Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 5 - Number Theory and the Real Number System - 5.3 The Rational Numbers - Exercise Set 5.3 - Page 285: 99

Answer

$\dfrac{1}{12}$

Work Step by Step

Simplify within each group by making the fractions similar using their LCD to obtain: \begin{align*} \require{cancel} &=\left[-\frac{4}{7}+\frac{2}{5}\right]\left[-\frac{3(9)}{8(9)}+\left(-\frac{1(8)}{9(8)}\right)\right]\\\\ &=\left[-\frac{4(5)}{7(5)}+\frac{2(7)}{5(7)}\right]\left[-\frac{27}{72}+\left(-\frac{8}{72}\right)\right]\\\\ &=\left[-\frac{20}{35}+\frac{14}{35}\right]\left[-\frac{27+8}{72}\right]\\\\ &=\left[\frac{-20+14}{35}\right]\left[-\frac{35}{72}\right]\\\\ &=\left[\frac{-6}{35}\right]\left[-\frac{35}{72}\right]\\\\ &=\left[\frac{-\cancel{6}}{\cancel{35}}\right]\left[-\frac{\cancel{35}}{\cancel{72}12}\right]\\\\ &=\frac{1}{12} \end{align*}
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