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: 69



Work Step by Step

Convert each mixed number to an improper fraction to obtain: $=\left(\dfrac{5\cdot 6 + 3}{5}\right)\div\left(\dfrac{10\cdot 1 + 1}{10}\right) \\=\dfrac{33}{5}\div\dfrac{11}{10}$ Use the rule $\dfrac{a}{b} \div \dfrac{c}{d} =\dfrac{a}{b} \cdot \dfrac{d}{c}$ to obtain: $=\dfrac{33}{5} \cdot \dfrac{10}{11}$ Cancel common factors to obtain: $\require{cancel} \\=\dfrac{\cancel{33}3}{\cancel{5}} \cdot \dfrac{\cancel{10}2}{\cancel{11}}$ Multiply the numerators together and the denominators together to obtain: $=\dfrac{3(2)}{1(1)} \\=\dfrac{6}{1} \\=6$
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