1. Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes

2. Warm Up
Divide. Round answers to the nearest tenth.
73 21
23.3
3.5
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: 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? d t
r =
Find the ratio of distance to time. =
356 mi
2 h
Substitute 356 for d and 2 hours for t.
= 178 mi/h
Divide to find the unit rate.
The driver's average speed is 178 mi/h.

15. 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
Substitute 500 for d and 178 for r.
Divide both sides by 178.
2.8 ≈ t
Simplify.
Yes; at an average speed of 178 mi/h, the race will take about 2.8 hours.

16. Helpful Hint
The formula r = is equivalent to d= rt,
as shown below.
r =
r ▪ t = ▪ t
rt = d
d t

17. 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 t
r =
Find the ratio of distance to time. =
14 mi
2 h
Substitute 14 for d and 2 hours for t.
= 7 mi/h
Divide to find the unit rate.
The cyclist's average speed is 7 mi/h.

18. 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.
_ ___
70 = 7t
Substitute 70 for d and 7 for r.
Divide both sides by 7.
10 = t
Simplify.
No; at an average speed of 7 mi/h, the race will take about 10 hours.

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

20. 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 $ 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 4
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. Lesson Quiz for Student Response Systems
Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems 22 22

23. Lesson Quiz: Part I
1. Meka can make 6 bracelets per half hour. How many bracelets can she make in 1 hour?
2. A penny has a mass of 2.5 g and a volume of approximately cm3. What is the approximate density of a penny?
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?
≈ 6.94 g/cm3 12
53 mi/h

24. Lesson Quiz: Part II
Determine the better buy.
5. A half dozen carnations for $4.75 or a dozen for $9.24
a dozen

25. 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 25 25

26. 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 26 26

27. 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 27 27