Changing modulus in modular arithmetic Is it true that
$$a\equiv b\pmod{m}\implies\frac{a}{n}\equiv\frac{b}{n} \pmod{\frac{m}{n}},$$ where $a, b, m, n, \frac{a}{n}, \frac{b}{n}, \frac{m}{n}\in\mathbb{N}$? If so, how do I prove it?

$$a\equiv b\pmod m$$
means
$$\frac{a-b}m\in\Bbb Z.$$
$$\frac{a}n\equiv \frac bn\pmod{\frac mn}$$
means
$$\frac{a/n-b/n}{m/n}\in\Bbb Z.$$
