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: 12



Work Step by Step

$\bf{\text{Solution Outline:}}$ Use the $LCD$ to convert the terms of the given expression, $ \dfrac{2}{3}+\dfrac{5}{6} ,$ 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 $ 3 $ is $ 3=3^1.$ The prime factorization of $ 6 $ is $ 6=2^1\cdot3^1.$ Getting each factor with the highest exponent, then the $ LCD=2^1\cdot3^1=6 .$ Converting the terms of the given expression to similar terms by using the $LCD$ results to \begin{array}{l}\require{cancel} \dfrac{2}{3}\cdot\dfrac{2}{2}+\dfrac{5}{6} \\\\= \dfrac{4}{6}+\dfrac{5}{6} \\\\= \dfrac{4+5}{6} \\\\= \dfrac{9}{6} \\\\= \dfrac{\cancel3(3)}{\cancel3(2)} \\\\= \dfrac{3}{2} .\end{array}
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