For$\displaystyle a/b$ and $\displaystyle c/d$ rational numbers, say $\displaystyle a/b \equiv c/d (mod 1)$ if $\displaystyle (a/b) - (c/d)$ is an integer. Call the set of congruence classes mod 1, $\displaystyle \mathbb{Q}/\mathbb{Z}$.

Show that every rational number is congruent (mod 1) to a rational number $\displaystyle a/b$ with $\displaystyle 0 \leq a/b \leq 1$.