Chapter 5 - Number Theory and the Real Number System - Chapter Summary, Review, and Test - Review Exercises - Page 335: 59

$\dfrac{15}{112}$

The rational number halfway between the two numbers is the average of the two numbers.\ln The average of two numbers can be found by dividing the sum of the numbers by $2$. Thus, the rational number halfway between the two numbers is: \begin{align*} &=\frac{\frac{1}{7}+\frac{1}{8}}{2}\\\\ &=\frac{\frac{8}{56}+\frac{7}{56}}{2}\\\\ &=\frac{\frac{15}{56}}{2}\\\\ &=\frac{15}{56(2)}\\\\ &=\frac{15}{112} \end{align*}