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: 76

Answer

$\dfrac{5}{8}$

Work Step by Step

To combine fractions, make sure that the fractions have the same denominators before combining their numerators. \begin{align} \dfrac{ 5 }{ 16 } - (-\dfrac{ 5 }{ 16 }) &= \dfrac{ 5 }{ 16 } + \dfrac{ 5 }{ 16 } &&\text{Change the sign} \\ &= \dfrac{ 5 + 5 }{ 16 } &&\text{Add the numerators} \\ &= \dfrac{ 10 }{ 16 } \\ &= \dfrac{ 10 \div 2 }{ 16 \div 2 } &&\text{Reduce to lowest terms} \\ &= \boxed{ \dfrac{ 5 }{ 8 } } \end{align}
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