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: 96

Answer

$\dfrac{5}{6}$

Work Step by Step

Make the fractions similar using their LCD of $18$ to obtain: \begin{align*} -1\frac{4}{9}-\left(-2\frac{5}{18}\right)&=-1\frac{8}{18}-\left(-2\frac{5}{18}\right)\\\\ &=-1\frac{8}{18}+2\frac{5}{18} \end{align*} Add the corresponding parts to obtain: \begin{align*} \require{cancel} -1\frac{8}{18}+2\frac{5}{18}&=-\left(1+\frac{8}{18}\right)+\left(2+\frac{5}{18}\right)\\\\ &=-1-\frac{8}{18}+2+\frac{5}{18}\\\\ &=(-1+2)+\left(-\frac{8}{18}+\frac{5}{18}\right)\\\\ &=1+\left(\frac{-3}{18}\right)\\\\ &=\frac{18}{18}+\frac{-3}{18}\\\\ &=\frac{18+(-3)}{18}\\\\ &=\frac{15}{18}\\\\ &=\frac{\cancel{15}5}{\cancel{18}6}\\\\ &=\frac{5}{6} \end{align*}
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