Definition:Mediant

Let $$r, s \in \Q$$, i.e. let $$r, s$$ be rational numbers.

Let $$r$$ and $$s$$ be expressed as $$r = \frac a b, s = \frac c d$$ where $$a, b, c, d$$ are integers such that $$b > 0, d > 0$$ (this is always possible by Divided By a Positive in Quotient Field).

Then the mediant of $$r$$ and $$s$$ is $$\frac {a + c} {b + d}$$.