## 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 285: 91

#### Answer

$1\frac{1}{6}$

#### Work Step by Step

Convert each mixed number to an improper fraction to obtain: $=\left(\dfrac{3\cdot 3 + 2}{3}\right) - \left(\dfrac{2\cdot 2 + 1}{2}\right) \\=\dfrac{11}{3} - \dfrac{5}{2}$ The fractions are not similar since they have different fractions. Make the fractions similar using their LCD of $6$. $\dfrac{11}{3} - \dfrac{5}{2} \\= \dfrac{11\color{blue}{(2)}}{3\color{blue}{(2)}}-\dfrac{5\color{blue}{(3)}}{2\color{blue}{(3)}} \\=\dfrac{22}{6}-\dfrac{15}{6}$ Now that the fractions are similar, subtract the numerators and copy the denominator to obtain: $=\dfrac{22-15}{6} \\=\dfrac{7}{6}$ Convert to a mixed number to obtain: $=\dfrac{6+1}{6} \\=\dfrac{6}{6} + \dfrac{1}{6} \\=1\frac{1}{6}$

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