GUIDED PRACTICE
Vocabulary Check
✓
Concept Check
✓
3 • 12 in.
18 in.
2. The ratio is }} = 2:1.
3 APPLY
p
r
?㛭㛭㛭
1. In the proportion ᎏᎏ = ᎏᎏ, the variables s and p are the 㛭㛭㛭㛭
㛭 of the
q
s
proportion and r and q are the 㛭㛭㛭㛭?㛭㛭㛭
㛭 of the proportion. means; extremes
✓
BASIC
ERROR ANALYSIS In Exercises 2 and 3, find and correct the errors.
2.
3.
A table is 18 inches wide
and 3 feet long. The ratio
of length to width is 1 : 6.
3. The Distributive Property
was not used correctly;
10x = 4(x + 6) = 4x + 24,
and x = 4.
Skill Check
ASSIGNMENT GUIDE
Day 1: pp. 461–464 Exs. 12, 16,
20, 24, 28, 32, 36, 40, 44,
45–47, 54–58, 62–66,
68–76 even
10
4
ᎏᎏ = ᎏᎏ
x + 6
x
10x = 4x + 6
AVERAGE
6x = 6
Day 1: pp. 461–464 Exs. 12, 16,
20, 24, 28, 32, 36, 40, 44,
45–47, 51–58, 62–66,
68–76 even
x=1
Given that the track team won 8 meets and lost 2, find the ratios.
ADVANCED
4. What is the ratio of wins to losses? What is the ratio of losses to wins? 4:1; 1:4
5. What is the ratio of wins to the total number of track meets? 4:5
In Exercises 6–8, solve the proportion.
2
3
6. ᎏᎏ = ᎏᎏ
x
9
5
6
7. ᎏᎏ = ᎏᎏ
8
z
6
BLOCK SCHEDULE
A
pp. 461–464 Exs. 12, 16, 20, 24, 28,
32, 36, 44, 45–47, 51–58, 62–66,
68–76 even (with Ch. 7 Assess.)
2
4
8. ᎏᎏ = ᎏᎏ º6
b+3
b
48
}}
5
9. The ratio BC:DC is 2:9. Find the value of x.
6
B
EXERCISE LEVELS
Level A: Easier
10–16
Level B: More Difficult
17–66
Level C: Most Difficult
67
x
27
D
C
PRACTICE AND APPLICATIONS
STUDENT HELP
SIMPLIFYING RATIOS Simplify the ratio.
Extra Practice
to help you master
skills is on p. 817.
16 students
10. ᎏᎏ }2}
24 students 3
48 marbles
11. ᎏᎏ }6}
8 marbles 1
6 meters
13. ᎏᎏ
9 meters
22 feet
12. ᎏᎏ }1}1
52 feet 26
2
}}
3
WRITING RATIOS Find the width to length ratio of each rectangle. Then
simplify the ratio.
14.
36 in.
12 in.
15.
HOMEWORK HELP
Example 1: Exs. 10–24
Example 2: Exs. 29, 30
Example 3: Exs. 31, 32
Example 4: Exs. 57, 58
continued on p. 462
16.
12 in.
3 ft 3
1 ft 1
17. }} or }}; }}
STUDENT HELP
Day 1: pp. 461–464 Exs. 12, 16,
20, 24, 28, 32, 36, 40, 44,
45–47, 51–58, 62–76 even
10 cm
16 mm
2 ft
20 mm
16 mm 4
}}; }}
20 mm 5
7.5 cm
7.5 cm 3
}}; }}
10 cm 4
HOMEWORK CHECK
To quickly check student understanding of key concepts, go
over the following exercises:
Exs. 16, 24, 28, 40, 46, 56, 62. See
also the Daily Homework Quiz:
• Blackline Master (Chapter 8
Resource Book, p. 23)
•
Transparency (p. 56)
12 in. 1
}}; }}
24 in. 2
CONVERTING UNITS Rewrite the fraction so that the numerator and
denominator have the same units. Then simplify.
350 g 350 g 7
3 ft
2 mi 10,560 ft 88
60 cm 60 cm 3
ᎏ
ᎏ
17. ᎏᎏ See margin.18. ᎏᎏ }
}; }}
; }} 19. ᎏ
}; }} 20. ᎏ
12 in.
1 kg }
3000 ft }
1 m 100 }
cm 5
3000 ft 25
1000 g 20
6 yd 18 ft 9
oz 8
2 lb 32 }
400 m 400 m 4
20 oz 20 oz 5
}; }}
; }} 23. ᎏᎏ }}; }} 24. ᎏᎏ }}; }}
21. ᎏᎏ }
22. ᎏᎏ }
10 ft 10 ft 5
20 oz 20 oz 5
0.5 km 500 m 5
4 lb 64 oz 16
8.1 Ratio and Proportion
461
461
STUDENT HELP
COMMON ERROR
EXERCISES 39–44 Students
often use the distributive property
incorrectly when the numerator or
denominator of one of the ratios has
more than one term. Encourage
students to write an intermediate
step using parentheses before
applying the distributive property.
Also, students should check their
work by substituting the value of the
variable into the original equation.
HOMEWORK HELP
continued from p. 461
Example 5: Exs. 33–44
Example 6: Exs. 48–53,
59–61
Example 7: Exs. 48–53,
59–61
FINDING RATIOS Use the number line to find the ratio of the distances.
A
B
0
2
C
4
D
6
8
E
10
14
12
7
}} = 1
BF
BD
7
?㛭㛭㛭
?㛭㛭㛭
26. = 㛭㛭㛭㛭
27. = 㛭㛭㛭㛭
㛭
㛭 }191}
AD
CF
AB
2
?㛭㛭㛭
25. = 㛭㛭㛭㛭
㛭 }3}
CD
F
CF
?㛭 }7}
28. = 㛭㛭㛭㛭㛭㛭
AB
2
29. The perimeter of a rectangle is 84 feet. The ratio of the width to the length is
2:5. Find the length and the width. 30 ft, 12 ft
30. The area of a rectangle is 108 cm2. The ratio of the width to the length is
3:4. Find the length and the width. 12 cm, 9 cm
31. The measures of the angles in a triangle are in the extended ratio of 1:4:7.
Find the measures of the angles. 15°, 60°, 105°
APPLICATION NOTE
EXERCISES 48–50 Additional
information about gravity is available at www.mcdougallittell.com.
32. The measures of the angles in a triangle are in the extended ratio of 2:15:19.
Find the measures of the angles. 10°, 75°, 95°
SOLVING PROPORTIONS Solve the proportion.
x
5
33. = 4
7
20
}}
7
4
10 6
36. = }5}
b
3
5
4
39. = x+3
x
2x
3x º 8
42. = 10
6
12
40
}}
9
y
9
34. = 8
10
36
}}
5
30
14
37. = 5
c
7
}}
3
10
7
35. = 25
z
35
}}
2
d
16
38. = 32
6
3
4
8
40. = 6
yº3
y
7
3
41. = 15
2z + 5
z
5y º 8
5y
43. = º}48}
7
6
5
4
10
44. = 2z + 6
7z º 2 17
USING PROPORTIONS In Exercises 45–47, the ratio of the width to the
length for each rectangle is given. Solve for the variable.
45. AB:BC is 3:8. 16
D
C
46. EF:FG is 4:5. 25
x
FOCUS ON
SCIENCE
6 B
CONNECTION
M
J
12
yⴙ7
APPLICATIONS
A
47. JK:KL is 2:3. 21
E
H
G
40
}}
2
L
F
zⴚ3
K
Use the following information.
The table gives the ratios of the gravity of four different planets to the gravity of
Earth. Round your answers to the nearest whole number.
Planet
RE
FE
L
AL I
MOON’S GRAVITY
INT
Neil Armstrong’s
space suit weighed about
185 pounds on Earth and
just over 30 pounds on the
moon, due to the weaker
force of gravity.
NE
ER T
APPLICATION LINK
www.mcdougallittell.com
462
462
Ratio of gravity
Venus
Mars
Jupiter
Pluto
9
10
38
100
236
100
7
100
48. Which of the planets listed above has a gravity closest to the gravity of Earth?
Venus
49. Estimate how much a person who weighs 140 pounds on Earth would weigh
on Venus, Mars, Jupiter, and Pluto.
Venus: 126 lb; Mars: 53 lb; Jupiter: 330 lb; Pluto 10 lb
50. If a person weighed 46 pounds on Mars, estimate how much he or she would
weigh on Earth. about 121 lb
Chapter 8 Similarity
BASEBALL BAT SCULPTURE A huge, free-standing baseball bat
sculpture stands outside a sports museum in Louisville, Kentucky. It was
patterned after Babe Ruth’s 35 inch bat. The sculpture is 120 feet long.
Round your answers to the nearest tenth of an inch.
STUDENT HELP NOTES
Homework Help Students can
find help for Exs. 57 and 58 at
www.mcdougallittell.com. The
information can be printed out for
students who don’t have access
to the Internet.
51. How long is the sculpture in inches? 1440 in.
52. The diameter of the sculpture near the base is
9 feet. Estimate the corresponding diameter of
Babe Ruth’s bat. about 2.6 in.
53. The diameter of the handle of the sculpture is
3.5 feet. Estimate the diameter of the handle of
Babe Ruth’s bat. about 1.0 in.
USING PROPORTIONS In Exercises 54–56, the ratio of two side lengths of
the triangle is given. Solve for the variable.
54. PQ:QR is 3:4.
P
m
3m ⴙ 6
U
24
3
V
T
j
R
56. WX:XV is 5:7. 4 }2}
55. SU:ST is 4:1. 6
18
2k
S
q
W
INT
STUDENT HELP
NE
ER T
HOMEWORK HELP
Visit our Web site
www.mcdougallittell.com
for help with problem
solving in Exs. 57 and 58.
ENGLISH LEARNERS
EXERCISES 59–61 Being
uncertain of the correct pronunciation of a number of terms in a
problem can distract students
and cause them to lose focus.
Before students begin working on
Exercises 59–61, you may want to
model the pronunciation of Gulliver,
Lilliput, Lilliputian, Brobdingnag,
and Brobdingnagian for the class.
kⴙ2
X
PYTHAGOREAN THEOREM The ratios of the side lengths of ¤PQR to the
corresponding side lengths of ¤STU are 1:3. Find the unknown lengths.
57.
58.
P
5
S
S
q
R
q
R
10
P
9
U
U
36
T
T
RQ = 12, PQ = 13, SU = 15, ST = 39
PR = 3, RQ = 兹91
苶, ST = 30, UT = 3兹91
苶
GULLIVER’S TRAVELS In Exercises 59–61, use the following information.
Gulliver’s Travels was written by Jonathan Swift in
1726. In the story, Gulliver is shipwrecked and
wanders ashore to the island of Lilliput. The
average height of the people in Lilliput is 6 inches.
59. Gulliver is 6 feet tall. What is the ratio of his
height to the average height of a Lilliputian? 12: 1
60. After leaving Lilliput, Gulliver visits the island
of Brobdingnag. The ratio of the average height
of these natives to Gulliver’s height is
proportional to the ratio of Gulliver’s height to
the average height of a Lilliputian. What is the
average height of a Brobdingnagian? 72 ft
ADDITIONAL PRACTICE
AND RETEACHING
For Lesson 8.1:
61. What is the ratio of the average height of
a Brobdingnagian to the average height of
a Lilliputian? 144:1
8.1 Ratio and Proportion
463
• Practice Levels A, B, and C
(Chapter 8 Resource Book, p. 13)
• Reteaching with Practice
(Chapter 8 Resource Book, p. 16)
•
See Lesson 8.1 of the
Personal Student Tutor
For more Mixed Review:
•
Search the Test and Practice
Generator for key words or
specific lessons.
463
xy USING ALGEBRA You are given an extended ratio that compares the
lengths of the sides of the triangle. Find the lengths of all unknown sides.
4 ASSESS
62. BC:AC:AB is 3:4:5.
DAILY HOMEWORK QUIZ
Transparency Available
1. The perimeter of a living room
is 64 ft. The ratio of width to
length is 3:5. What are the
dimensions of the living room?
xⴙ2
A
Test
Preparation
12 ft by 20 ft
2. The measures of the angles of
a triangle are in the extended
ratio of 1:3:5. Find the measures of the angles.
20°, 60°, 100°
8
20
b
C
yⴙ4
D
F
b
H
soil that contains sand, peat moss, and compost in the ratio 2:5:3. How many
pounds of compost does she need to add if she uses three 10 pound bags of
peat moss? D
10
2
4. ᎏᎏ = ᎏᎏ }32}
x+6
A
¡
D
¡
x
Challenge problems for
Lesson 8.1 are available in
blackline format in the Chapter 8
Resource Book, p. 20 and at
www.mcdougallittell.com.
★ Challenge
B
¡
12
C
¡
14
D
¡
15
E
¡
18
20
y
1
obtuse.
C
¡
right.
isosceles.
equilateral.
Æ
67. FINDING SEGMENT LENGTHS Suppose the points B and C lie on AD. What
Æ
AB
2 CD
1
is the length of AC if ᎏᎏ = ᎏᎏ, ᎏᎏ = ᎏᎏ, and BD = 24? 36
BD
3 AC
9
FINDING UNKNOWN MEASURES Use the figure shown, in which
¤STU £ ¤XWV. (Review 4.2)
68. What is the measure of ™X? 20°
S
69. What is the measure of ™V? 95°
W
U
20ⴗ
65ⴗ
70. What is the measure of ™T? 65°
each step of the process.
Sample answer: Use the cross
product property to rewrite the
equation as 10y = 5(3y – 1).
Use the distributive property
to rewrite the equation as
10y = 15y – 5. Subtract 15y from
both sides of the equation to get
–5y = –5, and finally divide by –5
to get y = 1.
B
¡
E
¡
acute.
MIXED REVIEW
ADDITIONAL TEST
PREPARATION
1. WRITING Show how to solve
10
5
the proportion ᎏᎏ = ᎏᎏ. Explain
3y – 1 y
⫺1
⫺1
G
66. MULTIPLE CHOICE If the measures of the angles of a triangle have the ratio
2:3:7, the triangle is D
EXTRA CHALLENGE NOTE
76.
bⴙ3
R
y
16
6
x
64. GH:HR:GR is 5:5:6.
E
AC = 8, AB = 10
EF = 20, DF = 24
GH = HR = 15, GR = 18
65. MULTIPLE CHOICE For planting roses, a gardener uses a special mixture of
A
¡
Solve the proportion.
a 6
3. ᎏᎏ = ᎏᎏ }15}2
63. DE:EF:DF is 4:5:6.
B
T
71. What is the measure of ™U? 95°
Æ
Æ
72. Which side is congruent to TU? WV
冉
1
2
冊
73 º1}}, 3 and (1, 3)
X
V
FINDING COORDINATES Find the coordinates of the endpoints of each
midsegment shown in red. (Review 5.4 for 8.2)
73.
冉 12 12 冊
1 1
1
75. 冉º}}, 3 }}冊 and 冉1}}, 1冊
2 2
2
74.
y
P(1, 1)
A(⫺1, 5)
74. (1, º2) and 3 }}, º1}}
75.
y
x
J(⫺2, 3)
K(1, 4)
x
x
1
A(1, ⫺3)
C (⫺2, 1)
B(3, 1)
x
A⬘(3, ⫺3)
R(1, ⫺5)
œ(6, ⫺4)
L(2, ⫺2)
Æ
76. A line segment has endpoints A(1, º3) and B(6, º7). Graph AB and its
Æ
Æ
image A§B§ if AB is reflected in the line x = 2. (Review 7.2) See margin.
B⬘(⫺2, ⫺7)
B(6, ⫺7)
464
464
Chapter 8 Similarity