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 - Chapter Summary, Review, and Test - Review Exercises - Page 335: 57



Work Step by Step

Perform division first: \begin{align*} \require{cancel} &=\frac{1}{2} - \left(\frac{2}{3} \times \frac{9}{5}\right) +\frac{3}{10}\\\\ &=\frac{1}{2} - \left(\frac{2}{\cancel{3}} \times \frac{\cancel{9}3}{5}\right) +\frac{3}{10}\\\\ &=\frac{1}{2} - \frac{6}{5} +\frac{3}{10}\\\\ \end{align*} Make the fractions similar using their LCD which is $10$ to obtain: \begin{align*} &=\frac{5}{10}-\frac{12}{10}+\frac{3}{10} \end{align*} Perform the subtraction first (since it comes first from the left) then addition next to obtain: \begin{align*} &=\frac{5-12}{10}+\frac{3}{10}\\\\ &=\frac{-7}{10}+\frac{3}{10}\\\\ &=-\frac{4}{10}\\\\ &=-\frac{2}{5} \end{align*}
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