Note If we get an improper fraction for a unit of measurement, we usually write it as a mixed number or as a decimal. d) To change 12 oz to pounds, we need to know that 16 oz 1 lb. We are changing from the smaller unit of ounces to the larger unit of pounds, so we will divide. 12 16 12 16 12 4 16 4 3 4 or 0.75 Divide numerator and denominator by 4 to simplify the fraction. Therefore, 12 oz 3 4 lb or 0.75 lb. YOU TRY 2 Convert each measurement to the indicated unit. a) 8000 lb to tons b) 1 1 2 qt to pints c) 12 sec to minutes d) 4.5 yd to feet 3 Use Unit Analysis to Convert Between Units Another way to convert between units is to use unit analysis. This method is commonly used in chemistry, nursing, and other science courses. Recall from our work with ratios that we can divide out common units that appear in the numerator and denominator of a fraction. For example, we can write the ratio 9 feet to 12 feet as 9 ft 12 ft 9 ft 12 ft 3 4 Divide 9 and 12 by 3. because the units divide out. In unit analysis, we divide out like units to help us convert between units and to guide us in performing the conversion correctly. Another concept we need to understand is that of a unit fraction. A unit fraction is a fraction that is equivalent to 1. The measurement equivalencies can be written as unit fractions. For example, we can think of the relationship 12 in. 1 ft as the ratio 12 in. to 1 ft. Then, we can write the ratio 12 in. 1 ft 12 in. 12 in. 1 12 in. 12 in. 1 1 1 1 So, 12 in. 1 ft is a unit fraction because it is equal to 1. All of the equivalencies in the table on p. 433 can be written as unit fractions. To convert from one unit of measurement to another, we will multiply the measurement we are given by the appropriate unit fraction. Write the equivalencies as unit fractions. www.mhhe.com/messersmith SECTION 7.1 Using U.S. Customary Measurements 435
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