Thinking Mathematically (6th Edition)

Published by Pearson

Chapter 5 - Number Theory and the Real Number System - 5.3 The Rational Numbers - Exercise Set 5.3 - Page 286: 137

Answer

The total distance traveled is 1$\frac{3}{20}$ miles. You walked $\frac{7}{20}$ miles farther than you jogged.

Work Step by Step

You walked $\frac{3}{4}$ mile and jogged $\frac{2}{5}$ mile. Let's go ahead and write both with a common denominator. The least common denominator for 4 and 5 is 20. $\frac{3}{4}$ = $\frac{15}{20}$ because 4 will go into 20 a total of 5 times. Then we multiply 5 times 3 to get 15 (the numerator). $\frac{2}{5}$ = $\frac{8}{20}$ because 5 will go into 20 a total of 4 times. Then we multiply the 4 times 2 to get 8 (numerator). The total distance traveled is the total of your distance walked and your distance jogged, so we add the two values. Total distance = $\frac{15}{20}$ + $\frac{8}{20}$ = $\frac{23}{20}$ = 1$\frac{3}{20}$ miles. To find out how much farther your walked than jogged, you subtract the distance jogged from the distance walked: Difference = $\frac{15}{20}$ - $\frac{8}{20}$ = $\frac{7}{20}$ miles.

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