Let p and q rational numbers (what does it means?), then, p and q coul be written as
[tex]p = \frac{a}{b},a, b \in \mathbb{Z}, b \neq 0\\\\q = \frac{c}{d}, c,d \in \mathbb{Z}, d \neq 0[/tex]
then,
[tex]p +q = \frac{a}{b} + \frac{c}{d} = \frac{ad +bc}{bd}[/tex]
and we know that ad+bc is an integer, so, p +q is a rational number.
