5.3 The Rational Numbers 237 Now let’s discuss converting a positive improper fraction to a mixed number. Therefore, = 8 5 1 3 5 The mixed number is 1 . 3 5 Example 2 Converting Mixed Numbers to Improper Fractions Convert the following mixed numbers to improper fractions. a) 3 5 6 b) 5 2 7 Now try Exercise 17 Solution a) = ⋅ + = + = 3 5 6 6 3 5 6 18 5 6 23 6 b) = ⋅ + = + = 5 2 7 7 5 2 7 35 2 7 37 7 Notice that both 23 6 and 37 7 have numerators that are larger than their denominators. Therefore, both numbers are improper fractions. 7 CONVERTING A POSITIVE IMPROPER FRACTION TO A MIXED NUMBER 1. Divide the numerator by the denominator. Identify the quotient and the remainder. 2. The quotient obtained in Step 1 is the integer part of the mixed number. The remainder is the numerator of the fraction in the mixed number. The denominator in the fraction of the mixed number will be the same as the denominator in the original fraction. PROCEDURE Example 3 From Improper Fraction to Mixed Number Convert the following improper fractions to mixed numbers. a) 8 5 b) 225 8 Solution a) Divide the numerator, 8, by the denominator, 5. ) 1 5 8 5 3 Divisor Quotient Dividend Remainder Quotient Remainder Divisor
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