Definition/Procedure Example Add Mixed Numbers with Regrouping Sometimes, the sum of mixed numbers must be simplifi ed using regrouping. (p. 259) Add 7 3 4 1 2 3 . 7 3 4 1 2 3 7 9 12 1 8 12 Write the fractions with the LCD. 8 17 12 Add. Is 8 17 12 in simplest form? No! 17 12 is an improper fraction. Simplify 8 17 12 by regrouping. 8 17 12 8 17 12 8 1 5 12 9 5 12 Write the improper fraction as a mixed number. The fi nal answer is 9 5 12 . Subtract Mixed Numbers with Regrouping We regroup in a subtraction problem when the fraction in the second mixed number is larger than the fraction in the fi rst mixed number. (p. 260) Subtract 6 2 9 3 7 9 . The fraction in the second mixed number is larger than the fraction in the fi rst mixed number. Therefore, we must regroup or borrow 1 from the whole-number part of the fi rst mixed number, 6 2 9 . Write 6 as 5 1. 6 2 9 6 2 9 u 5 1 2 9 5 9 9 2 9 5 11 9 Rewrite 1 as 9 9 . Now, subtract. 6 2 9 3 7 9 5 11 9 3 7 9 2 4 9 These are equivalent. Add and Subtract Mixed Numbers Using Improper Fractions 1) Change each mixed number to an improper fraction. 2) Add or subtract the fractions. 3) Write the answer in lowest terms. If it is an improper fraction, change it to a mixed number. (p. 262) Add 2 1 10 1 4 5 by changing the mixed numbers to improper fractions. 2 1 10 1 4 5 21 10 9 5 Write the mixed numbers as improper fractions. 21 10 18 10 Multiply 9 5 by 2 2 to get a common denominator. 39 10 Add. 3 9 10 Write the result as an improper fraction. Because the numbers in the original problem were mixed numbers, we write the result as a mixed number, if possible. 284 CHAPTER 4 Adding and Subtracting Fractions www.mhhe.com/messersmith
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