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 - Study Summary - Practice Exercises - Page 73: 13



Work Step by Step

$\bf{\text{Solution Outline:}}$ Use the $LCD$ to convert the terms of the given expression, $ \dfrac{3}{4}-\dfrac{3}{10} ,$ to similar terms. Once expressed as similar terms, operate on the numerators and copy the common denominator. $\bf{\text{Solution Details:}}$ The prime factorization of $ 4 $ is $ 4=2^2.$ The prime factorization of $ 10 $ is $ 10=2^1\cdot5^1.$ Getting each factor with the highest exponent, then the $ LCD=2^2\cdot5^1=20 .$ Converting the terms of the given expression to similar terms by using the $LCD$ results to \begin{array}{l}\require{cancel} \dfrac{3}{4}\cdot\dfrac{5}{5}-\dfrac{3}{10}\cdot\dfrac{2}{2} \\\\= \dfrac{15}{20}-\dfrac{6}{20} \\\\= \dfrac{15-6}{20} \\\\= \dfrac{9}{20} .\end{array}
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