1. Ratios, Rates, and Unit Rates
5-2
Ratios, Rates, and Unit Rates
Course 3
Warm Up
Problem of the Day
Lesson Presentation

2. Warm Up
Divide. Round answers to the nearest tenth.
420 18
73 21
23.3
3.5
380 16
430 18
23.9
23.8

3. 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

4. Learn to work with rates and ratios.

5. Vocabulary
rate
unit rate
unit price

6. A rate is a comparison of two quantities that have different units.90 3
Ratio:
Read as
“90 miles per 3 hours.”
90 miles
3 hours
Rate:

7. Unit rates are rates in which the second quantity is 1.
The ratio 90 3
can be simplified by dividing: 90 3 30 1 =
30 miles,
1 hour
unit rate:
or 30 mi/h

8. 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 minute 1 2
Write a rate.
30 words • minute • 2 1 2
60 words 1 minute
Multiply to find words per minute. =
Geoff can type 60 words in one minute.

9. 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 ÷ minutes ÷ 2
45 words 1 minute
Divide to find words per minute. =
Penelope can type 45 words in one minute.

10. 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.

11. 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.

12. Precious metal has a density of 4,532 kg/m3.
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.

13. The gem stone has a density of 14,160 kg/m3.
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.

14. Additional Example 3A: Estimating Unit Rates
Estimate each unit rate.
468 students to 91 computers
Choose a number close to 468 that is divisible by 91. 
468 students
91 computers
455 students
Divide to find students per computer. 
5 students
1 computer
468 students to 91 computers is approximately 5 students per computer.

15. Additional Example 3B: Estimating Unit Rates
Estimate each unit rate.
313 feet in 8 seconds
Choose a number close to 313 that is divisible by 8. 
313 feet
8 seconds
312 feet 
39 feet
1 second
Divide to find feet per second.
313 feet to 8 seconds is approximately 39 feet per second.

16. Check It Out: Example 3A
Estimate each unit rate.
583 soccer players to 85 soccer balls.
Choose a number close to 583 that is divisible by 85. 
583 players
85 soccer balls
595 players
Divide to find players per soccer ball. 
7 players
1 soccer ball
583 soccer players to 85 soccer balls is approximately 7 players per soccer ball.

17. Check It Out: Example 3B
Estimate each unit rate.
271 yards in 3 hours
Choose a number close to 271 that is divisible by 3. 
271 yards
3 hours
276 yards 
92 yards
1 hour
Divide to find yards per hour.
271 yards to 3 hours is approximately 92 yards per hour.

18. Unit price is a unit rate used to compare price per item.

19. 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 $ Which is the better buy?
Divide the price by the number of pens.
price for package
number of pens
$1.95 5 = 
$0.39
price for package
number of pens
$6.20 15 = 
$0.41
The better buy is the 5-pack for $1.95.

20. 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 $ Which is the better buy?
Divide the price by the number of ounces.
price for jar
number of ounces
$2.19 15 = 
$0.15
price for jar
number of ounces
$2.78 20 = 
$0.14
The better buy is the 20-oz jar for $2.78.

21. Check It Out: Example 4A
Golf balls can be purchased in a 3-pack for $4.95 or a 12-pack for $ Which is the better buy?
Divide the price by the number of balls.
price for package
number of balls
$4.95 3 = 
$1.65
price for package
number of balls
$18.95 12 = 
$1.58
The better buy is the 12-pack for $18.95.

22. Check It Out: Example 4B
John can buy a 24 oz bottle of ketchup for $2.19 or a 36 oz bottle for $ Which is the better buy?
Divide the price by the number of ounces.
price for bottle
number of ounces
$2.19 24 = 
$0.09
price for bottles
number of ounces
$3.79 36 = 
$0.11
The better buy is the 24-oz jar for $2.19.

23. Lesson Quiz Part 1
1. A penny has a mass of 2.5 g and a volume of approximately cm3. What is the approximate density of a penny?
2. Meka can make 6 bracelets per half hour. How many bracelets can she make in 1 hour?
Estimate the unit rate.
3. $2.22 for 6 stamps
4. 8 heartbeats in 6 seconds
≈ 6.94 g/cm3 12
$0.37 per stamp
 1.3 beats/s

24. Lesson Quiz: Part 2
Determine the better buy.
5. A half dozen carnations for $4.75 or a dozen for $9.24
6. 4 pens for $5.16 or a ten-pack for $12.90.
a dozen
They cost the same.