Chapter 5 - Number Theory and the Real Number System - 5.3 The Rational Numbers - Exercise Set 5.3 - Page 285: 108

$\dfrac{19}{30}$

The 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{3}{5}+\frac{2}{3}}{2}\\\\ &=\frac{\frac{9}{15}+\frac{10}{15}}{2}\\\\ &=\frac{\frac{19}{15}}{2}\\\\ &=\frac{19}{15} \times \frac{1}{2}\\\\ &=\frac{19}{30}\\\\ \end{align*}