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 - Chapter 5 Test - Page 337: 12

Answer

\[\frac{7}{12}\]

Work Step by Step

Take LCM of 2 and 3 as 6. Then convert the denominator of each rational number to 6 as follows: \[\begin{align} & \frac{1}{2}=\frac{1\times 3}{2\times 3} \\ & =\frac{3}{6} \\ & \frac{2}{3}=\frac{2\times 2}{3\times 2} \\ & =\frac{4}{6} \end{align}\] Now, the rational number halfway between the provided rational numbers is: \[\begin{align} & \frac{\text{3}\text{.5}}{6}\text{=}\frac{35}{60} \\ & =\frac{7}{12} \end{align}\] Hence, the rational number halfway between the provided numbers is \[\frac{7}{12}\].
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