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: 93



Work Step by Step

Convert each mixed number to an improper fraction to obtain: $=\left(-\dfrac{3\cdot 5 + 2}{3}\right) + \left(\dfrac{6\cdot 3 + 1}{6}\right) \\=-\dfrac{17}{3} + \dfrac{19}{6}$ The fractions are not similar since they have different fractions. Make the fractions similar using their LCD of $6$. $-\dfrac{17}{3} + \dfrac{19}{6} \\= -\dfrac{17\color{blue}{(2)}}{3\color{blue}{(2)}}+\dfrac{19}{6} \\=-\dfrac{34}{6}+\dfrac{19}{6}$ Now that the fractions are similar, add the numerators and copy the denominator to obtain: $=\dfrac{-34+19}{6} \\=\dfrac{-15}{6}$ Convert to a mixed number to obtain: $=\dfrac{-12+(-3))}{6} \\=\dfrac{-12}{6} + \dfrac{-3}{6} \\=-2+\left(\frac{-1}{2}\right) \\=-2\frac{1}{2}$
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