If you take two tests and get $a$ marks out of a maximum $b$ in the first, scoring $\frac{a}{b}$, and you do better with $c$ marks out of $d$ in the second, scoring $\frac{c}{d}$, you expect the result of combining the marks for the two tests, the mediant $\frac{a+c}{b+d}$, to lie between the results for the two tests separately. If 0 < $\frac{a}{b}$ < $\frac{c}{d}$ prove, with reference to the diagram, that

${\displaystyle \frac{a}{b}<\frac{a+c}{b+d}<\frac{c}{d}.}$