4 CHAPTER R Review of Basic Concepts Two numbers are reciprocals of each other if their product is 1. For example, 3 4 # 4 3 = 12 12 , or 1. Division is the inverse or opposite of multiplication, and as a result, we use reciprocals to divide fractions. Figure 3 illustrates dividing fractions. EXAMPLE 4 Multiplying Fractions Multiply 3 8 # 4 9. Write the answer in lowest terms. SOLUTION 3 8 # 4 9 = 3 # 4 8 # 9 Multiply numerators. Multiply denominators. = 12 72 Multiply. = 1 # 12 6 # 12 The greatest common factor of 12 and 72 is 12. = 1 6 1 # 12 6 # 12 = 1 6 # 1 = 1 6 S Now Try Exercise 27. Make sure the product is in lowest terms. 4 4 is equivalent to ∙ , which equals of the circle. 1 8 1 2 1 2 1 4 1 2 Figure 3 Dividing Fractions If a b and c d are fractions 1b≠0, d≠0, c ≠02, then a b ÷ c d = a b # d c . That is, to divide by a fraction, multiply by its reciprocal. (a) 3 4 , 8 5 = 3 4 # 5 8 Multiply by 5 8 , the reciprocal of 8 5. = 3 # 5 4 # 8 Multiply numerators. Multiply denominators. = 15 32 (b) 5 8 , 10 = 5 8 # 1 10 Multiply by 1 10 , the reciprocal of 10. = 5 # 1 8 # 2 # 5 Multiply and factor. = 1 16 Make sure the answer is in lowest terms. Remember to write 1 in the numerator. Think of 10 as 10 1 here. EXAMPLE 5 Dividing Fractions Divide. Write answers in lowest terms as needed. (a) 3 4 , 8 5 (b) 5 8 , 10 (c) 1 2 3 , 4 1 2 SOLUTION
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