Section 1.2 Fractions Review 19 ������������������������ Two numbers are reciprocals if their product is 1. The reciprocal of c d is d c since c d · d c = c · d d · c = 1 Dividing fractions is related to multiplying fractions. For example, we know 30 ÷ 6 = 5, but we also know 30 · 1 6 = 30 1 · 1 6 = 30 6 = 5 Therefore, 30 ÷ 6 = 30 · 1 6 This illustrates that dividing by a number is the same as multiplying by the reciprocal of the number. �������������������� Dividing Fractions For b, c, d 2 0, a b ÷ c d = a b · d c �� ������������������������ ������������������ Divide the fractions and write each answer in lowest terms. 5a. 8 7 ÷ 12 14 5b. 3 5 ÷ 9 5c. 3 3 7 ÷ 7 15 8 7 Solutions 5a. ÷ 12 14 = 8 7 · 14 12 = 8 · 14 7 · 12 = 2 · 2 · 2 · 2 · 7 7 · 2 · 2 · 3 = 2 · 2 3 = 4 3 3 5 5b. ÷ 9 = 3 5 · 1 9 Multiply by the reciprocal of 12 14 Multiply by the reciprocal of 9, which is 1 9 . = 3 · 1 5 · 9 Multiply the numerators and denominators. = 3 · 1 5 · 3 · 3 = 1 5 · 3 Divide out the common factor of 3. = 1 15 Multiply the remaining factors. , which is 14 12 . Multiply the numerators and denominators. Rewrite each number as a product of prime factors. 8 = 2 · 2 · 2, 14 = 2 · 7, 12 = 2 · 2 · 3 Divide out the common factors of 2, 2, and 7. Multiply the remaining factors. 9 = 3 · 3. Rewrite each number as a product of prime factors.
hendricks_beginning_algebra_1e_ch1_3
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