Precalculus (6th Edition)

Published by Pearson
ISBN 10: 013421742X
ISBN 13: 978-0-13421-742-0

Chapter R - Review of Basic Concepts - Chapter R Test Prep - Review Exercises - Page 83: 46



Work Step by Step

Make the fractions similar by using their LCD of $20$ to obtain: $=\left(-\dfrac{2^3(4)}{5(4)}-\dfrac{3(5)}{4(5)}\right)-\left(-\dfrac{1(10)}{2(10)}\right) \\=\left(-\dfrac{2^3(4)}{20}-\dfrac{15}{20}\right)+\dfrac{10}{20}$ Simplify using the PEMDAS rule for order of operations. The PEMDAS rule summarizes the order of operations: First Priority; P - parentheses Second Priority: E - exponents Third Priorirty: M/D - multiplication or division, whichever comes first from the left Fourth Priority: A/S - addition or subtraction, whichever comes first from the left Apply the exponent first:: $=\left(\dfrac{-8(4)}{20}-\dfrac{15}{20}\right)+\dfrac{10}{20} \\=\left(\dfrac{-32}{20} - \dfrac{15}{20}\right)+\dfrac{10}{20}$ Simplify within the parentheses to obtain: $=\dfrac{-32-15}{20}+\dfrac{10}{20} \\=\dfrac{-47}{20} + \dfrac{10}{20}$ Add the numerators and copy the denominator to obtain: $=\dfrac{-47+10}{20} \\\color{blue}{-\dfrac{37}{20}}$
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