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