LESSON
Ratios, Rates, and Unit Rates
5-2
Lesson Objectives
Work with rates and ratios
Vocabulary
rate (p. 226) ______________________________________________________
________________________________________________________________
unit rate (p. 226) __________________________________________________
________________________________________________________________
unit price (p. 227) _________________________________________________
________________________________________________________________
Additional Examples
Example 1
Geoff can type 30 words in half a minute. How many words can he type in
1 minute?
words
Write the rate.
minute
words
ⴢ2
minute
Geoff can type
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All rights reserved.
ⴢ2
⫽
words
Multiply to find words per minute.
minute
words in one minute.
98
Holt McDougal Mathematics
LESSON 5-2 CONTINUED
Example 2
A. Five cubic meters of copper has a mass of 44,800 kilograms. What is the
density of copper?
kg
Write the rate.
m3
kg ⫼ 5
Divide to find kilograms per 1 m3.
m3 ⫼ 5
kg
kg/m3.
Copper has a density of
m3
Example 3
A driver is competing in a 500-mile auto race.
A. In the first 2 hours of the race, the driver travels 356 miles. What is the
driver’s average speed?
d
r ⫽ ᎏt
Find the ratio of
⫽
mi
Substitute
h
⫽
mi/h
The driver’s average speed is
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All rights reserved.
to
.
miles for d and
hours for t.
Divide to find the unit rate.
mi/h.
99
Holt McDougal Mathematics
LESSON 5-2 CONTINUED
Example 4
A. Jamie can buy a 15 oz jar of peanut butter for $2.19 or a 20 oz jar for
$2.78. Which is the better buy?
price
$
number of ounces ⫽
⫽
per oz Divide the price by
oz
the number of ounces.
price
$
number of ounces ⫽
艐
per oz
oz
The better buy is the
jar for
.
Check It Out!
1. Heidi can type 90 words in 3 minutes. How many words can she type in
1 minute?
2. Seven cubic meters of bronze has a mass of 58,100 kilograms. What is
the density of bronze?
3. A runner is running a 26-mile marathon. In the first 3 hours of the race,
the runner travels 22.5 miles. What is the runner’s average speed?
4. Erasers can be purchased in a 10-pack for $2.40 or a 15-pack for $3.55.
Which is the better buy?
Copyright © by Holt McDougal.
All rights reserved.
100
Holt McDougal Mathematics
LESSON
Ratios, Rates, and Unit Rates
5-2
Lesson Objectives
Work with rates and ratios
Vocabulary
A comparison of two quantities that have different units.
rate (p. 226) ______________________________________________________
________________________________________________________________
A rate in which the second quantity in the comparison is 1.
unit rate (p. 226) __________________________________________________
________________________________________________________________
A unit rate used to compare price per item.
unit price (p. 227) _________________________________________________
________________________________________________________________
Additional Examples
Example 1
Geoff can type 30 words in half a minute. How many words can he type in
1 minute?
30
words
0.5
minute
30
words
0.5
minute
Write the rate.
ⴢ2
⫽
ⴢ2
Geoff can type 60
Copyright © by Holt McDougal.
All rights reserved.
60
words
1
minute
Multiply to find words per minute.
words in one minute.
98
Holt McDougal Mathematics
LESSON 5-2 CONTINUED
Example 2
A. Five cubic meters of copper has a mass of 44,800 kilograms. What is the
density of copper?
44,800
5
kg
44,800
5
kg ⫼ 5
Divide to find kilograms per 1 m3.
m3 ⫼ 5
8960
kg
1
Write the rate.
m3
Copper has a density of 8960
kg/m3.
m3
Example 3
A driver is competing in a 500-mile auto race.
A. In the first 2 hours of the race, the driver travels 356 miles. What is the
driver’s average speed?
d
Find the ratio of distance to time
r ⫽ ᎏt
⫽ 336
mi
2
⫽ 178
h
mi/h
The driver’s average speed is 178
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All rights reserved.
Substitute 336
2
.
miles for d and
hours for t.
Divide to find the unit rate.
mi/h.
99
Holt McDougal Mathematics
LESSON 5-2 CONTINUED
Example 4
A. Jamie can buy a 15 oz jar of peanut butter for $2.19 or a 20 oz jar for
$2.78. Which is the better buy?
price
$ 2.19
number of ounces ⫽
15 oz
⫽ $0.146
the number of ounces.
price
$ 2.78
number of ounces ⫽
20
per oz Divide the price by
艐 $0.139
per oz
oz
The better buy is the 20 oz
jar for $2.78
.
Check It Out!
1. Heidi can type 90 words in 3 minutes. How many words can she type in
1 minute?
30 words
2. Seven cubic meters of bronze has a mass of 58,100 kilograms. What is
the density of bronze?
8300 kg/m3
3. A runner is running a 26-mile marathon. In the first 3 hours of the race,
the runner travels 22.5 miles. What is the runner’s average speed?
7.5 mi/h
4. Erasers can be purchased in a 10-pack for $2.40 or a 15-pack for $3.55.
Which is the better buy?
15-pack for $3.55
Copyright © by Holt McDougal.
All rights reserved.
100
Holt McDougal Mathematics