Knot theory question

Question

Show that a (p,q) torus knot always has a projection with p(q-1) crossings.

I can show an example using (2,3) has 4 crossings. I think there is something more to this. Help please

Answer 1

So, this is pretty self explanatory from the picture, but we have $q$ strands and $p$ times that the outside strand wraps over the other $q-1$. Hence, $p(q-1)$ crossings.