# Chapter 1, Equations and Inequalities - 1.1 Apply Properties of Real Numbers - 1.1 Exercises - Skill Practice - Page 7: 56

$\displaystyle \frac{ad+bc}{2bd}$

#### Work Step by Step

The rational number that lies halfway between two rational numbers $q_{1}$ and $q_{2}$ is $\qquad \displaystyle \frac{q_{1}+q_{2}}{2}.$ \begin{align*} \displaystyle \frac{q_{1}+q_{2}}{2}&=\displaystyle \frac{\frac{a}{b}+\frac{c}{d}}{2} &\\ & =(\displaystyle \frac{a}{b}+\frac{c}{d})\div 2 &\text{... definition of division}\\ & =(\displaystyle \frac{ad+bc}{bd})\cdot\frac{1}{2}&\text{... adding fractions - common denominator}\\ & =\displaystyle \frac{ad+bc}{2bd} &\text{... simplify}\end{align*}

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