Multiples of 'k' less than 'n' How many positive integer multiples of a rational number k exist, that are less than a rational number n?

Hint: Write $k=\frac{a}{b}$ and $n=\frac{p}{q}$ with $a,b,p,q$ positive integers. Can you use this to reduce to the case where $k$ and $n$ are actually positive integers themselves?

Observe that for any positive integer $h$
$$
hk\leq n \iff h\frac{a}{b}\leq\frac{p}{q} \iff hqa\leq pb
$$
Now you can show (try to do so!) that there are exactly
$$
\left\lfloor\frac{pb}{qa}\right\rfloor
=\left\lfloor\frac{n}{k}\right\rfloor
$$
such integers $h$.
