136 Chapter 2 Fractions and Mixed Numbers: Multiplication and Division 4. Applications of Multiplication and Division of Fractions Sometimes it is difficult to determine whether multiplication or division is appropriate to solve an application problem. Division is generally used for a problem that requires you to separate or “split up” a quantity into pieces. Multiplication is generally used if it is necessary to take a fractional part of a quantity. 25 Answers 14. 50 batches 15. 10 segments of piping Using Division in an Application Example 5 A road crew must mow the grassy median along a stretch of highway I-95. If they can mow 5 8 mile (mi) in 1 hr, how long will it take them to mow a 15-mi stretch? Solution: Read and familiarize. Strategy/operation: From the figure, we must separate or “split up” a 15-mi stretch of highway into pieces that are mi in length. Therefore, we must divide 15 by . 15 1 3 15 1 24 8 5 8 51 Write the whole number as a fraction. Multiply by the reciprocal of the divisor. 15 ÷ 5 8 58 5 8 The 15-mi stretch of highway will take 24 hr to mow. Using Division in an Application Example 6 A -ft length of wire must be cut into pieces of equal length that are ft long. How many pieces can be cut? Solution: Read and familiarize. Operation: Here we divide the total length of wire into pieces of equal length. Multiply by the reciprocal of the divisor. Simplify. 9 4 9 3 41 6 8 3 8 2 31 9 4 3 8 Six pieces of wire can be cut. 38 9 4 Skill Practice 14. A cookie recipe requires package of chocolate chips for each batch of cookies. If a restaurant has 20 packages of chocolate chips, how many batches of cookies can it make? Skill Practice 15. A -yd ditch will be dug to put in a new water line. If piping comes in segments of yd, how many segments are needed to line the ditch? 54 25 2 5 mi 8 5 mi 8 5 mi 8 15 mi
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