College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter R - Review Exercises: 45

Answer

$-\dfrac{37}{18}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ Use the order of operations (PEMDAS - Parenthesis, Exponents, Multiplication/Division, Addition/Subtraction) to simplify the given expression, $ \left(-\dfrac{5}{9}-\dfrac{2}{3}\right)-\dfrac{5}{6} .$ $\bf{\text{Solution Details:}}$ Simplifying the expression/s in parenthesis by making the fractions similar (same denominator), the entire expression above becomes \begin{array}{l}\require{cancel} \left(-\dfrac{5}{9}-\dfrac{2}{3}\cdot\dfrac{3}{3}\right)-\dfrac{5}{6} \\\\= \left(-\dfrac{5}{9}-\dfrac{6}{9}\right)-\dfrac{5}{6} \\\\= \left(\dfrac{-5-6}{9}\right)-\dfrac{5}{6} \\\\= \left(\dfrac{-11}{9}\right)-\dfrac{5}{6} \\\\= \dfrac{-11}{9}-\dfrac{5}{6} .\end{array} Simplifying the sum/difference by making the fractions similar, the expression above becomes \begin{array}{l}\require{cancel} \dfrac{-11}{9}\cdot\dfrac{2}{2}-\dfrac{5}{6}\cdot\dfrac{3}{3} \\\\= \dfrac{-22}{18}-\dfrac{15}{18} \\\\= \dfrac{-22-15}{18} \\\\= \dfrac{-37}{18} \\\\= -\dfrac{37}{18} .\end{array}
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