# Thread: Congruence classes and rings

1. ## Congruence classes and rings

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

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

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

Show that every rational number is congruent (mod 1) to a rational number $a/b$ with $0 \leq a/b \leq 1$.
HINT: Use its decimal expansion.