Question

If `p/q` is a rational number and m is a non-zero common divisor of p and q, then `p/q = (p ÷ m)/(q ÷ m)`.

Options

• True

• False

Answer 1

This statement is True.

Explanation:

e.g. Let m = 1, 2, 3, ...

When m = 1, then `p/q = (p ÷ 1)/(q ÷ 1) = p/1 ÷ q/1 = p/1 xx 1/q = p/q`

When m = 2, then `p/q = (p ÷ 2)/(q ÷ 2) = p/2 ÷ q/2 = p/2 xx 2/q = p/q`

Hence, `p/q = (p ÷ m)/(q ÷ m)`.