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

2. Warm Up
Find each unit rate.
1. jump rope 192 times in 6 minutes
2. four pounds of bananas for $2.36
3. 16 anchor bolts for $18.56
movies on 9 shelves
32 jumps/min
$0.59/lb
$1.16/bolt
32 movies/shelf

3. Problem of the Day
Replace each • with a digit from 0 to 6 to make equivalent ratios. Use each digit only once.
Possible answer: 13 65 4 20 = •• • •• =

4. Learn to use one or more conversion factors to solve rate problems.

5. Vocabulary
conversion factors

6. The process of converting from one unit to another is called dimensional analysis, or unit analysis. To convert units, multiply by one or more ratios of equal quantities called conversion factors.
For example, to convert inches to feet you would use the ratio below as a conversion factor.
1 ft
12 in.

7. Multiplying by a conversion factor is like multiplying by 1.
1 ft
12 in.
12 in.
1 ft =
, or = 1

8. Be sure to put the units you are converting to in the numerator and the units you are converting from in the denominator.
Caution!

9. Additional Example 1A: Using Conversion Factors
Convert each measure.
63 feet to yards
Multiply by the conversion factor.
Divide out common units. Then multiply.
63 feet is equal to 21 yards.

10. Additional Example 1B: Using Conversion Factors
Convert each measure.
5.2 meters to centimeters
Multiply by the conversion factor.
Divide out common units. Then multiply.
5.2 meters is equal to 520 centimers.

11. 8 pounds is equal to 128 ounces.
Check It Out: Example 1
Convert each measure.
8 pounds to ounces
Multiply by the conversion factor.
Divide out common units. Then multiply.
8 pounds is equal to 128 ounces.

12. Additional Example 2: Problem Solving Application
A car traveled 60 miles on a road in 2 hours. How many feet per second was the car traveling?

13. Understand the Problem1
Understand the Problem
The problem is stated in units of miles and hours. The question asks for the answer in units of feet and seconds. You will need to use several conversion factors.
List the important information:
5280 ft
1 mi
• Feet to miles
1 h
60 min
• Hours to minutes
1 min
60 s
• Minutes to seconds

14. 2
Make a Plan
Multiply by each conversion factor separately, or simplify the problem and multiply by several conversion factors at once.

15. First, convert 60 miles in 2 hours into a unit rate.
Solve 3
First, convert 60 miles in 2 hours into a unit rate.
60 mi
2 h
(60÷2) mi
(2÷2) h =
30 mi
1 h =
Create a single conversion factor to convert hours directly to seconds:
minutes to seconds
1 min
60 s
hours to minutes
1 h
60 min
1 h
60 min
1 min
60 s
1 h
3600 s =
hours to seconds = •
30 mi
1 h •
5280 ft
1 mi
3600 s
Set up the conversion factors.

16. Do not include the numbers yet.3
Solve Continued
Do not include the numbers yet.
Notice what happens to the units. mi h • ft s
Simplify. Only remains. ft s •
30 mi
1 h
5280 ft
1 mi
3600 s
Multiply.
30 • 5280 ft • 1
1 • 1 • 3600 s =
158,400 ft
3600 s =
44 ft
1 s
The car was traveling 44 feet per second.

17. A rate of 60 miles in 2 hours is 30 mi/h or 0.5 mi/min.4
Look Back
A rate of 60 miles in 2 hours is 30 mi/h or 0.5 mi/min.
Since 0.5 mi/min is less than 3000 ft/
60 s or 50 ft/s and 44 ft/s is less than 50 ft/s, then 44 ft/s is a reasonable answer.

18. Check It Out: Example 2
A train traveled 180 miles on a railroad track in 4 hours. How many feet per second was the train traveling?

19. Understand the Problem1
Understand the Problem
The problem is stated in units of miles and hours. The question asks for the answer in units of feet and seconds. You will need to use several conversion factors.
List the important information:
5280 ft
1 mi
• Feet to miles
1 h
60 min
• Hours to minutes
1 min
60 s
• Minutes to seconds

20. 2
Make a Plan
Multiply by each conversion factor separately, or simplify the problem and multiply by several conversion factors at once.

21. First, convert 180 miles in 4 hours into a unit rate.
Solve 3
First, convert 180 miles in 4 hours into a unit rate.
180 mi
4 h
(180 ÷ 4) mi
(4 ÷ 4) h
45 mi
1 h = =
Create a single conversion factor to convert hours directly to seconds:
minutes to seconds
1 min
60 s
hours to minutes
1 h
60 min
1 h
60 min
1 min
60 s
1 h
3600 s =
hours to seconds = •
45 mi
1 h •
5280 ft
1 mi
3600 s
Set up the conversion factors.

22. Do not include the numbers yet.3
Solve Continued
Do not include the numbers yet.
Notice what happens to the units. mi h • ft s
Simplify. Only remains. ft s •
45 mi
1 h
5280 ft
1 mi
3600 s
Multiply.
45 • 5280 ft • 1
1 • 1 • 3600 s =
237,600 ft
3600 s =
66 ft
1 s
The train was traveling 66 feet per second.

23. 4
Look Back
A rate of 66 ft/s is more than 50 ft/s. A rate of 180 miles in 4 hours is 45 mi/h or 0.75 mi/min.
Since 0.75 mi/min is more than 3000 ft/60 s or 50 ft/s and 66 ft/s is more than 50 ft/s, then 66 ft/s is a reasonable answer.

25. Additional Example 3: Converting Between Systems
Owen is 6 feet tall. To the nearest whole number, what is his height in centimeters?
6 ft ·
12 in
1 ft
1 in
2.54 cm
Multiply by conversion factors.
6 ft 1
12 in
1 ft
2.54 cm
1 in
Divide out common units. Then multiply. cm 1
≈ 183 cm
Owen is about 183 centimeters in height.

26. Check It Out: Example 4
The ladder is 9 feet tall. To the nearest whole number, what is the height in centimeters?
9 ft ·
12 in
1 ft
1 in
2.54 cm
Multiply by conversion factors.
9 ft 1
12 in
1 ft
2.54 cm
1 in
Divide out common units. Then multiply. cm 1
≈ 274 cm
The ladder is about 274 centimeters in height.

27. Lesson Quiz for Student Response Systems
Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems 27 27

28. Lesson Quiz
Convert each measure.
pounds to ounces
2. 35 grams to kilograms
3. A cheetah was timed running 200 yards in 6 seconds. What was the average speed in miles per hour?
4. How many millimeters does a 2 quart container of milk hold?
72 oz
0.035 kg
≈ 68 mi/h mL

29. Lesson Quiz for Student Response Systems
1. Identify the appropriate factor for the conversion.
meter to centimeter A. B. C. D. 29 29

30. Lesson Quiz for Student Response Systems
2. A cow gives 18 liters of milk per day. How many gallons of milk does it give in a year?
A.  1720 gal/yr
B.  1736 gal/yr
C.  1756 gal/yr
D.  1776 gal/yr 30 30

31. Lesson Quiz for Student Response Systems
3. A large ant can move 24 cm in 3 seconds. What was its average speed in meters per hour?
A. 288 m/h
B. 278 m/h
C. 250 m/h
D. 208 m/h 31 31