Assuming that $\frac{a}{b}<\frac{c}{d} < 1 $, arrange $\frac{b}{a}$, $\frac{d}{c}$, $\frac{bd}{ac}$, $\frac{b+d}{a+c}$, and $1$

From $$ b = a \frac ba > a \frac dc $$ it follows that $$ \frac{b+d}{a+c} > \frac{a \frac dc+d}{a+c} = \frac dc $$ and in a similar way you get $$ \frac{b+d}{a+c} < \frac ba \, . $$

There is also a general theorem which states that for positive numbers, $$ \min \frac{a_i}{b_i} \le \frac{a_1 + ... + a_n}{b_1 + ... + b_n} \le \max \frac{a_i}{b_i} $$ and this is proved using the same ideas.