Changing Customary Units You can multiply and divide using the relationships below to change from one customary unit to another. Length Changing Customary Units 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 Units 7. Changing Units Using Multiplication EXAMPLE 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 R3R 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 There are 16 oz in a pound, so divide 35 by 16. Changing Customary Units 7. Changing Units Using Division EXAMPLE 2

Divide out “ft” so you are left with “yd.” Write the measurement in fraction form. Change 2 ft to yards yd 3 ft  = 9 ft  1 yd 4  3 ft Multiply by a form of 1. Use. 1 yd 3 ft 2 ft = 3434 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 Units 7. Multiplying by a Form of 1 EXAMPLE 3 2 ft ft 4 = 9 ft 4 =

Camels If a camel is very thirsty, it can drink 30 gallons of water in 10 minutes. How many cups of water is that? ANSWERA 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 c So, 1 gallon = 16 cups. 30 gal  16 c 1 gal = 30 gal  16 c 1 gal = 480 c Changing Customary Units 7. Finding a Relationship EXAMPLE 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. ANSWERThe 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 Units 7. Adding and Subtracting Measures EXAMPLE 5

Changing Customary Units 7. ANSWERThe 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 Measures EXAMPLE 5