Question

Let p and q be rational. Prove that p+q is rational

Answer 1

Let p and q rational numbers (what does it means?), then, p and q coul be written as

$p = \frac{a}{b},a, b \in \mathbb{Z}, b \neq 0\\\\q = \frac{c}{d}, c,d \in \mathbb{Z}, d \neq 0$

then,

$p +q = \frac{a}{b} + \frac{c}{d} = \frac{ad +bc}{bd}$

and we know that ad+bc is an integer, so, p +q is a rational number.