\begin{definition}[Definition:Mediant]
Let $r, s \in \Q$ be rational numbers.
Let $r$ and $s$ be expressed as:
:$r = \dfrac a b, s = \dfrac c d$
where $a, b, c, d$ are integers such that $b > 0, d > 0$.
Then the '''mediant''' of $r$ and $s$ is $\dfrac {a + c} {b + d}$.
\end{definition}