# Math Help - Proof: If p and q are rational numbers then p + q...

1. ## Proof: If p and q are rational numbers then p + q...

Hey all,
I want to prove that:
If p and q are rational numbers then p + q is also a rational number.

I have tried through direct proof:
$p = \frac{n}{m}$ and $q = \frac{r}{s}$ where $m, n \neq 0$ Then,

$\frac{n}{m}+\frac{r}{s} \rightarrow \frac{sn}{ms}+\frac{rm}{ms} \rightarrow \frac{sn+rm}{sm}$ which is rational.

Is this proof correct ?

2. This is all on the condition that m,n,r,s are integers. You're proof is correct if the following products sn, rm and sm are also integers.