Congruence of Quotient

Theorem
Let $a, b \in \Z$ and $n \in \N$.

Let $a$ be congruent to $b$ modulo $n$, i.e. $a \equiv b \pmod n$.

Let $d \in \Z: d > 0$ such that $d$ is a common divisor of $a, b$ and $n$.

Then:
 * $\dfrac a d \equiv \dfrac b d \pmod {n / d}$