Can you PROVE this using MEthod of proofs?

Question

1. The sum of two rational numbers is rational.

2. The product of two rational numbers is rational.

Answer 1

Yes

1. a + b = p/q + r/s = (ps + qr)/qs

2. ab = (p/q)(r/s) = (pr)/(qs)

Answer 2

Like JasonM, except that you are expected to explain at each step that if p,q,r and s are integers, then (ps+ qr) is an integer (because ps is an integer and qr is an integer); also, qs is an integer AND qs is not zero. Once you've shown that, then you can state that (ps + qr)/qs is a rational number made up of one integer divided by the other.