Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 5 - Number Theory and the Real Number System - 5.3 The Rational Numbers - Exercise Set 5.3 - Page 287: 150


Two rational numbers \[\frac{a}{b}\]and \[\frac{c}{d}\] can be added by first finding the least common multiple of their denominators also known as least common denominator. The rational numbers are then multiplied by a rational number of the form \[\frac{e}{e}\], so that the denominator of both the rational numbers becomes the least common denominator as found earlier. The least common denominator of the rational numbers \[\frac{5}{6},\frac{1}{2}\]is \[6\]. Thus, the addition of two rational numbers can be shown as, \[\begin{align} & \frac{5}{6}+\frac{1}{2}=\frac{5}{6}\times \frac{1}{1}+\frac{1}{2}\times \frac{3}{3} \\ & =\frac{5}{6}+\frac{3}{6} \\ & =\frac{8}{6} \\ & =\frac{4}{3} \end{align}\]
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