Congruence of Quotient/Proof 1

Proof
By definition of congruence modulo $n$:


 * $a = b + k n$

Dividing through by $d$ (which you can do because $d$ divides all three terms), we get:


 * $\displaystyle \frac a d = \frac b d + k \frac n d$

from which the result follows directly.