2 Add Mixed Numbers with Regrouping Sometimes, adding mixed numbers involves regrouping. Let’s learn what regrouping is. EXAMPLE 2 Write a procedure for regrouping mixed numbers in this way. Explain why 5 7 4 is not in simplest form. Then, write it in simplest form. Solution A mixed number is not in simplest form if its fractional part is an improper fraction. 5 7 4 is not in simplest form because 7 4 is an improper fraction. To simplify 5 7 4 , write 7 4 as a mixed number to regroup the fractional part with the whole-number part. 5 7 4 5 7 4 Meaning of a mixed number Change 7 4 to a mixed number to regroup the whole-number part. Add. 5 1 3 4 6 3 4 Written in simplest form, 5 7 4 6 3 4 . The fractional part is a proper fraction, and it is in lowest terms. YOU TRY 2 Explain why 6 8 5 is not in simplest form. Then, write it in simplest form. Now, let’s add two mixed numbers using regrouping. EXAMPLE 3 Add 3 7 9 1 1 2 . Solution Write 7 9 and 1 2 as equivalent fractions with the least common denominator. The LCD of 7 9 and 1 2 is 18. 7 9 2 2 14 18 1 2 9 9 9 18 3 7 9 1 1 2 3 14 18 1 9 18 Write the fractions with the LCD. 23 18 4 Add. www.mhhe.com/messersmith SECTION 4.5 Adding and Subtracting Mixed Numbers 259
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