Question

State whether the given statement is true or false: 

The sum of two rationals is always rational

Answer 1

This statement is true.

Explanation:

If `a = p/q` and `b = r/s` are rationals (p, q, r, s integers, q, s ≠ 0), then `a + b = (ps + rq)/(qs)`, which is a ratio of integers with nonzero denominator, so it is rational.