Summary 155 Section 2.5 Division of Fractions and Applications Key Concepts The reciprocal of is for The product of a fraction and its reciprocal is 1. For example, . Dividing Fractions To divide two fractions, multiply the dividend (the “first” fraction) by the reciprocal of the divisor (the “second” fraction). When dividing by a whole number, first write the whole number as a fraction by writing the whole number over 1. Then multiply by its reciprocal. When simplifying expressions with more than one operation, follow the order of operations. 6 11 11 6 1 a, b 0. ba ab Examples Example 1 The reciprocal of is The reciprocal of 4 is The number 0 does not have a reciprocal because is undefined. Example 2 Example 3 Example 4 3 7 . 58 2 3 d 5 42 7 85 2 12 1 10 7 5 42 1 12 5 42 c a1 6 b 5 42 c 1 36 12 3 1 1 d 9 8 4 9 8 4 1 9 8 1 4 9 32 18 25 30 35 18 25 5 35 30 5 21 25 10 1 4. Section 2.6 Multiplication and Division of Mixed Numbers Key Concepts Multiply Mixed Numbers Step 1 Change each mixed number to an improper fraction. Step 2 Multiply the improper fractions and reduce to lowest terms, if possible. Divide Mixed Numbers Step 1 Change each mixed number to an improper fraction. Step 2 Divide the improper fractions and reduce to lowest terms, if possible. Recall that to divide fractions, multiply the dividend by the reciprocal of the divisor. Examples Example 1 Example 2 6 2 3 2 7 9 12 20 3 25 9 4 20 31 9 3 25 5 12 5 2 2 5 4 4 5 2 1 2 24 51 5 1 21 12 1 12
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