Chapter 5 - Number Theory and the Real Number System - 5.3 The Rational Numbers - Exercise Set 5.3 - Page 285: 107

$\dfrac{7}{12}$

\lnThe number halfway between the numbers $a$ and $b$ can be found using the formula $\dfrac{a+b}{2}$ . Use this formula to find the number halfway the two given number to obtain: \begin{align*} \require{cancel} &=\frac{\frac{1}{2}+\frac{2}{3}}{2}\\\\ &=\frac{\frac{3}{6}+\frac{4}{6}}{2}\\\\ &=\frac{\frac{7}{6}}{2}\\\\ &=\frac{7}{6} \times \frac{1}{2}\\\\ &=\frac{7}{12}\\\\ \end{align*}