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: 75

Answer

$\dfrac{2}{3}$

Work Step by Step

To combine fractions, make sure that the fractions have the same denominators before combining their numerators. \begin{align} \dfrac{ 7 }{ 12 } - (-\dfrac{ 1 }{ 12 }) &= \dfrac{ 7 }{ 12 } + \dfrac{ 1 }{ 12 } &&\text{Change the sign} \\ &= \dfrac{ 7 + 1 }{ 12 } &&\text{Add the numerators} \\ &= \dfrac{ 8 }{ 12 } \\ &= \dfrac{ 8 \div 4 }{ 12 \div 4 } &&\text{Reduce to lowest terms} \\ &= \boxed{ \dfrac{ 2 }{ 3 } } \end{align}
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