Help me please to understand this exercise and probably to solve it.
Show that every positive rational number $\frac{m}{n}\in (0,1)$ can be represented as $\frac{m}{n} = \frac{1}{q_1} + \frac{1}{q_2} + \cdots + \frac{1}{q_r},$ where $q_1 \lt q_2\lt \cdots \lt q_r$ are positive integers and $q_i$ is a divisor of $q_{i+1}$ for all $i=1,2,\ldots,r-1$.
I don't get the last part? Tja, actually, I don't know in general how to solve it.