Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 1 - Introduction to Algebraic Expressions - Review Exercises: Chapter 1 - Page 77: 73



Work Step by Step

Since $a-(-b)=a+b,$ the given expression, $ -\left| \dfrac{7}{8}-\left(-\dfrac{1}{2} \right) -\dfrac{3}{4} \right| ,$ is equivalent to \begin{array}{l}\require{cancel} -\left| \dfrac{7}{8}-\left(-\dfrac{1}{2} \right) -\dfrac{3}{4} \right| \\\\= -\left| \dfrac{7}{8}+\dfrac{1}{2} -\dfrac{3}{4} \right| .\end{array} The $LCD$ of the denominators, $\{8,2,4\}$ is $8$ since it is the least number that can be divided evenly (no remainder) by all the denominators. Using the $LCD$ to express the fractions as similar fractions (fractions with same denominator) results to \begin{array}{l}\require{cancel} -\left| \dfrac{7}{8}+\dfrac{1}{2} -\dfrac{3}{4} \right| \\\\= -\left| \dfrac{7}{8}+\dfrac{1}{2}\cdot\dfrac{4}{4} -\dfrac{3}{4}\cdot\dfrac{2}{2} \right| \\\\= -\left| \dfrac{7}{8}+\dfrac{4}{8} -\dfrac{6}{8} \right| \\\\= -\left| \dfrac{7+4-6}{8} \right| \\\\= -\left| \dfrac{5}{8} \right| \\\\= -\left( \dfrac{5}{8} \right) \\\\= -\dfrac{5}{8} .\end{array}
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