Section 2.5 Division of Fractions and Applications 133 1 5 5 1 6 2 1 6 2 12 1 9 12 12 2. 12 21 Example 1 12 6 1 2 2 5 Dividing Fractions To divide two fractions, multiply the dividend (the “first” fraction) by the reciprocal of the divisor (the “second” fraction). The process to divide fractions can be written symbolically as provided b, c, and d are not 0. a b c d a b d c Change division to multiplication. Take the reciprocal of the divisor. Concept Connections Fill in the box to make the rightand left-hand sides equal. 6. 7. 5 1 2 3 1 5 4 7 3 5 4 7 Solution: a. The reciprocal of is . b. The reciprocal of is , or 9. c. First write the whole number 5 as the improper fraction . The reciprocal of is . d. The number 0 has no reciprocal because is undefined. 10 5 1 9 1 1 9 5 2 2 5 2. Division of Fractions To understand the division of fractions, consider 6 . This statement asks, “How many halves ( ) can be found in 6 wholes?” The answer is 12. This result can also be found by multiplying. That is, dividing by is equivalent to multiplying by the reciprocal, In general, to divide two nonzero numbers we can multiply the dividend by the reciprocal of the divisor. This is how we divide by a fraction. Answers 2. 3. 4 4. 5. 1 6. 7. 2 3 5 3 1 7 10 7 Finding Reciprocals Find the reciprocal. a. b. c. 5 d. 0 Skill Practice Find the reciprocal. 7 1 2. 3. 10 4 4. 7 5. 1
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