1 Review Operations with Fractions and Mixed Numbers Let’s put together everything we have learned about adding, subtracting, multiplying, and dividing fractions and mixed numbers. In your notes, summarize how to add, subtract, multiply, and divide fractions and mixed numbers. Perform the indicated operations. a) 7 12 1 6 5 8 b) 1 9 16 2 2 15 c) 21 8 14 3 d) 8 9 10 3 4 5 e) 3 5 12 9 4 5 f) 5 4 7 Solution a) We have to fi nd the sum 7 12 1 6 5 8 . Do we need a common denominator? Yes! Write each fraction with the LCD, then add. Step 1: Write down the LCD of 7 12 , 1 6 , and 5 8 . LCD 24 Step 2: Rewrite each fraction with the LCD. 7 12 2 2 14 24 1 6 4 4 4 24 5 8 3 3 15 24 Step 3: Add. 7 12 1 6 5 8 14 24 4 24 15 24 Write each fraction with the LCD. 33 24 Add. Ask yourself, “Is 33 24 in lowest terms?” No! Write it in lowest terms. 33 24 33 3 24 3 11 8 or 1 3 8 Therefore, 7 12 1 6 5 8 11 8 or 1 3 8 . We can write the answer as an improper fraction or as a mixed number as long as it is in lowest terms. b) Do we need a common denominator to multiply mixed numbers? No! To multiply 1 9 16 2 2 15 , fi rst change each mixed number to an improper fraction. Then multiply. 1 9 16 2 2 15 25 16 32 15 Write each mixed number as an improper fraction. Divide 25 and 15 by 5; divide 16 and 32 by 16. Multiply numerators, and multiply denominators. 5 25 16 1 2 32 15 3 5 2 1 3 10 3 or 3 1 3 Are 10 3 and 3 1 3 in lowest terms? Yes. EXAMPLE 1 www.mhhe.com/messersmith Putting It All Together 267
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