5-2
5-2 Ratios,
Ratios,Rates,
Rates,and
andUnit
UnitRates
Rates
Warm Up
Problem of the Day
Lesson Presentation
Course
Course
3 3
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
Course 3
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
Course 3
5-2 Ratios, Rates, and Unit Rates
Learn to work with rates and ratios.
Course 3
5-2 Ratios, Rates, and Unit Rates
Vocabulary
rate
unit rate
unit price
Course 3
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
Course 3
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
Course 3
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.
Course 3
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.
Course 3
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.
Course 3
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.
Course 3
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.
Course 3
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.
Course 3
5-2 Ratios, Rates, and Unit Rates
Additional Example 3A: Estimating Unit Rates
Estimate each unit rate.
468 students to 91 computers
Choose a number
455
students
468 students 
close to 468 that
91 computers 91 computers
is divisible by 91.
 5 students
1 computer
Divide to find
students per
computer.
468 students to 91 computers is approximately 5
students per computer.
Course 3
5-2 Ratios, Rates, and Unit Rates
Additional Example 3B: Estimating Unit Rates
Estimate each unit rate.
313 feet in 8 seconds
313 feet
8 seconds

312 feet
8 seconds
Choose a number
close to 313 that
is divisible by 8.

39 feet
1 second
Divide to find feet
per second.
313 feet to 8 seconds is approximately 39 feet per
second.
Course 3
5-2 Ratios, Rates, and Unit Rates
Check It Out: Example 3A
Estimate each unit rate.
583 soccer players to 85 soccer balls.
Choose a number
595
players
583 players 
close to 583 that
85 soccer balls 85 soccer balls
is divisible by 85.
 7 players
1 soccer ball
Divide to find
players per soccer
ball.
583 soccer players to 85 soccer balls is approximately
7 players per soccer ball.
Course 3
5-2 Ratios, Rates, and Unit Rates
Check It Out: Example 3B
Estimate each unit rate.
271 yards in 3 hours
271 yards
3 hours

276 yards
3 hours
Choose a number
close to 271 that
is divisible by 3.

92 yards
1 hour
Divide to find
yards per hour.
271 yards to 3 hours is approximately 92 yards
per hour.
Course 3
5-2 Ratios, Rates, and Unit Rates
Unit price is a unit rate used to compare
price per item.
Course 3
5-2 Ratios, Rates, and Unit Rates
Additional Example 4A: Finding Unit Prices to
Compare Costs
Pens can be purchased in a 5-pack for $1.95
or a 15-pack for $6.20. Which is the better
buy?
price for package = $1.95  $0.39 Divide the price
by the number
number of pens
5
of pens.
price for package = $6.20  $0.41
number of pens
15
The better buy is the 5-pack for $1.95.
Course 3
5-2 Ratios, Rates, and Unit Rates
Additional Example 4B: 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.
Course 3
5-2 Ratios, Rates, and Unit Rates
Check It Out: Example 4A
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.
Course 3
5-2 Ratios, Rates, and Unit Rates
Check It Out: Example 4B
John can buy a 24 oz bottle of ketchup for
$2.19 or a 36 oz bottle for $3.79. Which is the
better buy?
price for bottle
= $2.19  $0.09
number of ounces
24
Divide the price
by the number
of ounces.
price for bottles
= $3.79  $0.11
number of ounces
36
The better buy is the 24-oz jar for $2.19.
Course 3
5-2 Ratios, Rates, and Unit Rates
Lesson Quiz Part 1
1. 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? ≈ 6.94 g/cm3
2. Meka can make 6 bracelets per half hour. How
many bracelets can she make in 1 hour? 12
Estimate the unit rate.
3. $2.22 for 6 stamps
$0.37 per stamp
4. 8 heartbeats in 6 seconds
 1.3 beats/s
Course 3
5-2 Ratios, Rates, and Unit Rates
Lesson Quiz: Part 2
Determine the better buy.
5. A half dozen carnations for $4.75 or a dozen
for $9.24 a dozen
6. 4 pens for $5.16 or a ten-pack for $12.90.
They cost the same.
Course 3