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5-2 Ratios, Rates, and Unit Rates
Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes
5-2 Ratios, Rates, and Unit Rates
Warm Up
Divide. Round answers to the nearest tenth.
1. 420 23.3
18
2.
73
3.5
21
3. 380 23.8
16
4.
430 23.9
18
5-2 Ratios, Rates, and Unit Rates
Problem of the Day
There are 3 bags of flour for every 2
bags of sugar in a freight truck. A bag
of flour weighs 60 pounds, and a bag of
sugar weighs 80 pounds. Which part of
the truck’s cargo is heavier, the flour or
the sugar?
flour
5-2 Ratios, Rates, and Unit Rates
Learn to work with rates and ratios.
5-2 Ratios, Rates, and Unit Rates
Vocabulary
rate
unit rate
unit price
5-2 Ratios, Rates, and Unit Rates
A rate is a comparison of two quantities
that have different units.
Ratio: 90
3
Rate: 90 miles
3 hours
Read as
“90 miles per 3 hours.”
5-2 Ratios, Rates, and Unit Rates
Unit rates are rates in which the second
quantity is 1.
The ratio 90 can be simplified by dividing:
3
90 = 30
3
1
unit rate: 30 miles, or 30 mi/h
1 hour
5-2 Ratios, Rates, and Unit Rates
Additional Example 1: Finding Unit Rates
Geoff can type 30 words in half a minute. How
many words can he type in 1 minute?
30 words
1
2 minute
Write a rate.
30 words • 2 = 60 words
1
1 minute
2 minute • 2
Multiply to find words
per minute.
Geoff can type 60 words in one minute.
5-2 Ratios, Rates, and Unit Rates
Check It Out: Example 1
Penelope can type 90 words in 2 minutes. How
many words can she type in 1 minute?
90 words
2 minutes
Write a rate.
90 words ÷ 2 = 45 words
2 minutes ÷ 2 1 minute
Divide to find words
per minute.
Penelope can type 45 words in one minute.
5-2 Ratios, Rates, and Unit Rates
Additional Example 2A: Chemistry Application
Five cubic meters of copper has a mass of
44,800 kilograms. What is the density of
copper?
44,800 kg
5 m3
Write a rate.
44,800 kg ÷ 5
5 m3 ÷ 5
Divide to find
kilograms per 1 m3.
8,960 kg
1 m3
Copper has a density of 8,960 kg/m3.
5-2 Ratios, Rates, and Unit Rates
Additional Example 2B: Chemistry Application
A piece of gold with a volume of 0.5 cubic
meters weighs 9650 kilograms. What is the
density of gold?
9650 kg
0.5 m3
Write a rate.
9650 kg • 2
0.5 m3 • 2
Multiply to find
kilograms per 1 m3.
19,300 kg
1 m3
Gold has a density of 19,300 kg/m3.
5-2 Ratios, Rates, and Unit Rates
Check It Out: Example 2A
Four cubic meters of precious metal has a
mass of 18,128 kilograms. What is the
density of the precious metal?
18,128 kg
4 m3
Write a rate.
18,128 kg ÷ 4
4 m3 ÷ 4
Divide to find
kilograms per 1 m3.
4,532 kg
1 m3
Precious metal has a density of 4,532 kg/m3.
5-2 Ratios, Rates, and Unit Rates
Check It Out: Example 2B
A piece of gem stone with a volume of 0.25
cubic meters weighs 3540 kilograms. What
is the density of the gem stone?
3540 kg
0.25 m3
Write a rate.
3540 kg • 4
0.25 m3 • 4
Multiply to find
kilograms per 1 m3.
14,160 kg
1 m3
The gem stone has a density of 14,160 kg/m3.
5-2 Ratios, Rates, and Unit Rates
Additional Example 3A: Application
A driver is competing in a 500-mile auto race.
In the first 2 hours of the race, the driver
travels 356 miles. What is the driver's
average speed?
r=
d
t
356 mi
= 2h
= 178 mi/h
Find the ratio of distance to time.
Substitute 356 for d and 2 hours for t.
Divide to find the unit rate.
The driver's average speed is 178 mi/h.
5-2 Ratios, Rates, and Unit Rates
Additional Example 3B: Application
A driver is competing in a 500-mile auto race.
The driver estimates that he will finish the race
in less than 3 hours. If the driver keeps traveling
at the same average speed, is his estimate
reasonable? Explain.
Determine how long the trip will take.
Use the formula d = rt.
500
= 178t
_
___
178 178
2.8 ≈ t
Substitute 500 for d and 178 for r.
Divide both sides by 178.
Simplify.
Yes; at an average speed of 178 mi/h, the race will
take about 2.8 hours.
5-2 Ratios, Rates, and Unit Rates
Helpful Hint
The formula r = d is equivalent to d= rt,
t
as shown below.
r= d
t
r ▪ t =d ▪ t
t
rt = d
5-2 Ratios, Rates, and Unit Rates
Check It Out: Example 3A
A cyclist is competing in a 70-mile bike race.
In the first 2 hours of the race, the cyclist
travels 14 miles. What is the cyclist's average
speed?
d
r=
Find the ratio of distance to time.
t
14 mi
= 2h
= 7 mi/h
Substitute 14 for d and 2 hours for t.
Divide to find the unit rate.
The cyclist's average speed is 7 mi/h.
5-2 Ratios, Rates, and Unit Rates
Check It Out: Example 3B
A cyclist is competing in a 70-mile bike race.
The cyclist estimates that he will finish the race
in less than 8 hours. If the cyclist keeps traveling
at the same average speed, is the estimate
reasonable? Explain.
Determine how long the trip will take.
Use the formula d = rt.
7t
_70 = ___
7
7
10 = t
Substitute 70 for d and 7 for r.
Divide both sides by 7.
Simplify.
No; at an average speed of 7 mi/h, the race will
take about 10 hours.
5-2 Ratios, Rates, and Unit Rates
Unit price is a unit rate used to compare
price per item.
5-2 Ratios, Rates, and Unit Rates
Additional Example 4: Finding Unit Prices to
Compare Costs
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 for jar
= $2.19  $0.15
number of ounces
15
Divide the price
by the number
of ounces.
price for jar
= $2.78  $0.14
number of ounces
20
The better buy is the 20-oz jar for $2.78.
5-2 Ratios, Rates, and Unit Rates
Check It Out: Example 4
Golf balls can be purchased in a 3-pack for
$4.95 or a 12-pack for $18.95. Which is the
better buy?
price for package = $4.95  $1.65 Divide the price
by the number
number of balls
3
of balls.
price for package = $18.95  $1.58
number of balls
12
The better buy is the 12-pack for $18.95.
5-2 Ratios, Rates, and Unit Rates
Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems
5-2 Ratios, Rates, and Unit Rates
Lesson Quiz: Part I
1. Meka can make 6 bracelets per half hour. How
many bracelets can she make in 1 hour?
≈ 6.94 g/cm3
2. A penny has a mass of 2.5 g and a volume of
approximately 0.360 cm3. What is the
approximate density of a penny? 12
3. Melissa is driving to her grandmother's house.
In the first 3 hours of the drive, she travels
159 miles. What is Melissa's average speed?
53 mi/h
5-2 Ratios, Rates, and Unit Rates
Lesson Quiz: Part II
Determine the better buy.
5. A half dozen carnations for $4.75 or a dozen
for $9.24 a dozen
5-2 Ratios, Rates, and Unit Rates
Lesson Quiz for Student Response Systems
1. John can walk 16 miles in 4 hours. How many
miles can he walk in one hour?
A. 16 miles
B. 8 miles
C. 4 miles
D. 2 miles
5-2 Ratios, Rates, and Unit Rates
Lesson Quiz for Student Response Systems
2. Estimate the unit rate.
272 sailors in 17 ships
A. 12 sailors per ship
B. 14 sailors per ship
C. 16 sailors per ship
D. 18 sailors per ship
5-2 Ratios, Rates, and Unit Rates
Lesson Quiz for Student Response Systems
3. Which of the following would be a better buy
than purchasing 4 mangoes for $16?
A. 2 mangoes for $10
B. half a dozen mangoes for $25
C. 8 mangoes for $ 28
D. one dozen mangoes for $54
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