132 Chapter 2 Fractions and Mixed Numbers: Multiplication and Division 93. The Bishop Gaming Center hosts a football pool. There is $1200 in prize money. The firstplace 23 winner receives of the prize money. The 1 4 second-place winner receives of the prize money, and the third-place winner receives 1 12 of the prize money. How much money does each person get? 94. Frankie’s lawn measures 40 yd by 36 yd. In the 23 morning he mowed of the lawn. How many square yards of lawn did he already mow? How much is left to be mowed? Expanding Your Skills 95. Evaluate. 96. Evaluate. a2 7 2 b 1 36 a1 6 2 b a. b. a. b. B For Exercises 97–100, evaluate the square roots. 64 1 1 25 B 4 49 97. 98. 99. 100. B 100 B 81 101. Find the next number in the sequence: 102. Find the next number in the sequence: B B 4 1 4 1 4 2 3 12 1 8 1 8 1 2 12 14 , 2 3, 29 , , 18 1 16, , 2 27, 9 103. Which is greater, of or of ? 104. Which is greater, of or of ? 23 Section 2.5 Division of Fractions and Applications 1. Reciprocal of a Fraction Two numbers whose product is 1 are said to be reciprocals of each other. For example, consider the product of and . Because the product equals 1, we say that is the reciprocal of and vice versa. To divide fractions, first we need to learn how to find the reciprocal of a fraction. 83 3 8 3 8 8 3 3 1 81 8 1 31 1 83 38 Finding the Reciprocal of a Fraction To find the reciprocal of a nonzero fraction, interchange the numerator and denominator of the fraction. Thus, the reciprocal of is (provided and b 0). a 0 ba ab Concepts 1. Reciprocal of a Fraction 2. Division of Fractions 3. Order of Operations 4. Applications of Multiplication and Division of Fractions Concept Connections Fill in the blank. 1. The product of a number and its reciprocal is . Answer 1. 1
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