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:

$\displaystyle p = \frac{n}{m}$ and $\displaystyle q = \frac{r}{s} $ where $\displaystyle m, n \neq 0$ Then,

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

Is this proof correct ?