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Two numbers are reciprocals of each other if their product is 1. Every number except 0 has a reciprocal. 1 5 1 5 5 ª ᎏᎏ = 1, so 5 and ᎏᎏ are reciprocals. 2 3 2 3 ᎏᎏ ª ᎏᎏ = 1, so ᎏᎏ and ᎏᎏ are reciprocals. 3 2 3 2 1 4 4 5 5 4 4 5 1 4 4 5 1ᎏᎏ ª ᎏᎏ = ᎏᎏ • ᎏᎏ = 1, so 1ᎏᎏ and ᎏᎏ are reciprocals. To find the reciprocal of a number, write the number as a fraction. Then interchange the numerator and the denominator. 1 4 Find the reciprocal of 3ᎏᎏ. EXAMPLE 1 4 13 4 Write 3} } as a fraction. 4 ᎏᎏ 13 13 ᎏ 4 䉴 1 4 3ᎏᎏ = ᎏᎏ SOLUTION Interchange numerator and denominator. 4 13 1 4 The reciprocal of 3ᎏᎏ is ᎏᎏ. ✓CHECK 4 13 1 4 4 13 13 4 13 ª 4 4 ª 13 3ᎏᎏ ª ᎏᎏ = ᎏᎏ ª ᎏᎏ = ᎏᎏ = 1 To divide by a fraction, multiply by its reciprocal. EXAMPLE 3 5 3 6 ᎏᎏ ÷ ᎏᎏ = ᎏᎏ ª ᎏᎏ 4 6 4 5 3ª6 = ᎏᎏ 4ª5 2•9 2 • 10 Factor numerator and denominator. 9 10 Simplify fraction to lowest terms. = ᎏᎏ 1 6 5 25 2 6 5 6 = ᎏ ᎏ ª ᎏᎏ 2 25 2ᎏᎏ ÷ 4ᎏᎏ = ᎏᎏ ÷ ᎏᎏ Write mixed numbers as fractions. 25 6 6 25 The reciprocal of } } is } } . 5ª6 2 ª 25 Multiply numerators and denominators. 30 50 Simplify. 3 ª 10 5 ª 10 Factor numerators and denominators. 3 5 Simplify fraction to lowest terms. = ᎏᎏ = ᎏᎏ = ᎏᎏ = ᎏᎏ 782 Multiply numerators and denominators. Simplify. = ᎏᎏ 1 2 6 5 18 20 = ᎏᎏ EXAMPLE 5 6 The reciprocal of } } is } } . Student Resources