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: 90



Work Step by Step

Convert each mixed number to an improper fraction to obtain: $=\left(\dfrac{8\cdot 2 + 1}{8}\right) + \left(\dfrac{4\cdot 3 + 3}{4}\right) \\=\dfrac{17}{8} + \dfrac{15}{4}$ The fractions are not similar since they have different fractions. Make the fractions similar using their LCD of $8$. $\dfrac{17}{8} + \dfrac{15}{4} \\= \dfrac{17}{8}+\dfrac{15\color{blue}{(2)}}{4\color{blue}{(2)}} \\=\dfrac{17}{8}+\dfrac{30}{8}$ Now that the fractions are similar, add the numerators and copy the denominator to obtain: $=\dfrac{17+30}{8} \\=\dfrac{47}{8}$ Convert to a mixed number to obtain: $=\dfrac{40+7}{8} \\=\dfrac{40}{8} + \dfrac{7}{8} \\=5\frac{7}{8}$
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