(a rational number) + (a rational number) = a rational number Is this always or sometimes

This probably isnt rigorous enough but here's what I think:

A rational number can always be expressed in the form p / q for integers p and q

then (using m/n for the other rational number):

p/q + m/n = (np+mq)/qn.

two integers multiplied together will always be integers so in the end the numerator/denominator will still be integers so it will always be a rational number