## 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: 89

#### Answer

$4\frac{5}{12}$

#### Work Step by Step

Convert each mixed number to an improper fraction to obtain: $=\left(\dfrac{3\cdot 2 + 2}{3}\right) + \left(\dfrac{4\cdot 1 + 3}{4}\right) \\=\dfrac{8}{3} + \dfrac{7}{4}$ The fractions are not similar since they have different fractions. Make the fractions similar using their LCD of $12$. $\dfrac{8}{3} + \dfrac{7}{4} \\= \dfrac{8\color{blue}{(4)}}{3\color{blue}{(4)}}+\dfrac{7\color{blue}{(3)}}{4\color{blue}{(3)}} \\=\dfrac{32}{12}+\dfrac{21}{12}$ Now that the fractions are similar, add the numerators and copy the denominator to obtain: $=\dfrac{32+21}{12} \\=\dfrac{53}{12}$ Convert to a mixed number to obtain: $=\dfrac{48+5}{12} \\=\dfrac{48}{12} + \dfrac{5}{12} \\=4\frac{5}{12}$

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