Multiples of Divisors obey Distributive Law/Proof 2

Theorem
In modern algebraic language:
 * $a = \dfrac m n b, c = \dfrac m n d \implies a + c = \dfrac m n \left({b + d}\right)$

Proof
A direct application of the Distributive Property:
 * $\dfrac m n b + \dfrac m n d = \dfrac m n \left({b + d}\right)$