11-1 Ratios and Rates
Name
Date
A bag of marbles contains 28 red marbles,
30 green marbles, and 24 yellow marbles. What is
the ratio of red marbles to yellow marbles, written
as a fraction in simplest form?
Remember: A ratio is a comparison of two numbers
by division. The ratio a to b can also be written a : b
a
and , where b ⫽ 0.
b
28
number of red marbles
number of yellow marbles
24
28 ⫼ 4 ⫽ 7
Simplify.
24 ⫼ 4 6
Lois walked 12 mi in 5 h. What is her unit rate?
Remember: A rate compares quantities with different
types of units. A unit rate is a rate in which the
denominator is 1.
12 mi
Write as a fraction.
5h
12 mi ⫼ 5 ⫽ 2.4 mi
Divide the numerator and
1h
5h⫼5
denominator by 5.
The unit rate is 2.4 miles per hour
or 2.4 mi/h.
The ratio of red marbles to
yellow marbles is 7.
6
A classroom has 15 boys and 20 girls. Write each ratio as a fraction
in simplest form.
1. girls to boys
2. boys to girls
3. boys to the
entire class
4. girls to the
entire class
3
7
4
7
7. red cars to
blue cars
8. red cars to
black cars
20
20 ⴜ 5
ⴝ
15
15 ⴜ 5
Copyright © by William H. Sadlier, Inc. All rights reserved.
4
3
3
4
A car dealer has 15 red, 22 blue, 8 black, and 30 white cars for sale.
Write each ratio as a fraction in simplest form.
5. red cars to
white cars
6. blue cars to
white cars
15
15 ⴜ 15
ⴝ
30
30 ⴜ 15
1
2
9. white cars to
all cars
2
5
15
22
11
15
10. blue cars to
all cars
11. all cars to
black cars
22
75
Lesson 11-1, pages 280–283.
75
8
15
8
12. all cars to
red cars
5
1
Chapter 11 277
For More Practice Go To:
Write each situation as a unit rate.
13. 620 mi in 8 h
14. 750 mi in 12 h
15. 675 words in 30 min
77.5 mi
620 mi ⴜ 8
ⴝ
1h
8hⴜ8
750 mi ⴜ 12 62.5 mi
ⴝ
1h
12 h ⴜ 12
675 words ⴜ 30 22.5 words
ⴝ
1 min
30 min ⴜ 30
77.5 mi/h
62.5 mi/hr
22.5 words/min
16. 1300 words in 40 minutes
17. $2.25 for 12.5 oz
18. $3.92 for 24.5 ounces
1300 words ⴜ 40 32.5 words
ⴝ
1 min
40 min ⴜ 40
$0.18
$2.25 ⴜ 12.5
ⴝ
1 oz
12.5 oz ⴜ 12.5
$0.16
$3.92 ⴜ 24.5
ⴝ
1 oz
24.5 oz ⴜ 24.5
32.5 words/min
$0.18/oz
$0.16/oz
Convert the units of measure as indicated.
19. 90 km per h to m per min
20. 120 km per h to m per min
1h
90 km
m 1500 m
•
ⴝ
• 1000
60 min
1h
1 km
1 min
1h
1000 m 2000 m
120 km
•
•
ⴝ
60 min
1 km
1 min
1h
1500 m/min
2000 m/min
21. 58 oz per min to lb per h
22. 74 oz per min to lb per h
217.5 lb
58 oz 60 min 1 lb
ⴝ
•
•
1h
1h
1 min
16 oz
74 oz 60 min 1 lb
277.5 lb
•
•
ⴝ
1h
16 oz
1 min
1h
217.5 lb/h
277.5 lb/h
23. 0.5 mm per s to m per h
24. 0.1 km per h to cm per s
1.8 m
1m
0.5 mm 3600 s
ⴝ
•
•
1h
1000 mm
1s
1h
1h
0.1 km
100,000 cm 2.7 cm
≈
•
•
1s
3600 s
1h
1 km
1.8 m/h
2.7 cm/s
25. Shanille bought 4.5 yd of fabric for $28.95
and John bought 2.5 yd of the same fabric for
$14.25. Who spent less per yard of fabric?
Compare unit rates.
$28.95
艐 $6.43/yd
Shanille:
4.5 yd
$14.25
ⴝ $5.70/yd; $5.70 , $6.43;
John:
2.5 yd
John spent less per yard.
5
26. Nancy drove 451.5 mi on 14 gal of gas. Luis
drove 382.2 mi on 12 gal of gas. Whose gas
mileage was better?
Compare unit rates.
451.5 mi
ⴝ 32.25 mi/gal
Nancy:
14 gal
382.2 mi
Luis:
ⴝ 31.85 mi/gal
12 gal
32.25 . 31.85;
Nancy’s car has better milage.
27. A kilometer is about 8 mi. About how many ft per min is 110 km per h?
5 mi
110 km
1h
5280 ft
6050 ft
•
• 8
•
ⴝ
1h
60 min 1 km
1 mi
1 min
110 km/h is about 6050 ft/min.
278 Chapter 11
Copyright © by William H. Sadlier, Inc. All rights reserved.
Solve. Show your work.