Changing Customary Units You can multiply and divide using the relationships below to change from one customary unit to another.

Length

Changing Customary Units7 7.

1 ft = 12 in.

1 yd = 3 ft = 36 in.

1 mi = 1760 yd = 5280 ft

Weight

1 lb = 16 oz

1 T = 2000 lb

Capacity

1 c = 8 fl oz

1 pt = 2 c

1 qt = 2 pt

1 gal = 4 qt

Change 3 ft 7 in. to inches.

a = (3 12) in. + 7 in. Change the feet to inches.

Multiply. = 36 in. + 7 in.

Add. = 43 in.

3 ft 7 in. = 3 ft + 7 in. Write the measure as a sum.

Changing Customary Units7 7.

Changing Units Using MultiplicationEXAMPLE 1

Change 35 oz to pounds. Express the answer in two ways.

ANSWER

There are 2 lb 3 oz in 35 oz. This can also be written as 2 lb.316

16 352 R3

323

You can also interpret the remainder as 3 oz.

You can interpret the remainder as lb, because

the remaining division 3 ÷ 16 can be written as .

316

316

There are 16 oz in a pound, so divide 35 by 16.

Changing Customary Units7 7.

Changing Units Using DivisionEXAMPLE 2

Divide out “ft” so you are left with “yd.”

Write the measurement in fraction form.

Change 2 ft to yards.14

1 yd3 ft

=

9 ft 1 yd

4 3 ft

Multiply by a form of 1. Use . 1 yd3 ft

2 ft = 34

yd

3

1

Multiplying by a Form of 1 You can also change units without deciding whether to multiply or divide. Instead, you always multiply by a fraction that is equal to 1. For example, 1 gal = 4 qt, so = 1. 4 qt

1 gal

Changing Customary Units7 7.

Multiplying by a Form of 1EXAMPLE 3

2 ft14

9 ft4=

9 ft4=

Camels If a camel is very thirsty, it can drink 30 gallons of water in 10 minutes. How many cups of water is that?

ANSWER

A very thirsty camel can drink 480 cups of water in 10 minutes.

Find the relationship between gallons and cups. Use the three relationships 1 gal = 4 qt, 1 qt = 2 pt, and 1 pt = 2 c.

Multiply 30 gal by a form of 1 that relates gallons and cups.

1 gal

4 qt 1 qt

2 pt 1 pt

2 c= 1 gal 1 qt 1 pt

4 qt 2 pt 2 c=

1 gal

16 cSo, 1 gallon = 16 cups.

30 gal 16 c1 gal = 30 gal 16 c

1 gal= 480 c

Changing Customary Units7 7.

Finding a RelationshipEXAMPLE 4

SOLUTION 1

2

Solving a Related Problem To add or subtract customary units, think about how you added and subtracted units of time. You will set up the problem and rename units in the same way.

Model Trains A steam locomotive on a large model train has a length of 3 ft 2 in. The length of a passenger car is 1 ft 11 in.

ANSWER

The train is 5 ft 1 in. long.

SOLUTION

Add. Then rename the sum.

3 ft 2 in.1 ft 11 in.

4 ft 13 in.

+

Rename 4 ft 13 in. as 5 ft 1 in.

How long is a model train with the locomotive and one passenger car?

Changing Customary Units7 7.

Adding and Subtracting MeasuresEXAMPLE 5

Changing Customary Units7 7.

ANSWER

The difference is 1 ft 3 in.

SOLUTION

Rename. Then subtract.

3 ft 2 in.1 ft 11 in.

1 ft 3 in.–

What is the difference in the lengths of the two cars?

2 ft 14 in.1 ft 11 in.–

Rename one of the feet as 12 in.

Solving a Related Problem To add or subtract customary units, think about how you added and subtracted units of time. You will set up the problem and rename units in the same way.

Model Trains A steam locomotive on a large model train has a length of 3 ft 2 in. The length of a passenger car is 1 ft 11 in.

Adding and Subtracting MeasuresEXAMPLE 5