Name
Class
Date
Practice 4-1 Ratios
Write a ratio for each situation in three ways.
1. Ten years ago in Louisiana, schools averaged 182 pupils for every 10 teachers.
2. Between 1899 and 1900, 284 out of 1,000 people in the United States were 5–17 years old.
All rights reserved.
Use the chart below for Exercises 3–4.
Three seventh-grade classes were asked whether they wanted chicken
or pasta served at their awards banquet.
Room Number
201
202
203
Chicken
10
8
16
Pasta
12
17
10
3. In room 201, what is the ratio of students who prefer chicken to
students who prefer pasta?
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4. Combine the totals for all three rooms. What is the ratio of the
number of students who prefer pasta to the number of students
who prefer chicken?
Write each ratio as a fraction in simplest form.
5. 12 to 18
6. 81 : 27
7.
6
28
Tell whether the ratios are equivalent or not equivalent.
8. 12 : 24, 50 : 100
9.
22 1
,
1 22
10. 2 to 3, 24 to 36
11. A bag contains green, yellow, and orange marbles. The ratio of
green marbles to yellow marbles is 2 : 5. The ratio of yellow
marbles to orange marbles is 3 : 4. What is the ratio of green
marbles to orange marbles?
Practice
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Name
Class
Practice 4-2 Date
Unit Rates and Proportional Reasoning
Write the unit rate for each situation.
1. travel 250 mi in 5 h
3. read 80 pages in 2 h
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2. earn $75.20 in 8 h
4. type 8,580 words in 2 h 45 min
3
7
5. complete of a puzzle in h
4
8
6. drink
4
L in 1 h
5
4
Find each unit price. Then determine the better buy.
7. paper: 100 sheets for $.99
8. peanuts: 1 lb for $1.29
500 sheets for $4.29
12 oz for $.95
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9. crackers: 15 oz for $1.79
10. apples: 3 lb for $1.89
12 oz for $1.49
5 lb for $2.49
11. mechanical pencils: 4 for $1.25
12. bagels: 4 for $.89
25 for $5.69
6 for $1.39
13. a. Yolanda and Yoko ran in a 100-yd dash.When Yolanda
crossed the finish line,Yoko was 10 yd behind her. The girls
then repeated the race, with Yolanda starting 10 yd behind the
starting line. If each girl ran at the same rate as before, who
won the race? By how many yards?
b. Assuming the girls run at the same rate as before, how far
behind the starting line should Yolanda be in order for the
two to finish in a tie?
Practice
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Name
Class
Date
Practice 4-3
Proportions
Determine if the ratios in each pair are proportional.
1. 12 , 30
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16 40
4. 45 , 75
24 40
7. 2 , 20
14 35
10. 3 , 8 4 10
2. 8 , 15 12 21
5. 5 , 80
9 117
8. 9 , 21
6 14
11. 20 , 17 4 3
27
,
21
15
6. ,
25
24
9. ,
15
25
12. ,
6
3.
81
56
75
125
16
10
9
8
Decide if each pair of ratios is proportional.
13. 14  9 10
7
14. 18  36
8
16
15. 6  15 10
25
16. 7  4
9
16
17. 6  12 4
8
18. 19  114
8
3
19. 5  6 14
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15
20. 6  8
27
36
21. 27  45 15
25
22. 3  4
18
20
23. 5  15 2
6
24. 20  4
3
15
Solve.
25. During the breaststroke competitions of the 1992 Olympics,
Nelson Diebel swam 100 meters in 62 seconds, and Mike
Bowerman swam 200 meters in 130 seconds. Are the rates
proportional?
26. During a vacation, the Vasquez family traveled 174 miles in
3 hours on Monday, and 290 miles in 5 hours on Tuesday. Are the
rates proportional?
Practice
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Name
Class
Date
Practice 4-4
Solving Proportions
Use mental math to solve for each value of n.
1. n 5 20 35
14
24
3.
5 16 n
10
2. 9 5
6
4. 3 5
4
21
n
n 10
Solve each proportion using cross products.
5. k 5 14 All rights reserved.
8
4
k 5
9. 36 5 n 32
8
n 5
6. u 5 10 5
3
u 5
7. 14 5 d 6
15
d 5
8. 5 5 m
1
4
m 5
10. 5 5 1x 30
x 5
11. t 5 5 10
4
t 5
12. 9 5 v
2
4
v 5
Solve.
13. A contractor estimates it will cost $2,400 to build a deck
to a customer’s specifications. How much would it cost to
build five similar decks?
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14. A recipe requires 3 c of flour to make 27 dinner rolls. How much
flour is needed to make 9 rolls?
Solve using a calculator, paper and pencil, or mental math.
15. Mandy runs 4 km in 18 min. She plans to run in a 15 km race.
How long will it take her to complete the race?
16. Ken’s new car can go 26 miles per gallon of gasoline. The car’s gasoline
tank holds 14 gal. How far will he be able to go on a full tank?
17. Eleanor can complete two skirts in 15 days. How long will it take
her to complete eight skirts?
18. Three eggs are required to make two dozen muffins. How many
eggs are needed to make 12 dozen muffins?
Practice
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Name
Class
Date
Practice 4-5 Similar Figures
k MNO , k JKL. Complete each statement.
N
32
M
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1. M corresponds to
20
24
O
24
.
15
L
2. L corresponds to
.
4. MN corresponds to
.
5. What is the ratio of the lengths of the corresponding sides?
The pairs of figures below are similar. Find the value of each variable.
6. 5
5
5
x
4
7.
18
24
5
y
16
5
8.
6
20
9.
y
20
14
x
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18
J
.
3. JL corresponds to
K
15
10.
5
8
x
11.
x
10
8
x
15
6
9
4
12. On a sunny day, if a 36-inch yardstick casts a 21-inch shadow,
how tall is a building whose shadow is 168 ft?
13. Oregon is about 400 miles from west to east, and 300 miles from
north to south. If a map of Oregon is 15 inches tall (from north
to south), about how wide is the map?
Practice
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Name
Class
Date
Practice 4-6
Maps and Scale Drawings
The scale of a map is 2 cm : 21 km. Find the actual distances for the
following map distances.
1. 9 cm 2. 12.5 cm
3. 14 mm
4. 3.6 m
5. 4.5 cm 6. 7.1 cm All rights reserved.
A scale drawing has a scale of 1 in. : 12 ft. Find the length on the
4
drawing for each actual length.
7. 8 ft 8. 30 ft
9. 15 ft
10. 18 ft
11. 20 ft
12. 40 ft
Use a metric ruler to find the approximate distance between the towns.
13. Hickokburg to Kidville
scale: 1 cm to 20 km
14. Dodgetown to Earp City
47
180
15. Dodgetown to Kidville
Holiday
Lake
Dodgetown
Earp City
16. Kidville to Earp City
Hickokburg
17. Dodgetown to Hickokburg
47
Kidville
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18. Earp City to Hickokburg
Solve.
19. The scale drawing shows a two-bedroom
apartment.The master bedroom is 9 ft 3 12 ft.
Use an inch ruler to measure the drawing.
.
b. Write the actual dimensions in place of the
scale dimensions.
Master
Bedroom
Bedroom
Living
Room
Dining
Room
Den
Kitchen
a. The scale is
Practice
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Name
Class
Date
Practice 4-7 Proportional Relationships
Determine whether each table or graph represents a proportional
relationship. Explain your reasoning.
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1.
x
1
3
6
8
9
y
4.5
13.5
24
36
38
2.
3. 12
10
8
6
4
2
0
x
1
5
8
11
12
y
8
5
40
5
64
5
88
5
96
5
4. 20
16
12
8
4
0
2
4
6
8
0
10
0
2
4
6
8
10
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
Find the constant of proportionality for each table of values.
5.
Roses
Price
6
12
Gallons
Miles
c 5
6. Tomatoes (lb)
3
7
$4.47
Price
$22.50 $45.00 $90.00
9
$10.43 $13.41
c 5
c 5
7.
24
5
10
15
120
240
360
8.
Seconds
Feet
2
500
6
8
1,500 2,000
c 5
Write an equation using the constant of proportionality to describe
the relationship.
9. A boat that has traveled 8 leagues from shore is 24 nautical
miles out. Find the number of miles m in l leagues.
10. Four score years ago is 80 years past. Find the number of
years y in s scores.
Practice
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