Question

State whether the given statement is true or false:

The product of two rationals is always rational

Answer 1

This statement is true.

Explanation:

If `x = m/n` and `y = p/q` are rational (m, n, p, q integers, n, q ≠ 0) then `xy = (m p)/(nq)`, which is a ratio of integers with nonzero denominator, so xy is rational.