Section 1.1 Fractions 11 5. Dividing Fractions Before we divide fractions, we need to know how to find the reciprocal of a fraction. Notice from Example 5 that and 5 15 The numbers and 13 13 2 are said to be reciprocals because their product is 1. Likewise the numbers 5 and are reciprocals. The Reciprocal of a Number Two nonzero numbers are reciprocals of each other if their product is 1. Therefore, the reciprocal of the fraction because a b b a 1 a b is b a 15 2 2 1. 13 13 2 1 Number Reciprocal Product 15 2 (or equivalently 8) 1 6 2 15 1 8 aor equivalently 6 1 b 2 15 1 8 15 2 1 8 1 8 1 6 6 1 6 1 To understand the concept of dividing fractions, consider a pie that is halfeaten. Suppose the remaining half must be divided among three people, that is, However, dividing by 3 is equivalent to taking of the remaining of the 12 16 12 3 Figure 1-4 pie (Figure 1-4). 1 2 3 1 2 1 3 1 6 12 1 3 1 2 3. This example illustrates that dividing two numbers is equivalent to multiplying the first number by the reciprocal of the second number. Dividing Fractions Let a, b, c, and d be numbers such that b, c, and d are not zero. Then, multiply a b d c reciprocal a b c d To divide fractions, multiply the first fraction by the reciprocal of the second fraction.
miller_beginning_intermediate_algebra_4e_ch1_3
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