Let $[\cdot]$ denote the integral part of a real number, that is the only integer $a$ satisfying
$a \leq x < a+1$.
Let $0<r<1$ be a rational number and $m \geq 0$ a positive integer.
How do you prove that the following equality?
$[rm]+[(1-r)m]=m-1$
This should be completely elementary but I don't manage!!