d
_
_
_
_
37. The fraction × c × × e can be simplified
b
d
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 _ae .
39. C
1
43. 30 minutes 45. _ or 13_
40
3
41. H
47. 120 in2
3
2
49. Sample answer: _
× 18 = 12
3
51. 6 lb
Pages 113–115
Lesson 2-2D
3
9
1. 1_
3. 4_
5. 9
16
10
7 Sample answer: Multiply the amount of flour
1
for one batch of waffles by 1_
to find how much
2
flour Chun needs for his larger batch.
9
3
1
1
2_
cups × 1 _
=_
×_
4
37
=_
recipe.
R4 Selected Answers and Solutions
4
1
19. 19_
2
2
2
4
1
= 9_
4
1
The distance the carp travels is 9_
miles.
4
3
_
23.
5
35 _
_1
_5
_1 1 × _
×5
25 7 × 5 6 × 1 4 = _
7
6
4
5
Write the mixed numbers
as improper fractions.
35
5 Divide 7 and 35 by
1
=_
×_
×_
7
4 their GCF, 7.
6
1
Multiply the numerators
and multiply the
denominators.
Simplify.
25
=_
24
1
= 1_
24
27
7
27a. about 69_
million mi 27b. about 139_
20
40
29
million mi 27c. about 487_
million mi 27d. about
11
1
882_
million mi 29. 2_
20
40
3
_1
_3
31 bc = 3 2 × 1 4 Substitute.
Write the mixed numbers as
7
7
=_
×_
2
improper fractions.
Multiply the numerators and
multiply the denominators.
Simplify.
4
49
=_
8
1
= 6_
8
1
1
4
33. Sample answer: 1_
× 1_
= 1_
5
2
5
35. B; The
2
1
product must be greater than _
and less than 2_
.
3
2
15
3
38
1
_
_
_
37. D 39.
41.
43. 28 45. 15 47.
or 19_
28
Pages 122–123
20
2
2
Lesson 2-3B
3
5
1
1. _ 3. _ 5. 6 7. 2_
2
2
2
9 110 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
2
by _
bale for each horse.
5
5
2
44
2
44
_
÷_
=_
×_
Multiply by the reciprocal of _
.
5
5
2
1
1
22
5
44
=_
×_
2
2
4
27
_
=
8
3
= 3_
8
3
Chun needs 3 _
cups of flour to make the waffle
8
3
17. 12_
15
21 Sample answer: Use the distance formula,
distance = rate × time, and the given information
to answer the question.
d=r×t
7
1
= 3_
× 2_
37 _
=_
×5
_1 _3
7 Sample answer: Juanita spent 2 of 4 of her
1
allowance on earphones. Multiply to find _
of
2
_3 ; _1 × _3 = _3 . She spent _3 of her allowance on new
2
15. 10_
17
20
2
10
Lesson 2-2B
1
1
1. _ 3. 8 5. _
16
4
13. _
1
11. 1_
8
1
220
=_
2
= 110
11. 10
13. _
9
7
Divide 44 and 2 by their GCF, 2.
2
1
Multiply the numerators and
multiply the denominators.
Simplify.
15. 1
1
17. 3_
3
19. 14
21. 6
1
23. 4_
2
6
5
1
48
=_
5
3
= 9_
5
4
45 Divide 4 and 8 by their GCF, 4.
3
3
2
=_
Simplify.
3
1
1
19. 13_ ÷ 2_; 6 photos
2
4
2
17. 2_
5
21 Sample answer: The distance around the
2
feet, needs to be divided by the amount
kitchen, 24_
3
3
of border in each strip, 1 _
feet.
4
3
2
74
7 Write the mixed numbers as
24 _
÷ 1_
=_
÷_
3
4
3
4
74
=_
×_
Lesson 2-3D
9
10
4
improper fractions.
7
Multiply by the reciprocal of _ .
4
7
3
3. _ 5. _
1
24
2
1
24
1
2
8
1
15
8 Divide 15 and 45 by their GCF, 15.
=_
×_
There will be 9 whole pieces to use for the steps
3
with _
foot left over.
5
29. Sample answer: Multiplication is repeated
addition. Multiplication and division are inverse
operations. Multiplication is commutative and
1
1
associative; division is not. 31. I 33. 5_
35. 23_
1. _
45
Multiply by the reciprocal of _ .
45
4
Multiply the numerators and
multiply the denominators.
Simplify.
Pages 128–129
_
15
=_
× 8
5
6
296
2
=_
or 14 _
Multiply and simplify.
21
21
7 Sample answer: Area = base × height, so
base = area ÷ height. Divide the area by one
3
3
measurement to find the other. _
÷1=_
foot
They will need to have 15 strips and there will be
some left over.
2
1
23. Sample answer: 8_
÷ 3_
25. less than;
9. _
5
2
> 2_
, the quotient of
Sample answer: Since 3 _
3
4
11. _
13. _ 15. _
1
12
7
24
1
24
4
17. _
2
5
4
5
12
3
19. _
8
21 2 T-shirts; Sample answer: Use the table to find
the amount of orange dye available, then divide
3
that amount by the _
cup needed for each shirt.
_3 cup of orange dye 8÷ _3 cup for each shirt
4
8
_3 ÷ _3 = _3 × 8 Multiply by the reciprocal of _3 .
8
3
8
4
4
24
=_
or 2 Simplify.
12
8
4
3
1
1
23. _ 25. _ or 1_
27. Sample answer: _
÷_
9
3
3
2
5
c
29a. _; When the numerators are the same, the
b
_
5
5
5
1
1
2
1
5_
÷ 3_
< 5_
÷ 2_
. The expression 5 _
÷ 3_
6
8
6
5
6
6
5
6
divided into a greater number of parts, each part
1
will be smaller. 27. D 29. _ qt 31. 800 mi
2
33. 54 35. 15
Chapter Study Guide and Review
6
1. false; 21 3. true 5. false; Sample answer: _
7
1
7. true 9. Sample answer: _
× 12 = 2 11. Sample
6
1
1
answer: _
× 1 = _ 13. Sample answer: 300 sq. ft
2
2
15. 8
17. 10
2
27. 6_
3
37. 6
2
19. $8.75
7
29. 1_
12
9
31. 8_
39. 27 bags
2
49. 1_
gallons
20
1
41. _
6
21. _
23. _
5
12
1
12
6
9
1
43. 2_
45. _ 47. 1_
1
2
2
Chapter 3 Ratios and Rates
1
10 _
inches, by the amount needed for each slice,
Page 146
7
4
2
3
8
21
=_
×_
1
1
1
3
5
33. 12_
sq. ft 35. 12
1. 7 3. 6
5 Sample answer: Divide the dough Jay has,
_
25. _
28
5
Lesson 2-3E
2
_3 inch.
8
3
3
1
21
÷_
=_
÷_
10 _
2
8
2
8
8
21
_
=
×
3
2
8
1
represents 5 _
being divided into a greater number
6
1
2
1
of parts than the expression 5 _
÷ 2_
. If 5 _
is
Pages 136–139
quotient is a fraction of the denominators.
a
29b. _; When the denominators are the same, the
c
quotient is a fraction of the numerators. 31. D
3
33. Yes; the shelf can hold 24 ÷ _
or 64 cases.
8
1
_
35. 24
37. 4
Pages 131–133
4
1. 29
Write the mixed numbers
as improper fractions.
3
Multiply by the reciprocal of _ .
8
Divide 21 and 3 by their GCF, 3.
Divide 2 and 8 by their GCF, 2.
28
=_
or 28 slices Simplify.
1
5
2
1
_
_
7.
9. 2
11. 39 13. 4_
12
3
26
For Homework Help, go to Hotmath.com
Chapter 3
3. 6
Are You Ready?
5. $32
Pages 152–155
7. _
2
3
9. _
3
5
11. _
13
25
Lesson 3-1B
3
3
1. _; For every 3 pens, there are 4 pencils. 3. _; For
2
4
every 3 action thrillers showing, there are 2
romantic comedies showing. 5. 12 in the first
2
group and 16 in the second group 7. _; For every
1
2 flutes, there is 1 drum.
6
3 _
_2 _
÷_
= 2 ; For every 2 boys, there are 5 girls
9 ;
5 15
3
5
in the class.
Selected Answers and Solutions
R5
Selected Answers and Solutions
6
Multiply by the reciprocal of _ .
5
8
6
8÷_
=_
×_
Write the mixed numbers as
improper fractions.
45
_3
_5 15 ÷ _
15 3 4 ÷ 5 8 = _
8
4
25 Sample answer: To cut the large 8-foot board
5
into pieces that are _
foot each, use division.
11. _; For every 3 ruby rings on sale, there are
5
5
5 emerald rings on sale. 13. _, 5 to 12, or 5:12;
12
Every 5 out of 12 books Salvador read was a
1
mystery. 15. _, 1 to 5, or 1:5; One out of every five
5
articles of clothing Ramona packed was a pair of
jeans. 17. 24, 40
5
_
19 a. 16 ; The Rangers have made 5 Stanley Cup
final appearances for every 16 appearances made
by the Canadiens.
23
19b. _; The Maple Leafs have made 23 Stanley
17
Cup appearances to every 17 Bruins’ appearances.
1
21. 21, 24 23. _; 1:3; or 1 to 3 25. 15
3
27. Sample answer:
2,144
_
21 a. The unit rate, miles in one hour, is 8 , or
268
_
, or 268 miles per hour.
1
21b. To find 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
Pages 166–168
1. $28
7
Lesson 3-2A
3. 15 tsp 5. 8 pounds
÷10
÷3
American
Dollars
270
27
9
Mexican
Pesos
3,000
300
100
÷10
29. If the fraction is in simplest form, the GCF of the
numerator and denominator is 1, and the ratio is
simplified. 31. G 33. D
Pages 160–162
11 points
1 quarter
$3
1 case
5. $8
7 Divide the numerator and denominator by 8 to
40.8 gallons
5.1 gal
8 _
make the denominator 1; _ ÷ _
=
8 containers
$0.50
11. _
1 bottle
60 words
9. _
1 min
8
1 container
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
1000
800
600
400
200
ing
y
m
rse
People Served
24
Liters of Soda
4
Pints of Sherbet
2
Cups of Ice
6
15b.
Number
of
People
Liters
of
Soda
Pints
of
Sherbet
Cups
of
Ice
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.
State
R6 Selected Answers and Solutions
Steps
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.
yo
W
a
wa
Je
Ne
w
Io
r id
rn
li fo
Ca
F lo
ia
0
÷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.
15 a.
Lesson 3-1D
1. _ 3. _
People per Square Mile
Selected Answers and Solutions
3
Number of Girls
10
5
15
Number of Boys
8
4
12
21. G
11 parts
1h
23. _
25. _; For every 3 soccer
3
5
6 problems
1 problem
_ _
15 no; Kiera did 30 minutes or 5 minutes , and
18 problems
40 minutes
9 problems
20 minutes
balls there are 5 footballs.
Heath did __ or _. Heath took
Pages 170–171
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
10
15
and _
cheapest. 19. Sample answers: _
14
21
21. $10 23. about 1,200 miles
Lesson 3-2C
PSI
1. Sample answer: Use this strategy when the
change between events is the same.
3 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 find 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.
Pages 175–177
Lesson 3-3A
$8
$7.43
1. no; Since the unit rates, _ and _, are not
1 wk
1 wk
the same, the rates are not equivalent.
3h·3
9h
_
, the fractions are
3 yes; Since $12 · 3 = _
$36
3h
9h
equivalent; _
=_
. Also, the ratios both
$12
$36
1
simplify to equal _
, so they are equivalent to each
4
other.
25 push-ups
5. no; Micah’s unit rate is __ and Eduardo’s
1 min
26 push-ups
7. no; Since the unit rates,
1 min
4 points
6 points
_
_
and
, are not the same, the rates are
1 game
1 game
unit rate is __.
1. 170
Lesson 3-3C
3. 90 cookies
120 gallons _
_
= 5
4 days
28 days
×7
_
= 120
4×7
840
=_
28
Write equivalent ratios.
Since 4 times 7 is 28,
multiply 120 by 7.
A Clydesdale will drink 840 gallons of water in
28 days.
7. $30 9. 2 min
11 Sample answer: Since there were 20 students
who responded to the original survey and 3 of them
favored science, set up equivalent ratios to find the
number who would favor science out of 400 students.
3 science
_
= __
Write equivalent ratios.
20 students
400 students
Since 20 times 20 is 400,
3 × 20
=_
20 × 20
60
=_
multiply 3 by 20.
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
1
x
correct order. She should have set it up as _
=_
.
276
There are 23 teachers at the preschool. 19. 15 people
9 First find the unit rate for each.
21. C
23. 27
25. yes; Since the unit rates are the
1 poster
same, _, the rates are equivalent;
$3
3÷6
_
=_
3 students
6÷6
6 bagels
Pages 183–185
12
not equivalent.
So, the unit rate is _.
12 posters
21 posters
_
= _. 27. $75 29. $2.40 per
36 students
63 students
2
hot dog 31. _, 2 to 9, or 2:9; Every 2 out of 9 shoes
$9
9 ÷ 24
_
=_
sold last week were running shoes.
$0.50
=_
1 bagel
24 bagels
24 ÷ 24
$0.38
=_
1 bagel
Selected Answers and Solutions
19. C
$0.50
1 bagel
9
Pages 188–191
$0.38
1 bagel
So, the unit rate is _.
Since the rates do not have the same unit rate, they
are not equivalent.
15 computers · 3
45 computers
45 students · 3
135 students
15
computers
45 computers
fractions are equivalent; __ = __.
45 students
135 students
16 students __
240 students
_
13. no; Since
≠
, the ratios
28 students
560 students
11. yes; Since __ = __, the
are not equivalent.
For Homework Help, go to Hotmath.com
Chapter Study Guide and Review
1. false; division 3. true 5. false; ratio 7. true
3
6
11
1
9. false; 2:3 11. _ 13. _ 15. _ 17. _, 1 to 3, or
5
7
20
3
1:3; One out of 3 DVDs Amos owns is an action
6 passengers
15.75 lb
DVD. 19. _
21. __ 23. $4 million
1 car
1 wk
25. $6
27. $18
29. 2
14 _
21 _
31. no; _
= 2 and _
= 21
21
34
3
34
3 _
79.50 _
12 _
33. yes; _
= 1 and _
= 1 35. yes; _
= 26.50
9
36
3
3
3
1
132.50
8
26.50
4
1
1
and _ = _
37. yes; _
=_
and _
=_
5
1
39. 1,000 words
48
6
24
6
Selected Answers and Solutions
R7
Selected Answers and Solutions
Chapter 4 Fractions, Decimals,
and Percents
Page 198
1. 4
Chapter 4
3. 12
5. 3
Pages 202–203
Are You Ready?
7. $3
9. 18
11. 72
13. 120
Lesson 4-1A
16
2
21
7
3
3
1. _ 3. _ 5. _ 7. 2_
9. 23_
mpg 11. _
5
25
40
10
4
4
5
13 0.5 = _ Say five tenths.
10
Simplify. Divide the numerator and
denominator by the GCF, 5.
1
=_
2
21
41
17
1
17
15. _ 17. _ 19. _ 21. _ 23. _ mi
50
250
20
100
40
3
1
24
121
25. 12_
27. 17_
29. 42_
31. 50_
25
200
10
100
8
4
_
_
33 Write each decimal in fraction form, 100 and 10 .
40
4
Write _ as _. Now you can pick any two fractions
10
100
8
40
that are between _
and _
. Simplify the fractions
100
100
20
35
1
if necessary. Sample answer: _
or _
in. and _
5
100
100
7
or _
in.
20
35. Mei wrote the wrong place value in the
denominator, so her fraction was incorrect;
28
7
4.28 = 4_
or 4_
. 37. Sample answer: Since
25
100
6 is in the hundredths place, write 0.36 as a
36
fraction with a denominator of 100. So, 0.36 = _
.
100
36
9
_
_
Then simplify by using the GCF, 4:
= .
9
Therefore, 0.36 = _
.
25
Pages 206–207
1. 0.9
100
25
5. 0.36
= 0.385
7. 3.7
9. 4.225
11. 0.05
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.
25 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:
× 4 Rewrite the fraction to have a
24
_
87 _
= 87 24
25
25 × 4 denominator of 100.
96
= 87 _
100
= 87.96
Venus:
7
224 _
= 224.7
10
Multiply.
Read 87.96 as eighty-seven and
ninety-six hundredths.
Read 224.7 as two hundred twenty-four
and seven tenths.
Mars:
× 2 Rewrite the fraction to have a
49
_
686 _
= 686 49
50
50 × 2 denominator of 100.
98
= 686 _
Multiply.
100
= 686.98
Pages 212–213
Lesson 4-2B
3
33
3
23
7
1. _ 3. _ 5. _ 7. _ 9. _
20
50
50
100
4
11 Write the percent number as a fraction with a
denominator of 100 and then simplify the fraction
if necessary.
2
2% = _
Definition of percent
100
1
=_
Divide the numerator and
denominator by the GCF, 2.
50
13. _
15. _
17. _
43
50
1
5
1
25
19. _
18
25
21. _
7
25
23. _
27
50
25 Eighty-two percent of the students use the
Internet at home, so 100% - 82%, or 18%, use the
Internet elsewhere.
18
18% = _
Definition of percent
100
9
=_
50
Divide the numerator and
denominator by the GCF, 2.
3 _
55
11
27. Sample answer: _
=_
or 55%, _
= 60 or
20
5
100
100
7
70
60%, _ = _
or 70% 29. Sample answer: I received
10
100
a 95% on my science test. What fraction of the
19
problems did I get correct? _
31. H 33. 0.75
35. _
73
100
7
37. 11_
20
50
Pages 215–217
77 × 5 Rewrite the fraction to have a
77
=_
13 _
200
200 × 5 denominator of 1,000.
385
=_
Multiply.
1,000
1
4
39. H 41. C
Lesson 4-1B
3. 3.5
−
7
29. Sample answer: _
= 0.583 31. C
12
−−
−
33. 0.333… or 0.3 35. 0.8181… or 0.81
27. _, 0.25
Read 686.98 as six hundred eighty-six
and ninety-eight hundredths.
R8 Selected Answers and Solutions
Chapter 4-2C
1. 25%
3
3×5
15
_
=_
or 15%
3 20 = _
20 × 5
100
5. 90% 7. 30% 9. 30% 11. 44% 13. 72%
15 Two sections out of the 10 sections are shaded.
2
Write 2 out of 10 as a fraction, _
. Since 10 × 10 gives
10
a denominator of 100, multiply both the numerator
20
and denominator by 10 and write the fraction as _
.
100
Write the fraction as a percent, 20%.
17. 70% 19. 90% 21. 70% 23. 36%
25 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
×5
_
_
= 16
20
20 × 5
80
=_
100
= 80%
4×5
4
_
=_
20
20 × 5
20
=_
100
= 20%
The sum of the percents, 80% + 20%, is equal to 100%.
8
9
27. _; The other numbers are equivalent to _
.
45
20
25
Pages 220–221
25
Lesson 4-2D
1. 0.27 3. 0.04
13. 70%
5. 0.18
7. 32%
9. 91%
11. 82%
Rewrite as a fraction with a
denominator of 100.
= 0.35 Write thirty-five hundredths as a decimal.
35
15 35% = _
100
17. 0.03 19. 0.01 21. 0.95 23. 0.96
27. 62% 29. 60% 31. 87%
25. 99%
12
Write twelve hundredths as a fraction.
33 0.12 = _
100
= 12% Write the fraction as a percent.
3
35. Sample answer: 0.6; _
; 60% 37. Sample answer:
5
Niko scored a 92% on his math test. Express this
19
percent as a decimal. 39. 0.25 41. 18% 43. _
50
7
45. _ 47. 0.3
20
Pages 223–225
Lesson 4-2E
1
4
1. 3.25; 3_
3. 4.8; 4_
5
4
5 0.15% = 0.00.15
Divide by 100 and remove
the % symbol.
= 0.0015
15
=_
Write as a fraction.
10,000
Simplify. Divide the numerator
3
=_
2,000
and denominator by the GCF, 5.
9
_
7. 0.009;
9. 0.15% 11. 275% 13. 325%
1,000
3
1
11
15. 3.5; 3_ 17. 6 19. 0.006; _
21. 0.0055; _
2
500
2,000
1
23. 0.001; _
25. 850% 27. 264% 29. 0.9%
1,000
31. 0.34%
33 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%
3
39. 0.00125 41. 0.0012 43. 0.003; _
; 3 out of
1,000
every 1,000 people are Japanese.
45 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
1
45b. Change _
to a percent by dividing;
400
1
_ = 0.0025. Change 0.0025 to 0.25%. Sulfur is
400
0.25% of the human body. 47. 30 mph 49. D
51. 0.37 53. 0.62 55. 78%
Pages 231–233
Lesson 4-3B
1. > 3. <
For Homework Help, go to Hotmath.com
3
3
6
7
_
_
_
_
5 2 10 2 20 Rewrite 10 as 20 using the LCD.
6
7
2_
< 2_
Compare the numerators.
20
Selected Answers and Solutions
29. Rewrite the fraction with a denominator of 100.
Write the new numerator as the percent with the
21
2
percent symbol. 31. D 33. _ 35. _ 37. 0.7
20
3
7
2_
< 2_
Rewrite in original form.
20
10
1 3 _
9
7. _, _
, 4, _
9. garbage odors 11. > 13. >
2 4 5 10
15. = 17. =
5
19. _ foot
8
0
2 11 _
5
21. _, _
, 2, _
9 18 3 6
2
8
4
8
6
8
1
5 _
1 _
23. 3_
, 3 9 , 3_
, 33
2 16 8 4
25 The LCD of the fractions is 48. Rewrite each
fraction with a denominator of 48.
×8
×6
40
_5 = _
42
_7 = _
×8
×6
6
8
48
×3
3
9
_
=_
48
16
48
×3
7
So, the bead that is _
inch long is the longest of the
8
three. 27. < 29. >
31 To compare the distances, you need to rewrite
12
2
the improper fractions as mixed numbers: _
= 2_
5
5
9
1
and _
= 2_
. Then rewrite the fractions using the
4
4
LCD. The least common denominator of 5, 3, and
4 is 60.
× 12
2
= 2 2_
2_
5
5 × 12
24
= 2_
60
× 20
1
2_
= 2 1_
3
3 × 20
20
= 2_
60
× 15
1
2_
= 2 1_
4
4 × 15
15
= 2_
60
15
20
24
Compare the mixed numbers: 2 _
< 2_
< 2_
.
60
60
60
15
Since 2 _
is the least mixed number, it is closest to
60
2 miles. Dominic rode the closest to 2 miles.
3 _
5
33. Sample answer: _
, 2, _
35. Sample answer: In
8
3
6
1
the fraction _
, the numerator is much less than the
6
7
denominator, so it is very close to 0. In the fraction _
,
9
the numerator is very close to the denominator, so it
1 _
is very close to 1. So, _
< 7 . 37. H 39. 0.2% 41. 89%
6
Pages 239–241
9
Lesson 4-3D
1. >
_
3 5 0.04 Write the sentence.
0.6 > 0.04 Write _35 as a decimal.
_3 > 0.04 Compare.
3
5
1
7
5. < 7. Cora 9. _, 0.33, _
11. 0.39, _
, 44% 13. >
3
10
3
16
Selected Answers and Solutions
R9
Selected Answers and Solutions
15
_1 0.4
Write the sentence.
0.25 < 0.40 Write the fraction as 0.25 and
annex a zero to 0.4.
_1 < 0.4 Compare.
of 20, 10% of 20, 20% of 20 29. B
4
Pages 250–251
4
17. > 19. > 21. < 23. < 25. Save More
5
27. Tricia 29. 38%, 0.4, _
8
1
3
31. _, 0.22, 22.2% 33. 135%, 1.4, _
5
2
161
35. mean: _; median: 0.18
900
37 Change each response portion to a decimal
written to the nearest hundredth.
17
17% = _
Rewrite as a fraction with a denominator of 100.
100
= 0.17 Write seventeen hundredths as a decimal.
11 × 5
11
_
=_
Rewrite with a denominator of 100.
20
20 × 5
55
=_
100
= 0.55
0.2 = 0.20
8
8% = _
100
Multiply.
8 16 32 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
36
9
numerator. 45. < 47. _ = _
100,000
Pages 244–246
25,000
Lesson 4-4B
1. Sample answer: _ of $50 is $10
1
5
3 Estimate 47% of 118. 47% is close to 50%, which
1
1
is _
. 118 is close to 120.47% of 118 is close to _
of 120,
2
2
or 60.
3
5. Sample answer: _ of 15 is 9 7. Sample answer:
5
1
1
_ of $30 is $15 9. Sample
answer: _ of 60 is 30
2
2
1
11. Sample answer: _ of 150 is 50
3
_2
13 42% is close to 40% or 5 . Round 16 to 15.
_2 of 15 is 6.
1. 19.2 3. 16.5 5. 0.216 7. 11 9. $10.50 11. 115
13. 161 15. 138
17 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.
=9
19. 336 21. 0.45
23 Find 20% of $42.
20% = 0.2
Write 20% as a decimal.
20% of 42 = 0.2 × 42 Write the multiplication problem.
= 8.4
The amount off during this sale was $8.40.
25. 95 27a.
3
3
17. Sample answer: _
of 44 is 33 19. Sample answer:
_3 of 20 yr is 15 yr 4
4
21 Sample answer: 71 - 37 = 34 missed shots and
34
35
1
1
_
is about _
, or _
. Since _
= 50%, he missed about
2
2
50% of his shots.
2 _
23. about 75% 25a. No; 40% is _
. 2 of 15 is 6. He
5 5
1
needs 7 baskets to win a prize. 25b. 50% 27. _%
5
R10 Selected Answers and Solutions
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
3
1 _
answer: $30 37. = 39. 3_
, 3 1 , 5_
41. 8%
4 3 4
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
9 Sample answer: To find 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
Pages 256–261
20
So, 42% of 16 is 6.
2
15. Sample answer: _ of 300 is 200
70
Number
Correct
Test
Chapter Study Guide and Review
1. percent 3. decimal 5. 5% 7. 0.09 9. 287
7
1
3
11
2
11. _ 13. _ 15. 4_
17. savings: _
; charity: _
;
5
71
25
Lesson 4-4D
Read 0.55 as fifty-five hundredths.
Annex a zero to the 0.2 to make it hundredths.
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.
11
8%, 17%, 0.2, _
Rewrite in original form.
20
39. Greatest to least; when fractions have the same
numerator, the fraction with the larger denominator
1 3 _
3
will be the smaller fraction. 41. B 43a. _, _
, 11 , _
;
4
31. G 33. 1_
8
20
5
20
9
shopping: _
19. 0.6 21. 4.125 23. 8.5625
20
12
25. photos: 0.48; songs: 0.12; movies: 0.4 27. _
25
4
29. 87.5% 31. 19% 33. _ 35. 0.02 37. 0.46
5
1
1
39. 3% 41. 29% 43. 0.3 45. 1.25; 1_
47. 0.005; _
4
200
3 _
7
49. 475% 51. 1.35; 1_
53. = 55. > 57. _, _
,37,
20
5
3_
59. > 61. > 63. >
6
5
8 4
2
12
_
65. , 0.42, 44%, _
5
25
12
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.
Page 268
Chapter 5
Are You Ready?
2
1. 65 3. 28 5. 144 7. 128 9. 1,000,000 11. _ or 1_
3
3
3
1
19
13. _ 15. 2_
17. _
5
10
28
20
5. d = cost of one drink; 3d + 3.50
7. a = the number of apples; 4a
9 t represents Tracey’s age. Less than means to
subtract. Therefore, t - 6 represents six years less
than her age.
1
11. p = the number of points the Panthers scored; _
p
3
Pages 272–273
Lesson 5-1A
1. 7 3. 47 5. 29 7. 4 × $24 + 2 × $10; $116 9. 6
11. 13 13. 61 15. 199
17 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
29 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 + 7
31b. 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.
Pages 276–278
Lesson 5-1B
1. 7 3. 5 5. 14 7. $8 9. 24 11. 6 13. 6 15. 12
17. 18 19. 1 21. 4
23 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. 48
37a. $14.50 37b. $43.50 39. 15 41. 29 43. 49
45 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.
Pages 284–285
Lesson 5-1D
1. m = money Elliot saved; 4m
3. = the length of the box; − 4
For Homework Help, go to Hotmath.com
or p ÷ 3 13. j = the cost of James’s dinner; j - 5
15 s represents the number of members in the
Senate. The number of representatives in the House
of Representatives is defined 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.
3
Team 1
Team 2
Team 3
Team 4
Student
1
Student
2
Student
3
Student
4
Student
5
Student
6
Student
7
Student
8
Student
9
Student
10
Nate
Nate will be on Team 3.
5. 5 students 7. 6 9. about 5 times 11. 120 words
Pages 291–293
Lesson 5-2A
1. yes; Associative Property
3 72 - (63 - 8) (72 - 63) - 8
72 - (55) (9) - 8
17 ≠ 1
no; The first expression is equal to 17 and the second
is equal to 1.
5. no; The first 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 first expression is equal to 11 and the
second is equal to 21. 13. yes; Associative Property
15. no; The first expression is equal to 9 and the
Selected Answers and Solutions
R11
Selected Answers and Solutions
Chapter 5 Algebraic Expressions
Selected Answers and Solutions
second is equal to 1. 17. no; The first expression is
1
1
equal to 32, not 0. 19. 4_
+ 5_
+ 6 = 16 in.
2
2
21 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
m + 0.5 25. 25 s 27. no; The first expression is
1
. 29. no;
equal to 8 and the second is equal to _
8
The first expression is equal to 17, not 1. 31. 14 +
2
(16 + 11) and (14 + 16) + 11 33. 7 × 4_
= 7(4) +
7
2
_
7
= 28 + 2 = 30 35. 6 × 5.4 = 6(5) + 6(0.4) =
33 17 + x = 3 + 17 Write the original equation.
17 + x = 17 + 3 Commutative Property of Addition
x=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
Chapter 6 Equations
(
Pages 298–299
)
Lesson 5-2C
1. 4(30) + 4(8) = 152
3. 11(20) + 11(7) = 297
1
1
= 20_
5. 3x + 3 7. 4x + 24 9. 4(5) + 4 _
8
2
11 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.
Add.
= 26.6
13 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. F
25. 8 days 27. b = price of a book; b × 3 29. 4
(7)
30 + 2.4 = 32.4 37. 4x + 12 39. 9x + 18
41. 4($9.50) + 4($5.50) = 4($15) = $60
Page 312
Chapter 6
30
Pages 316–317
1. 8
13
3. 2
Chapter Study Guide and Review
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;
R12 Selected Answers and Solutions
Lesson 6-1A
5. 12
7. 2
9. 34
11. 15 votes
Are both
sides equal?
Value
of d
29 + d = 54
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
35 Sample answer:
Try 45.
700 - d = 665
700 - 45 665
655 ≠ 665
Try 40.
700 - d = 665
700 - 40 665
660 ≠ 665
Try 35.
700 - d = 665
700 - 35 665
665 = 665
Therefore, there are 35 fewer students this year.
37. Sample answer: m + 8 = 13 39. True; m + 8 is
not equal to any specific 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
find the number of baseball cards that Juan
has. 43. 7 45. 4 × 14 = 56; Each side is 14 units.
Pages 318–319
Pages 302–305
Are You Ready?
13
1
11
5
5
1. _ 3. 1_
5. 1_
c 7. _ 9. _ 11. mowing the
3
35
24
8
12
19
lawn, _ h
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.
5 To use the work backward strategy, begin with the
final answer and do the opposite of each operation
Pages 324–326
Lesson 6-1D
1. 2
3 Solution:
c + 3 = 6 Write the equation.
- 3 = - 3 Subtract 3 from each side.
c
= 3
Check:
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
17 The length of a Black Mamba plus 22 inches is
118 inches. Let represent the length of a Black
Mamba.
+ 22 = 118
- 22 - 22
= 96
So, a Black Mamba is 96 inches.
19. 15.4 = x + 4.9; 10.5 ft 21. 0.3
23 Solution:
7.8 = x + 1.5 Write the equation.
- 1.5 = - 1.5 Subtract 1.5 from each side.
6.3 = x
Check:
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.
1
_
25.
27. Sample answers: 56 = 44 + x; 36 = 24 + m
2
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
9 Solution:
1 = g - 3 Write the equation.
+ 3 = + 3 Add 3 to both sides.
4=g
Check:
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
10
1
19. 1 21. _ or 1_
9
9
For Homework Help, go to Hotmath.com
23 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.
Pages 337–338
Lesson 6-2B
1. 3 3. 2 5. 18x = 90; 5; To check, multiply 18 by 5.
The result should be 90. 7. 4 9. 3
11 Solution:
4g = 24 Write the original equation.
4g
24
_
=_
4
4
Divide both sides by 4.
g=6
Check:
4g = 24 Write the original equation.
4(6) 24 Replace g with 6.
24 = 24 The equation is true.
1
13. 2 15. 4e = 58; $14.50 17. 2 19. 9 21. _
2
23 a. p = the number of points Blanda scored
each year.
26p = 2,002 Write the original equation.
26p
2,002
_
=_
26
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
1,736
_
=_
16
16
Divide both sides by 16.
p = 108.5
Norm 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.
Pages 341–343
Lesson 6-2D
1. 60 3. 40
5 Solution:
p
5=_
Write the original equation.
4
p
5(4) = _ (4) Multiply both sides by 4.
4
20 = p
Check:
p
5 = _ Write the original equation.
4
20
5
_
Replace p with 20.
4
5=5
The equation is true.
h
_
7. = 12; 72 oz 9. 32 11. 36
6
17. 133 19. 100
13. 132
15. 36
Selected Answers and Solutions
R13
Selected Answers and Solutions
but in reverse order. 18 was the final 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 find the original value. It was 3.
7. 127 pictures 9. 17 rungs 11. 8 13. 37 spaces
Selected Answers and Solutions
21 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 = 3
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
12.5
_
= _
4
2.5
_x (4) = 3(4)
4
x = 12
So, she baked 12 dozen cookies in all.
r
23. _ = 16; 64 in.
4
25 Solution:
g
4.7 = _
Write the original equation.
3.2
g
_
4.7(3.2) =
(3.2) Multiply both sides by 3.2.
3.2
15.04 = g
Check:
g
Write the original equation.
4.7 = _
3.2
15.04
4.7 _
Replace g with 15.04.
3.2
4.7 = 4.7
The equation is true.
27. 10.08 29. 1.4 31a. 20 = 5x; 4 books
x
31b. _ = 7; 35 points 33. True; Sample answer:
5
1
Dividing by 3 is the same as multiplying by _
.
3
35. A 37. H 39. 10 41. a - 3 = 11; 14 yr
43. 21
2.5
Divide each side by 2.5.
x=
5
It 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
first 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 flat
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
45. $29
Pages 354–357
Pages 348–351
Lesson 6-3B
1. 4
3 Solution:
9k - 4 = 32 Write the original equation.
+ 4 = + 4 Add 4 to each side of the equation.
9k = 36 Simplify.
9k
= 36 Divide both sides by 9.
9
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. 5
15. 15x + 89 = 149; 4 wk 17. 3.1 19. 1.98
21. 4.2
23 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
12.00
_
= _
3.00
3.00
Divide each side by 3.00.
g= 4
You can bowl 4 games.
25 current temp + increase = new temp
R14 Selected Answers and Solutions
Chapter Study Guide and Review
1. false; coefficient 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
s
37. 48 39. 60 41. _ = 15; 45 mph 43. 3 45. 2
3
47. 5
Chapter 7 Functions, Inequalities,
and Integers
Page 364
1. >
Chapter 7
3. >
5. 300 > 206
Pages 369–370
1–4.
9
8
7
6
5
4
3
2
1
0
Are You Ready?
7. 14
9. 25
Lesson 7-1A
y
"
$
#
%
1
2
3
4
5x
5a. (0, 0), (1, 3), (2, 6), (3, 9)
5b. The points appear to fall on a line.
11. 8
13. 5
7 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.
9
8
7
6
5
4
3
2
1
O
Total
Time (h)
Number of
Paintings
0
0
3
1
6
2
9
3
Pages 375–376
1.
x+3
Output
0
0+3
3
2
2+3
5
4
4+3
7
Input (x)
x-1
Output
1
1-1
0
3
3-1
2
5
5-1
4
R
N
Q
A
M
3.
B
P
L
1 2 3 4 5 6 7x
5.
_1
_1
_3
15 a. (5, 20), 5 4 , 21 , 5 2 , 22 , 5 4 , 23
(
)(
)(
)
Pounds (x)
3x + 2
Cost ($)
2
3(2) + 2
8
3
3(3) + 2
11
4
3(4) + 2
14
15b. The points appear to fall on a line.
24
23
22
21
20
19
18
17
16
0
y
3
(5 4 , 23)
1
(5 2 , 22)
15
1
(5 4 , 21)
(5, 20)
Lesson 7-1C
Input (x)
y
Selected Answers and Solutions
23.
y
9
(3, 9)
8
7
6
(2, 6)
5
4
3
(1, 3)
2
1(
0, 0)
0 1 2 3 4 5 6 7x
y
(4 lb, $14)
(3 lb, $11)
12
9
(2 lb, $8)
6
5
6
x
3
17. Sample answer: Laureen earned $7 an hour
tutoring. Make a table showing the relationship
between the number of hours she tutors and the
amount of money she earns.
Hours
Amount
Earned ($)
1
7
2
14
3
21
For Homework Help, go to Hotmath.com
2
3
5x
4
7 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.
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
1
0
Input (x)
2x + 4
Output
7
2(7) + 4
18
9
2(9) + 4
22
15
2(15) + 4
34
Selected Answers and Solutions
R15
Selected Answers and Solutions
11
Number of
Guests (x)
30 ÷ x
Cupcakes
per Guest
6
30 ÷ 6
5
10
30 ÷ 10
3
15
30 ÷ 15
2
5
35.
Input (x)
4x + 2
Output
4
4(4) + 2
18
5
4(5) + 2
22
6
4(6) + 2
26
36–39.
y
(6, 5)
4
(10, 3)
3
(15, 2)
2
1
4
O
13.
8
12
16
223 million × $10 × x
1
$2,230,000,000
2
$4,460,000,000
3
$6,690,000,000
3.
Lesson 7-1D
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
2
4
4
1
1
19. 11_
21. 24_
2
"(7, 0)
$(0, 0)
2
23 arithmetic sequence; Each term is found by
adding 2 to previous term.; 10 + 2 = 12; 12 boxes
25. arithmetic sequence; 4.75, 5.75 27. Sample
3
1 _
answer: 1, 2_
, 3 1 , 4_
, ... 29. Sample answer: Both
4 2 4
are numerical patterns, but arithmetic sequences
are additive and geometric sequences are
multiplicative. 31. B 33. 4x + 1
R16 Selected Answers and Solutions
10
9
8
7
6
5
4
3
2
1
1 2 3 4 5 6 7 8 9 10 x
Lesson 7-1E
y
1
O
5.
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, 4,374
11a. The amount increases by $8.
11b. 8x + 5 13. add 12; 52, 64 15. add 2.4; 11.1, 13.5
3
1 _
17. add _
; 4 1 , 4_
%(6, 2)
1. y = 4x
1. multiply the position number by 2; 2n; 30
3. 2x + 1
5
#(0, 4)
Pages 385–387
15. 4 17. B
Pages 380–382
y
0
20 x
Years (x)
10
9
8
7
6
5
4
3
2
1
10
9
8
7
6
5
4
3
2
1
O
2
3
x
y
1 2 3 4 5 6 7 8 9 10 x
7. y = 6x
9. y = 15x
11 To graph the equation, make a table of values
using any three values for x, and calculate y. Then
graph the line passing through the three ordered
pairs.
x
x+4
y
(x, y)
0
0+4
4
(0, 4)
3
3+4
7
(3, 7)
5
5+4
9
(5, 9)
1 2 3 4 5 6 7 8 9 10 x
0
10
9
8
7
6
5
4
3
2
1
10
9
8
7
6
5
4
3
2
1
0
17.
21c. No; the graph is curved; it does not form a line.
x
25. y = _
- 3 27. C 29. Sample answer: The
2
graph could represent the growth of a tree.
Pages 391–393
1a. t = 3n
Chapter 7-1F
1b. Number of
Lunches, n
Total Cost ($), t
1c.
1 2 3 4 5 6 7 8 9 10 x
y
10
9
8
7
6
5
4
3
2
1
O
Health Club Costs
50
3c.
40
30
20
x
1
2
2
3
3
6
9
y
(3, 9)
(2, 6)
(1, 3)
1 2 3 4 5 6 7 8 9 10 x
400
Pounds Eaten, v
y
10
0
1
1d. The graph is a line because each ticket
costs $3.
3 a. Use v = 400d because 400 multiplied by the
number of days will give you the total amount of
vegetation eaten.
3b. Number of Days, d
1
2
3
1 2 3 4 5 6 7 8 9 10 x
60
Total Charge
1 2 3 4 5 6 7 8 9 10 x
O
y
0
15.
y
10
9
8
7
6
5
4
3
2
1
Pounds Eaten
13.
21b.
y
3
Number of Classes
1400
1200
1000
800
600
400
200
0
800
1,200
y
(3, 1,200)
(2, 800)
(1, 400)
1
2
3
x
Number of Days
19 a. Input (d)
Output (t)
1
2
3
4
5
10
15
20
19b. The equation for the money spent t on lunch
for d days is y = 5x. 21a. y = x · x or y = x2
For Homework Help, go to Hotmath.com
3d. The graph is a line because with each day, the
amount of vegetation increases by 400.
5a. Music Man: t = 45n; Road Tunes: t = 35n; where
t represents the total cost and n represents the
number of hours 5b. The Music Man; The Music
Man charges more.
7 a. t = 3 + 1.75c; where t represents the total
Selected Answers and Solutions
R17
Selected Answers and Solutions
10
9
8
7
6
5
4
3
2
1
7b. Number of
1
2
3
4.75
6.50
8.25
Chores Completed
Total Earned ($)
She went over her limit of text messages in January
and February.
112
17. true; _
+ 2 ≥ 15 + 4(2) - 7, so 16 ≥ 16
8
21a. h = 5w
21b. Weeks Hours
Total Earned
7c.
11
10
9
8
7
6
5
4
3
2
1
(w)
(h)
1
5
2
10
3
15
y
(3, 8.25)
(2, 6.5)
21c.
(1, 4.75)
15
y
19. A
(3, 15)
12
1
0
2
3
x
(2, 10)
9
Hours
Total Earned ($)
Selected Answers and Solutions
earned and c represents the number of chores
6
Number of Chores
(1, 5)
3
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 + 5s
17.
Feet
Yards
3
1
6
2
9
3
12
4
3n
n
Pages 398–399
2
3
4
5x
Weeks
Pages 400–401
Lesson 7-2C
PSI
1. Sample answer: when you are trying to find the
solution of an equation 3. 5 problems worth
2 points each and 2 problems worth 4 points each
5. 8 quarters, 1 dime, 1 nickel, and 5 pennies
7. Sample answer: 7 and 13
9 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
3rd grading period
?
; 12 ft
Lesson 7-2B
1. 7
11
3. no 5. Friday and Saturday 7. 8 9. 0
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
15
1
0
Month
Number
of Texts
t > 55
True
or
False
January
56
56 > 55
True
February
57
57 > 55
True
March
55
55 > 55
False
April
51
51 > 55
False
R18 Selected Answers and Solutions
9
13. Sample answer: The sum of four coins is thirtytwo cents. What are the coins? To solve this
problem, choose any four coins and find 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.
Pages 404–405
Lesson 7-2D
1. ≤ 90
3.
2
3
4
5
6
7
8
9 10 11 12
5.
2
3
4
5
6
7
8
9 10 11 12
7. p ≤ 35
9 s = the amount spent; s ≤ 50
0.10x
5.00
_
≤_
Divide each side by 0.10.
0.10
0.10
11. f > 800
13.
0
1
2
3
4
5
6
7
8
9 10 11
15.
0
1
2
3
4
5
6
7
8
9 10 11
x ≤ 50
1
2
3
4
5
6
7
8
12
10
+ 7
+ 7
_
_
21 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
1 _
1
23. Sample answer: _
, 1, _
5 4 3
11 1
54 3
1
5
50
60
51
60
3
5
20
6
21
17
7
22
6
18
19
20
21
22
8
9
5. 2x ≤ 10; x ≤ 5
10
2
2
3
x≥
4
4
5
11
10
11
12
Divide both sides by 6.
Simplify.
6
1
2
3
3
4
4
5
6
7
8
1
2
3
4
5
6
7
11. t ≤ 4
13. d ≤ 6
4
5
6
7
15. r > 72
71
72
6
2
13 8x + 3 ≥ 43
-3 -3
8x
≥ 40
3
3
5
1
2
70
9
4
5
6
7
8
9
10
11. x ≤ 3
9. w < 5
2
8
6
0
7. y ≤ 1
1
69
12
9. x < 6
Simplify.
1
11
5. 12 + 9.5x ≤ 50; 4 hours
7. x ≥ 5
Divide both sides by 7.
0
10
Write the inequality.
Subtract 4 from each side.
Simplify.
6x
24
_
≥ _
4
-2 -1
9
Lesson 7-2G
3 6x + 4 ≥ 28
-4 -4
6x
≥ 24
Write the inequality.
7
8
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
Lesson 7-2F
16
6
55
60
7
6
4
5
1. h ≥ 19
5
54
60
21. g > 9
27. ham and turkey
_ _
53
60
1. x > 8
25. n > 21
3 7x > 56
56
7x
>
7
7
x>8
52
60
Pages 413–415
2
5
Pages 409–411
7
12
53
_
Simplify.
60
p>
13 14 15 16 17 18 19 20 21 22 23 24
Add _ to both sides.
12
12
_____________
9 10 11
19. s < 20
0
Simplify.
So, Bobby can have a maximum of 50 letters
engraved.
3
7
_
Write the inequality.
19 p - _ >
17.
0
Selected Answers and Solutions
letters. The inequality is 0.10x ≤ 5.00.
0.10x ≤ 5.00 Write the inequality.
73
74
75
17 The number of letters times $0.10 must be less
than or equal to $5.00. Let x = the number of
For Homework Help, go to Hotmath.com
3
4
5
Write the inequality.
Subtract 3 from each side.
Simplify.
8x
40
_
≥ _
Divide each side by 8.
8
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
4
5
6
7
8
9
10
19. b ≥ 3
0
1
2
3
4
5
6
21 current weight + weight gained > 178 pounds
Let x be the number of months.
Selected Answers and Solutions
R19
Selected Answers and Solutions
Then 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
15
>
Divide both sides by 3.
3
3
x>
5
It will take him greater than 5 months.
23. Sample answer: 2x + 2 ≥ 16
25. x ≥ 3
_
9–11.
,(-3, 3)
_
0
1
2
3
4
5
13. U
0
1
2
3
4
5
6
0
1
2
3
4
5
6
33. C and I or G and L
24–29.
Lesson 7-3B
3. 24
-5 -4 -3 -2 -1
0
1
2
3
4
5
7. 5 9. 28 11. 45
13 Spending money means a loss, so the integer
would be -25.
15. -2
17.
-12
-8
-4
0
4
8
12
15. S
17. J
Z
5
4
#(-3, 4)
3
()
% 1.5, 2.5
2
/(1, 2) 3
1
" 4 4, -1 4
5(0, 0) 1 O
Y
-5-4-3-2-1
-1 1 2 3 4 5
'(5, -2)
)(-4, -1) -2
1
1
-3
+ 2 2, -2 2
-4
,(-2, -5) -5
31–33.
19.
%(-1.5, 2.5)
-14 -12 -10 -8 -6 -4 -2
0
2
4
6
8
10
5
4
3
2
1
y
0
-5-4-3 -2-1
-1
21.
-12
-8
-4
0
4
8
+ 2 12 , -2 12
35 The length of the base AB is 4 units. The length
of the height AC is 3 units. Use the formula to find
the area of the triangle.
1
A=_
bh
Area of triangle
2
1
_
A = (4)(3)
2
Replace b with 4 and h with 3.
A=6
Multiply.
The area of the triangle is 6 square units.
y
$
-6 -5 -4 -3 -2
x
0
"
Pages 425–427
1. H
Lesson 7-3C
3. B 5. (0, -2); none 7. gym
R20 Selected Answers and Solutions
" 4 34 , -1 14
1 2 3 4 5x
-2
-3
-4
-5
12 14
23. 18 25. 25
27 ⎪-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
35 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
%(2, 1)
O
19 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
31. x ≥ 3
Pages 421–422
y
x
-5-4-3-2-1
-1 1 2 3 4 5
(
)
0,
-1
/
-2
-3
-4
-5
6
27. 425
29. f > 3
1. 15
5.
5
4
3
2
1
#
23. y = 16x
Batches of
Pretzels (x)
Butter (y)
1
16
2
32
3
48
Selected Answers and Solutions
37. Quadrants II and IV; Sample answer: In both
Quadrants II and IV, the coordinates have different
signs. 39. Sample answer: The first 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 define its unique location.
Any given point is defined by only one ordered
pair. 41. G 43. -3
25. no 27. 27 small cars 29. p ≤ 45
31.
8
9
10
11
12
13
14
33. x > 3
0
Pages 428–433
Chapter Study Guide and Review
1. true 3. true
y
6–8.
10
9
8
7
6
5
4
3
2
1
1
2
3
4
5
6
7
8
9 10 11
5
6
7
8
9 10 11
35. 4g ≤ 12; g ≤ 3
37. x ≥ 8
5. false; x > 7
Z (2, 8 2 )
1
0
1
2
3
4
39.
Y (4.75, 6)
-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
41. 6 43. 16
50–53.
45. 21
47. 5 49. (-4, 3)
y
)(-2, 4)
((4, 1)
X (5, 0)
1 2 3 4 5 6 7 8 9 10 x
O
x
0
9. (11, 5), (12, 5.5), (11.5, 5.25), (12.5, 5.75); They
appear to form a line.
&(2, -1)
'(-3, -2)
y
7
6
(12, 5.5)
5
(11, 5) (11.5, 5.25)
(12.5, 5.75)
Chapter 8 Properties of Triangles
and Quadrilaterals
4
Page 440
3
1. 46
2
Pages 443–445
1
O
11.
2
4
6
8
10
12
Input (x)
3x + 1
1
3(1) + 1
4
3
3(3) + 1
10
7
3(7) + 1
22
2x + 4
Output
5
2(5) + 4
14
6
2(6) + 4
16
7
2(7) + 4
18
13. Input (x)
14
x
Output
15. 2x 17. Multiply each term by 8; 12,288, 93,304
19. y = 7x + 1 21. y = x - 12
For Homework Help, go to Hotmath.com
Are You Ready?
3. 58
5. 19
7. 58
9. 181
11. yes
Lesson 8-1A
1. p
plane; plane JKL
3 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
or FE
; The figure shown is a line that
11 line; EF
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
is parallel to DF
because
23 Sample answer: AC
the lines are the same distance apart and do not
and BE
intersect. AC
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
Selected Answers and Solutions
R21
Selected Answers and Solutions
continues in both directions without
line AB
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.
Pages 448–450
Lesson 8-1B
1 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
11 Using a protractor, the angle of the roof
measures 120°. Since this angle is between 90° and
180° it is an obtuse angle.
13 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 first 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
1
as the _
fraction circle, it is a right angle. If it is less
4
than this fraction circle, it is an acute angle.
Anything greater is an obtuse angle.
29.
1
31.
33.
2
Pages 461–463
35.
Pages 453–456
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
33 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 definition, 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. adjacent
47. Sample answer:
Lesson 8-1C
1. supplementary 3. complementary
30° + x° = 180°
5
- 30
= - 30
x° = 150°
So the value of x is 150. 7. 70 9.
supplementary
pp
11. complementary
13 85° + 95° = 180°
Since the sum of their measures is 180°, the angles
are supplementary. 15. 88 17. 155 19. 35
21. Sample answer: If the measure of ∠1 is 50°,
R22 Selected Answers and Solutions
Lesson 8-2B
1. obtuse 3. scalene
5 60 + 73 + x = 180
133 + x = 180
- 133
= - 133
x =
47
So the value of x is 47.
7. 120 9. obtuse 11. acute
13 The 96° angle is obtuse. This is an obtuse
triangle. 15. equilateral; also isosceles 17. 130
19. 63 21. 35
23 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 flagpole
27. Sample answer: If you know the length of the
sides of a triangle, you can determine if any lengths
Pages 464–465
Lesson 8-2C
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
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
41.
4.6 cm
39. G
3
1 4 in.
4.6 cm
11. $76.95 13 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.
3
1 4 in.
43. 60 45. complementary 47. supplementary
49. 90°; right
Pages 476–479
Pages 470–473
Lesson 8-3B
1. q
quadrilateral 3. square 5. 97
7 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
360
19 62 + 84 + 114 + ∠U =
260 + ∠U = 360
- 260
= - 260
∠U = 100
21. 134.5
23 52 + 52 + 2x + 2x = 360
104 + 4x = 360
- 104
= - 104
4x = 256
256
4x
_
=_
4
4
x = 64
For Homework Help, go to Hotmath.com
3
1 4 in.
Lesson 8-3C
1 The figure is a polygon because no sides cross,
it is a closed figure, 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 figure is not closed.
13 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
21 A decagon has 10 sides. Since it is a regular
decagon, each side is equal. To find the perimeter,
we can multiply 10 times the length of each side,
Selected Answers and Solutions
R23
Selected Answers and Solutions
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
3
1
1
form a triangle because 3_
+ 4_
is less than 8_
and
2
4
4
the theorem states that the sum must be greater
than the sum of both sides.
Selected Answers and Solutions
3.2 centimeters. So the perimeter is 32 centimeters.
23. 1,080° 25a. octagon 25b. 1,080°
25c.
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°
Pages 492–495
1. "
27. Sample answer:
Lesson 8-4B
y
#
$
" #
%
x
0
%
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 find 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
$
3 The figures 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.
y
5.
8
9
8
0
Lesson 8-3D
1. congruent
3 The figures 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
15 Corresponding sides represent the same side of
−−
−−
similar figures. So, DE corresponds to KL.
−−
17. LN 19. similar 21. not similar 23. not similar
25. 132 ft; 112 ft
27 Use equivalent ratios to solve this problem.
;
7.
x
;
9
:
:
y
+
,
+
.
x
0
-
,
× 1.75
12
21
_
=_
.
x
8
× 1.75
So the value of x is 14.
29. Sample answer: Triangle JKL is similar to
triangle TUV.
+
5
7
6
,
Parallelogram DEFG is congruent to
parallelogram QRST.
%
&
2
9 The figures 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.
+
) + y )
19 J(-6, 9)
3
'
(
'
-
5
(
4
31. Sample answer: The figure will have exactly the
R24 Selected Answers and Solutions
( '
0
x
y
9.
Selected Answers and Solutions
21. Sample answer: Z(-1, -4)
y
0
9
:
;
9
x
9
:
;
1
Lesson 8-4C
5
y
3
2
4
3
2
4
0
1
x
1
P(-3, -2), Q(-3, 4), R(-5, 6), S(-5, 0)
3
4
4
11
13.
y
2
x
:
X(1, 0), Y(2, -4), Z(3, -1)
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 find the new
coordinates of rectangle QRST by adding 7 to each
x-coordinate and subtracting 4 from each
y-coordinate. Then graph rectangle QRST and
rectangle QRST on the same coordinate plane.
31. I 33. A(-5, -2), B(-4, 2), C(0, 2), and D(1, -2)
Pages 498–501
;
0
x
0
3
5
15.
2
Q(-2, -4), R(4, -1), S(-1, 0), T(-3, -2)
3.
17.
y
5.
3
x
0
5
19. The figures do not have the same shape and
size. They are not congruent. S was reflected over
the y-axis and the distance from the y-axis did not
change, but the reflection of T was 1 unit up from
the original figure.
21. A and B, C and D 23. figure C
25a. Sample answer:
4
R(-3, -1), S(-2, -3), T(2, -3)
y9
7.
8
:
;
;
25b. Sample answer:
0
:
x
8
9
W(-4, -2), X(1, -4), Y(2, -2), Z(-3, 0)
For Homework Help, go to Hotmath.com
Selected Answers and Solutions
R25
Selected Answers and Solutions
25c. Sample answer:
A(-4, -1), B(0, 0), C(-4, -4)
9. $
27. neither 29. Sample answer: E, H, I
31. Sample answer: When an image is reflected
over the x-axis, the y-coordinates of the vertices are
opposites. When an image is reflected over the
y-axis, the x-coordinates of the vertices are
opposites.
33. F
35.
y
.
/
.
/
-
0
-
0
x
A(-1, 4), B(0, 0), C(-4, 4)
y
11
1
0
0
/
2
x
.
M(3, -4), N(1, -3), P(0, 0), Q(3, -1)
37. neither
Pages 504-506
#
x
0
y
"
13.
Lesson 8-4D
y
y
1.
1
2 x
0
$
"
x
0
/
#
M(3, -4), N(1, -3), P(0, 0), Q(3, -1)
A(0, 0), B(0, -3), C(-3, 0)
y
3.
"
#
x
0
.
15. yes; 45°, 90°, 135°, 180°, 225°, 270°, 315°, and 360°
17 The figure 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:
$
A(0, 0), B(3, 0), C(0, -3)
5 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.
y
21. No; Sample answer: if a figure has rotational
symmetry, then it has at least one line of symmetry.
#
"
0
x
$
R26 Selected Answers and Solutions
8 lines of
symmetry
6 lines of
symmetry
3 lines of
symmetry
y
45.
#
$
" "
Pages 508–513
0
Chapter Study Guide and Review
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. 61
27. rhombus 29. parallelogram 31. yes; 11-sided
polygon 33. 1,440° 35. similar
#
A(0, 0), B(3, -1), C(1, -4)
y
47.
#
$
" "
5
x
0
x
0
$
3
x
$
y
37.
Selected Answers and Solutions
23. Sample answer: Both rotations give the same
result. 25. (4, -3) 27. 75 29. 19
#
A(0, 0), B(-1, -3), C(-4, -1)
4
R(3, 2), S(2, -2), T(6, 2)
39.
y
3
Chapter 9 Perimeter, Area, and
Volume
5
Page 520
Chapter 9
1. 31.4 3. 50.24
11. 103.5 in2
4
Are You Ready?
14
5. 2_
15
3
7. 2_
9. $12.56
4
x
0
Pages 525–527
Lesson 9-1A
units2
R(-2, 5), S(-3, 1), T(1, 5)
y
41.
"
"
$
$
x
0
#
#
A(1, 3), B(-2, -2), C(-4, 0)
1. 12
3. 77 m2 5. 325 yd2 7. 12 units2
Area of parallelogram
9 A = bh
A=8·9
Replace b with 8 and h with 9.
A = 72 cm2 Multiply.
1 2
11. 180 in2 13. 8 ft 15. 166_
ft 17. 227 ft2
2
No;
19
A = bh
Area of parallelogram
20,000 = 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:
y
43. /
-
50 in2
10 in.
23. Sample answer:
.
-
5 in.
7 ft
x
0
.
/
L(-2, 1), M(1, -2), N(-5, -4)
For Homework Help, go to Hotmath.com
196 ft2
28 ft
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
Selected Answers and Solutions
R27
Selected Answers and Solutions
y is less than 5 and the height of the parallelogram is
not greater than y. 31. D 33. D
15. 1,904 in2
17. 50 in2
8 in.
5 in.
Pages 532–534
Lesson 9-1C
1. 6 units2 3. 87.75 m2 5. 45 cm2
9. 198.4 cm2
1
Area of triangle
11 A = _bh
2
1
1
A=_
41 _
(36) Replace b with 41 _12 and h with 36.
2
2
( )
A = 747
Multiply.
The area of the triangle is 747 square feet.
13. 19 cm 15. 4,853.52 ft2
1
bh
Area of triangle
17 a. A = _
2
1
A=_
(5)(n) Replace b with 5 and h with n.
2
5n
A=_
2
O
y
(8, 20)
(6, 15)
(4, 10)
1 2 3 4 5 6 7 8 9 10 x
2
8 cm
12 cm
Pages 537–539
27. 20 m2
29. 38.76 cm2
Lesson 9-1D
ft2
1. 90.4
3. 112 m2
1
_
7 A = 2 h(b1 + b2)
5. 161.5 ft2
Area of trapezoid
Replace h with 12, b1 with 5,
1
A=_
(12)(5 + 23)
and b2 with 23.
2
1
A=_
(12)(28)
Add 5 and 23.
2
A = 168
Multiply.
The area is 168 square yards.
1 2
9. 121 ft2 11. 470_
ft 13. 81 tiles
4
R28 Selected Answers and Solutions
7
22
19. _ × 35 = 110 ft 21. _ × 42 = 132 mm
7
7
23. 37.7 cm
25 First calculate the approximate circumference
of the tree, then divide that number by 6 feet to
find the number of people needed to reach around
the base of the tree.
C = πd
Circumference of a circle
C ≈ 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.
31 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 cm
37. Sample answer:
22
(2, 5)
25. B
Chapter 9-2B
22
17c. The points appear to form a line.
1
19. The formula is _
bh, not bh.
2
b_
· 20
100 =
2
b = 10 m
21. Sample answer:
4 cm
Area of first triangle is
2
24 cm ; Area of second
12 cm
triangle is 48 cm2; 1:2
1
_
or .
23. 40
12
1. 1.5 m 3. 10 in. 5. _ × 21 = 66 ft
7
Circumference of a circle
7 C = πd
C ≈ 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.
22
14
14
9. _ × _
= 2_
in. 11. 2.5 mm 13. 34 cm
7
15
15
22
15. 3.14 × 8 = 25.1 ft 17. _ × 7 = 22 mi
2
30
27
24
21
18
15
12
9
6
3
19 a. You need to calculate the area of the
trapezoid and subtract the area of the building to
find 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.
1
21. 100 cm2 23. Since 9 = _
(1)(b1 + b2), the
2
possible lengths have a sum of 18. 25. 11,000 cm2
7
27. G 29. 988 ft2 31. 21 m 33. 8_
ft 35. 13 yd
Pages 543–546
Multiply.
5n
The expression is _
.
17b.
12 in.
7. 7.5 units2
7 in.
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
9 Since the diameter is 11 feet, we know the
radius is 5.5 feet.
A = πr2
Area of a circle
A = 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
17 circle; You need to calculate the area of the
triangle and the area of the circle and compare them.
1
A=_
bh
Area of triangle
2
1
A=_
(100)(100) Replace b with 100 and h with 100.
2
A = 5,000
Multiply.
The area of the triangle is 5,000 square feet.
A = πr2
Area of a circle
A = 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
Pages 556–558
Lesson 9-3A
Perimeter of a rectangle
1 P = 2b + 2h
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
5 Add all of the distances around the composite
figure.
P = 40 + 21 + 21 + 40 + 21 + 21 Sum of all sides
P = 164 yd
Add.
The perimeter is 164 yards.
7. 62.27 cm 9. 64 ft 11. 106 yd
13 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
30 cm
20 cm
20 cm
17. Sample answer: Perimeter is the distance
around the outside of a figure while area is the
measure of the amount of space enclosed by the
perimeter. 19. D
22
22
3
7
7
×_
= 1_
in2 23. _ × 7 = 22 ft
21. _ × _
7
7
11
11
11
25. 56 ft2
Pages 563–565
1
A=_
h(b1 + b2)
Area of trapezoid
2
Replace h with 4, b1 with 5.3, and
1
A=_
(4)(5.3 + 8)
2
b2 with 8.
1
A=_
(4)(13.3)
Add 5.5 and 8.
2
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
15 a. Find the area of the triangle.
1
A=_
bh
Area of triangle
2
1
_
A = (22.8)(12) Replace b with 22.8 and h with 12.
2
A = 136.8
Multiply.
The area of the triangle is 136.8 square feet.
Find the area of the rectangle.
A = bh
Area of rectangle
A = 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
Pages 566–567
Lesson 9-3D
PSI
1. Sample answer: By making a model, D.J. could
first see if he had enough chairs before setting
them all up. 3. 3 or 4 blocks 5. 16 students
7. 3 hours
9 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
Pages 572–574
1. 15
For Homework Help, go to Hotmath.com
Lesson 9-3C
1. 112 m2 3. 145 m2 5. 189 ft2
7 The figure can be separated into a rectangle
and a trapezoid. Find the area of each and then add
them together.
A = bh
Area of parallelogram
A=8·4
Replace b with 8 and h with 4.
A = 32
Multiply.
The area of the rectangle is 32 square inches.
ft3
Lesson 9-4B
3. 4,986.875 in3
5. 20 in.
Selected Answers and Solutions
R29
Selected Answers and Solutions
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
Selected Answers and Solutions
7
V = bwh
Volume of a rectangular prism
3
3
_
V = (6)(6) 4
Replace b with 6, w with 6, and h with 4 _ .
4
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. >
23 a.
( )
V = bwh
V = (5)(4.5)(2.25)
Volume of a rectangular prism
Replace b with 5, w with 4.5, and h
with 2.25.
Multiply.
V = 50.625
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 overflows.
23c. 50.625 of the total 67.5 cubic inches are filled
50.625
with sand. So, _
= 0.75. After changing 0.75
67.5
to a percent, you know that 75% of the container is
now filled 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
Pages 579–581
Lesson 9-4D
m2
1. 292
3. 298 cm2 5. 256 in2 7. 384.62 cm2
9 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
19 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
R30 Selected Answers and Solutions
Package B
In 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
4
9, or _
27. 231 in3 29. 301.4 ft2
9
Pages 584–589
Chapter Study Guide and Review
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
1
31. _ × 3.14 × 30 × 30 ≈ 1,413 yd2 33. 40 cm
2
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
Page 596
1. 48
Chapter 10
3. 80
Pages 600–601
5. 5 h
Are You Ready?
7. 11.3 in2
Lesson 10-1B
1. 45 ft3 3. 90 in3 5. 336 m3 7. 140.4 m3
Volume of a prism
9 V = Bh
1
_
V = (5.7)(7.6)h Replace B with _12 (5.7)(7.6).
2
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
13 To find the height, substitute the given values
into the formula and then solve for h.
V = Bh
Volume of a prism
(2 )
1
108 = ( _
· 3 · 8) · h
2
108 = 12h
108
·h
_
_
= 12
12
Replace V with 108, b with 3, and
h with 8.
Multiply.
Divide both sides by 12.
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 find the volume. The difference is when
you find the B in the formula for triangular prisms,
1
you will use _
bh instead of base times height.
2
19. H 21. Cabinet A: 3,888 in3; Cabinet B: 4,760 in3;
Tia should purchase cabinet B.
Pages 605–606
1
V=_
(8 · 5)h
3
1
504 = _
(14 · 12)h Replace V with 504 and B with 14 · 12.
3
56
226.2 ≈ 28.26h
226.2
28.26h
_
≈_
28.26
4 ft
4 ft
23. Sample answer: The formula V = πr2h uses
πr2 to find the area of the first “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
Pages 614–616
Divide both sides by 56.
3
than a pyramid. 21. F
3
1
≈_
· 3.14 · 72 · 13
3
3.14(2.5)2(6.2)
Volume of a cone
Replace π with 3.14, r with 7,
and h with 13.
Multiply.
≈ 666.726
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
13 Since the diameter is 250 meters, use 125 meters
for the radius.
1 2
V=_
πr h
Volume of a cone
3
1
V≈_
· 3.14 · 1252 · 1,500
Replace r with 125 and
h with 1,500.
Multiply.
3
23. F
V ≈ 24,531,250
The volume of the volcano is about 24,531,250
cubic meters.
15. 11.0 in.
Volume of a cylinder
Replace π with 3.14, r
with 2.5, and h with 6.2.
Multiply.
17a.
Lesson 10-2B
1. 6,612.8 in3
3 V = πr2h
Lesson 10-2D
1. 307.7 yd3
1
3 V = _πr2h
1
a pyramid multiplies by _
. A prism is 3 times larger
V≈
Divide both sides by 28.26.
8≈h
Simplify.
21. Sample answer: radius, 4 ft; height, 4 ft
Multiply.
9=h
Simplify.
The height is 9 inches.
17. Sample answer: The base of the pyramid is a
1 _
triangle. He should have found V = _
(1 × 6 ×
3 2
7)10; 70 ft3
19. Sample answer: The formula for the volume of
Pages 609–611
28.26
Replace V with 226.2, π with 3.14, and
r with 3.
Multiply.
Replace B with 8 · 5 since the
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
15 To find the height, substitute the given values
into the formula and then solve for h.
1
V=_
Bh
Volume of a pyramid
56
226.2 ≈ 3.14(3)2h
Volume of a pyramid
3
base is a rectangle.
1
V=_
(8 · 5)(10) Replace h with 10.
3
504 = 56h
11. 95.5 in3 13. 150.7 cm3 15. 2,355,000 mm3
17. 2,256.9 cm3
19 The formula calls for the radius, and since the
diameter is 6 cm, the radius is 3 cm.
V = πr2h
Volume of a cylinder
Lesson 10-1D
1. 196 ft3 3. 70 ft3
1
Bh
5 V=_
3
504
56h
_
=_
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.
V ≈ 121.675
The volume is about 121.7 cubic yards rounded to
the nearest tenth.
5. 117.8 ft3 7. 1,921.7 m3
Volume of a cylinder
9 V = πr2h
For Homework Help, go to Hotmath.com
Radius
Height
Volume
(ft3)
Radius
Height
Volume
(ft3)
4
6
100.5
4
6
100.5
5
6
157.0
4
7
117.2
6
6
226.1
4
8
134.0
Selected Answers and Solutions
R31
Selected Answers and Solutions
1
V= _
· b · h · h Triangular base
Volume (ft3)
203
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
y
174
145
Pages 623–624
116
58
= 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.
7 The surface area formula uses radius, and
1
since the diameter is given as 1 inch, the radius is _
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)
1 2 3 4 5 6 7 8 9 x
Radius (ft)
Cone
17c.
203
y
174
145
116
87
58
29
1 2 3 4 5 6 7 8 9 x
Replace π with 3.14, r with 0.5, and h with 180.
Height (ft)
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:
8m
2m
≈ 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
Pages 628–629
1. 450 in3
8m
21. A 23. 3,014.4 mm3
Pages 618–619
Lesson 10-3C
1. 3,014.4 yd2 3. 301.4 in2
5 S.A. = 2πrh + 2πr2 Surface area of a cylinder
87
29
Volume (ft3)
Selected Answers and Solutions
Cone
17b.
Lesson 10-3A
4m
25. 7,385.3 m3
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.
3 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 ft
3 ft
8 ft
R32 Selected Answers and Solutions
Lesson 10-4B
3. 326 m2
5 The top of the figure is a rectangular pyramid
and the bottom is a rectangular prism. To find the
volume of the whole figure, you will find the
volume of each piece and add them together.
1
V=_
Bh
Volume of a pyramid
3
1
=_
(8 · 8)h
Replace B with 8 · 8 since the base is
a rectangle.
3
1
_
= (8 · 8)(6) Replace h with 6.
3
= 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
11 You need to find the surface area of the
television and the surface area of the sides of the
Pages 632–636
Chapter Study Guide and Review
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
Pages 646–648
Lesson 11-1B
1. 2 siblings 3. 7.24 km 5. $7
7 87 + 93 + 86 + 90 + 84 = 440, 440 ÷ 5 = 88;
The mean is 88%.
9 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
For Homework Help, go to Hotmath.com
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; 10
3. mean: $15.98
median: $15.89
mode: $19.99
range: $8.04
5. 23; none; 29
__
7 Mean:
4
97 + 85 + 92 + 86
360
=_
or 90
4
{
Mode: There is no mode.
Median: 85, 86, 92, 97
86
+ 92
178
_
=_
2
2
= 89
9. mean: 45.6; median: 44; mode: 44; range: 12
11. mean: 10; median: 10; mode: 8; range: 9
13 Mode; The mode of the temperatures in
Louisville is 70° and the mode for Lexingtons
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: 6
15b. 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
1 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.
5 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. 1,148
7b. 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. I
15. median: $17; mode: $18; range: $12
Selected Answers and Solutions
R33
Selected Answers and Solutions
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.
Television
In 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.
Cylinder
In 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
Lesson 11-2A
Pages 670–672
1. The mode is Republican. It means that more U.S.
presidents have been Republican than any other
political party.
Tally
Frequency
3
9
3
2
3–4
5–6
7–8
9–10
Students in Marty’s Class
10
3b. _
4
17
5 a. Sample answer:
per hour)
Tally
Frequency
20–29
30–39
40–49
50–59
2
7
4
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
R34 Selected Answers and Solutions
25
–2
9
15
–1
9
20
–2
4
9
–39
9
9
–34
350
10
300
7b. The mode is medium. More T-shirts were sold
9
3
in medium than any other size. 7c. _ or _
30
10
8
6
4
2
0
–29
Frequency
9
11
6
4
9
T-Shirts Sold
Tally
250
5b. Most of the temperatures were either between
42 and 43 or 46 and 47.
–24
7
9
|||| ||
200
46–47
11 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 students
15.
Calories of Various Types of Frozen Bars
–19
4
10
–1
4
||||
9
44–45
Number of States
–14
8
150
|||| |||
5–
9
42–43
99
1
50–
|
0–
4
40–41
0
9
Frequency
9a. Speed (miles
4
0–4
Tally
T-Shirt Size
S
M
L
XL
6
2
Temperatures
7 a.
8
100
Number of
Letters
Frequency
3a.
Lesson 11-2C
1. 36 3. $60.00 - $69.99
5 The bar that shows the greatest number of
cyclists is the interval from 60–64 with a frequency
of 9.
7. 16
9.
Number of States Visited by
Number of Bars
Selected Answers and Solutions
Pages 663–665
Calories
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
Pages 678–680
1.
Lesson 11-3B
Do You Like Surprise Parties?
No Answer
3%
No
25%
Yes
72%
3 42%; There is 11% of students who said they
Troy
25%
1830
Year of
Independence
Omar
19%
11. Sample answer: bar graph;
Melissa
31%
Selected Answers and Solutions
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
Independence of Latin American
Countries
1826
1822
1818
1814
1810
a
a
a ile
or ico ru ela
in vi
bi
nt Boli Ch om uad ex Pe ezu
e
l
M
g
n
Eq
Ar
Co
Ve
Country
Lacey
25%
13 Sample answer:
Number of Neighbors
7 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%
13 135 students; Since 54% of the students that
were surveyed said they preferred apples as their
favorite fruit, find 54% of 250 students.
250 × 0.54 = 135 students
So, 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. A
19.
Test Scores
×
×
×
7
8
9
×
10
11
12
13
14
15
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
five 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.
Bridges
6
12
5
Number of Bridges
Number of Students
10
8
6
4
4
3
2
1
2
0
0
50–
59
60–
69
70–
79
80–
89
240– 311– 361– 411–
310 360 410 460
90–
99
Length (ft)
Percentage on Test
Pages 691–693
Pages 683–685
Lesson 11-4A
1. line plot; The line plot shows the greatest value
as a numerical value rather than a bar. 3. line
graph;
g
p A line graph shows the trend over time.
5 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.
For Homework Help, go to Hotmath.com
Lesson 11-4C
1 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
Selected Answers and Solutions
R35
Monthly Cost to Rent an Apartment
625
Heights (in.)
Tally
Frequency
3
|
1
9
||||
⁄|
6
10
||||
4
11
|
1
12
|||
3
23. 14 students
25.
Favorite Movie Type
600
Rent ($)
Selected Answers and Solutions
because they are much closer in value to most of
the pieces of data. 9. Sample answer: The scale of
the graph is not divided into equal intervals, so
differences in heights appear less than they actually
are.
11 A line graph would allow you to see the
dramatic increase from year to year.
Romance
10%
575
550
525
500
475
0
1
2
3
4
5
Action
25%
Year
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.
Pages 694–695
Comedy
40%
Drama
25%
Lesson 11-4D PSI
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
9 6; 10; In order to find 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
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 Probability
Page 710
Are You Ready?
1. certain 3. impossible 5. _ 7. _ 9. 1
1
2
Pages 714–716
1
1. _
9
1
8
11. _
7
10
Lesson 12-1A
2
3. _
9
5. _ 7. The complement of selecting a
9
“Go Back 1 Space” card is selecting any card other
3
than that card. Its probability is _
, 0.75, or 75%.
5
4
0
9. 0 or _
11. _ 13. _
8
4
1
15 There are 2 chances out of 10 to draw a 7 or 9.
So, the probability of selecting either of those
2
1
numbers is _
or _
.
3
10
5
5
3
7
1
17. _ 19. _ 21. _
2
5
10
Pages 698–703 Chapter Study Guide and Review
1. false; mean 3. false; median 5. true 7. false;
scale 9. 27 days 11. $55 13. 24; 23; 9 15. 42; 36;
46 17. 84; 82; 7 19. Sample answer: Since the set
of data has no extreme values or numbers that are
identical, the mean, 7.1, would best represent the
data.
21. mean: 9.6 in.; median: 10; mode: 9; range: 9;
outlier: 3
R36 Selected Answers and Solutions
23. Picking a black jelly bean is impossible since the
probability of picking a black jelly bean is 0%.
25. Picking a purple, red, or yellow jelly bean is
very likely to happen since the probability of
picking a purple, red, or yellow jelly bean is 90%.
p
27 The complement of selecting a girl is selecting
37
a boy. The probability of the complement is _
,
100
0.37, or 37%.
1
29a. 9 outcomes 29b. _ 31. Sample answer: The
3
9.
#BHFM
5PQQJOH
CVUUFS#
KFMMZ+
DSFBNDIFFTF$
QFBOVUCVUUFS1
CVUUFS#
KFMMZ+
DSFBNDIFFTF$
QFBOVUCVUUFS1
CVUUFS#
KFMMZ+
DSFBNDIFFTF$
QFBOVUCVUUFS1
TFTBNF4
SBJTJO3
Pages 721–723
Lesson 12-1C
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.
1
_
_1
3 16 ; Sample answer: There is a 4 chance she will
1
choose the waves screen saver and a _
chance she
4
will choose the family background photo. So, the
1
1
1
probability of selecting both of those is _
×_
=_
.
4
4DSFFO4BWFS
TUBST
HFPNFUSZ
GMPXFST
XBWFT
4
0VUDPNF
POJPO0
4#
4+
4$
41
3#
3+
3$
31
0#
0+
0$
01
16
1IPUP
0VUDPNFT
GBNJMZ
QVQQJFT
LJUUFOT
TDFOJD
GBNJMZ
QVQQJFT
LJUUFOT
TDFOJD
TUBSTGBNJMZ
TUBSTQVQQJFT
TUBSTLJUUFOT
TUBSTTDFOJD
HFPNFUSZGBNJMZ
HFPNFUSZQVQQJFT
HFPNFUSZLJUUFOT
HFPNFUSZTDFOJD
GBNJMZ
QVQQJFT
LJUUFOT
TDFOJD
GBNJMZ
QVQQJFT
LJUUFOT
TDFOJD
GMPXFSTGBNJMZ
GMPXFSTQVQQJFT
GMPXFSTLJUUFOT
GMPXFSTTDFOJD
XBWFTGBNJMZ
XBWFTQVQQJFT
XBWFTLJUUFOT
XBWFTTDFOJD
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
11. -FUUFS
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13. _;
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USJBOHMF
IFBETUSJBOHMF
IFBSU
IFBETIFBSU
Book
The Poky Little Puppy
Gift Bag
yellow
The Poky Little Puppy
green
The Tale of Peter Rabbit
yellow
DJSDMF
IFBETDJSDMF
The Tale of Peter Rabbit
green
TRVBSF
IFBETTRVBSF
Tootle
yellow
USJBOHMF
UBJMTUSJBOHMF
IFBSU
UBJMTIFBSU
DJSDMF
UBJMTDJSDMF
TRVBSF
UBJMTTRVBSF
Tootle
green
Green Eggs and Ham
yellow
Green Eggs and Ham
green
For Homework Help, go to Hotmath.com
IFBET
UBJMT
Selected Answers and Solutions
R37
Selected Answers and Solutions
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
Selected Answers and Solutions
1
_
15 12 ; 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 threeperson 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
reflect 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.
than having to draw a tree diagram to determine
the probability. 23. G
25. 12
27.
Coin
Spinner
Heads
A
Heads
B
Heads
C
Heads
D
Tails
A
Tails
B
Tails
C
Tails
D
29. _
31. _
3
7
33. _
9
14
4
7
Pages 734–736
Pages 728–730
1. _
1
10
Lesson 12-1E
1. 42 3. 12 5. _ 7. 48 9. 20
64
11 There are 3 possible outcomes to be captain
and 3 possible outcomes to be co-captain.
So, 3 × 3 = 9 possible outcomes.
1
13. 50 15. _
9
3# XIJUFSPBTUCFFG
17 a.
1
8IJUF
8IFBU
Lesson 12-2B
1
_
3 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
1
2
2
1
getting an A is _
×_
=_
or _
.
8
5
20
40
9
1
1
5. _, 0.09, 9% 7. _ 9. _
8
10
4
3
_
; There are 3 green tiles out of 10 so the
11
100
)
XIJUFIBN
5
XIJUFUVSLFZ
#
XIJUFCPMPHOB
3
probability of selecting a green tile is _
. There is
10
1 blue tile out of 10 so the probability of selecting a
1
blue tile is _
. So, the probability of green and blue
4
XIJUFTBMBNJ
3
3
1
is _
×_
=_
.
3#
XIFBUSPBTUCFFG
13. _
)
XIFBUIBN
5
XIFBUUVSLFZ
#
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_
15 a. 4 ; The probability of the DVD being comedy
12
1
is _
or _
and the probability of the DVD not being
4
XIFBUTBMBNJ
10
10
100
1
2
24
12
1
1
1
1
comedy is _
or _
. So, _
×_
=_
.
17b. Sample answer: You can use the
Fundamental Counting Principle to find the total
number of outcomes by multiplying the number of
bread choices (two) by the number of meat choices
(five). So, there are a total of 10 possible
sandwiches.
1
17c. _, 0.1, 10%; Sample answer: There are 2 × 5
10
or 10 different possible outcomes of sandwich
choices. There is 1 possible outcome for a sandwich
that includes white bread and ham. The probability
1
.
of randomly selecting this sandwich is _
10
19. Sample answer: William has 4 shirts that he can
wear with a choice of 3 different pants. He has 12
different possible outfits. 21. Sample answer: You
can use the Fundamental Counting Principle to
calculate the total possibilities of a situation quicker
R38 Selected Answers and Solutions
10
1
25
2
24
2
2
4
15b. _; The probability of the DVD being drama
1
18
8
1
is _
or _
and the probability of the DVD being
3
24
4
1
1
1
1
action is _
or _
. So, _
×_
=_
.
6
24
3
6
18
15c. _; The probability of the DVD being comedy
5
36
20
5
or _
and the probability of the DVD
or drama is _
6
24
5
5
4
1
1
being action is _
or _
. So, _
×_
=_
.
24
6
6
6
36
2
1
1
17. _ 19. _ 21. 72 23. _
5
20
12
Pages 740–742
1
1. _
6
1
3. _
12
Lesson 12-2D
5. _
1
45
7 independent; Sample answer: Spinning the
spinner will not affect the results of rolling a
number cube.
7
5
2
10
3
1
girl is _
and then selecting a boy would be _
. So,
5
2
the probability of selecting a girl then a boy is
3
_3 × _1 = _
.
5
2
one out of four sixth-graders will attend the dance.
25
1
=_
, about 25 of the sixth-graders will
Since _
4
100
15
77
Video 1, Video 2, Video 3
Video 1, Video 3, Video 2
Video 2, Video 1, Video 3
Video 2, Video 3, Video 1
Video 3, Video 1, Video 2
Video 3, Video 2, Video 1
25. _
27. _
7
15
1
5
10
3
1
1
1 1
21a. _ 21b. _ 23. _ 25. B 27. 5/68 29a. _; _
6
8
5 3
12
1
_
29b.
15
29c.
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CMVF
HSFFO
SFE
CMVF
HSFFO
SFE
CMVF
HSFFO
SFE
CMVF
HSFFO
SFE
CMVF
HSFFO
SFE
CMVF
HSFFO
SFE
CMVF
HSFFO
SFE
CMVF
HSFFO
SFE
CMVF
HSFFO
SFE
CMVF
HSFFO
Pages 750–751
Lesson 12-3C PSI
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
9 Sample answer: 2,000 pieces/day × 6 days/
week × 50 wk/yr × 5 yr, or about 3,000,000 pieces
11. 30
Pages 754–757
31. 30
21. _
attend the dance. 19. 35
23. 6 ways
1. true 3. false; multiplication 5. false;
3
3
complement 7. false; outcome 9. _ 11. _
4
4
13. Color
6
outcomes
Style
33. 120
Pages 745–747
Lesson 12-3A
3
3
3
1. _, 0.12, or 12% 3. _, 0.3, or 30% 5. _, 0.6, or
25
5
10
60% 7. 180
9 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
2
in gymnastics. So, _
× 500 = 40 students who
25
would participate in gymnastics.
11a. about 60,000 11b. about 72,500
11c. about 7,200
13 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
3
make about _
× 40 = 6 free throws.
20
15. about 100 times 17. Yes; Mitch can predict that
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Chapter Study Guide and Review
15.
black
classic fit
black
stretch
black
bootcut
blue
classic fit
blue
stretch
blue
bootcut
Pie
apple (A)
peach (P)
cherry (C)
Beverage
Outcome
milk (M)
AM
juice (J)
AJ
tea (T)
milk (M)
AT
PM
juice (J)
PJ
tea (T)
milk (M)
PT
CM
juice (J)
CJ
tea (T)
CT
1 −
1
17. 12 19. _, 0.3, 33_
%
3
3
25. 60 students 27. 4
21. _ 23. _
1
6
3
13
Selected Answers and Solutions
R39
Selected Answers and Solutions
9. _ 11. _ 13. _
34
17
18
15. independent; Sample answer: The first roll will
not affect the results of the second roll.
17 dependent; Sample answer: The first student
already picked a partner, which will affect the pick
for the second student because there will be less
students to choose from.
3
_
, 0.3, 30%; The probability of selecting a
19