Section 2.6 Multiplication and Division of Mixed Numbers 143 Multiplication and Division of Mixed Numbers Section 2.6 Concepts 1. Multiplication of Mixed Numbers 2. Division of Mixed Numbers 3. Applications of Multiplication and Division of Mixed Numbers Answer 1. 26 5 6 1. Multiplication of Mixed Numbers Recall that to multiply fractions, we write the product of the numerators over the product of the denominators and then simplify. In order to apply this procedure to mixed numbers, we must first convert the mixed numbers to fractions. We have outlined the steps below. Multiplying Mixed Numbers Step 1 Change each mixed number to an improper fraction. Step 2 Multiply the improper fractions and simplify to lowest terms, if 4 TIP: To check whether the answer from Example 1 is reasonable, we can round each factor and estimate the product. 1 5 3 rounds to 3. 3 4 4 rounds to 5. ⎫⎪⎬⎪⎭ 1 5 Thus, which is close to 15 1 5 a3 . b a4 3 4 b 132 152 15, possible (see Section 2.4). Answers greater than 1 may be written as an improper fraction or as a mixed number, depending on the directions of the problem. Example 1 demonstrates this process. Multiplying Mixed Numbers Multiply and write the answer as a mixed number. Solution: Write each mixed number as an improper fraction. Simplify. Multiply. Write the improper fraction as a mixed number. 15 576 5 26 25 1 15 1 5 76 5 16 5 19 41 a3 1 5 b a4 3 4 b 16 5 19 4 a3 1 5 b a4 3 4 b Example 1 Skill Practice Multiply and write the answer as a mixed number. 1. a4 3 5 b a5 5 6 b
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