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: 70

Answer

$\dfrac{2}{3}$

Work Step by Step

Convert each mixed number to an improper fraction to obtain: $=\left(\dfrac{4\cdot 1 + 3}{4}\right)\div\left(\dfrac{8\cdot 2 + 5}{8}\right) \\=\dfrac{7}{4}\div\dfrac{21}{8}$ Use the rule $\dfrac{a}{b} \div \dfrac{c}{d} =\dfrac{a}{b} \cdot \dfrac{d}{c}$ to obtain: $=\dfrac{7}{4} \cdot \dfrac{8}{21}$ Cancel common factors to obtain: $\require{cancel} \\=\dfrac{\cancel{7}}{\cancel{4}} \cdot \dfrac{\cancel{8}2}{\cancel{21}3} \\=\dfrac{1}{1} \cdot \dfrac{2}{3}$ Multiply the numerators together and the denominators together to obtain: $=\dfrac{1(2)}{1(3)} \\=\dfrac{2}{3}$
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