Question

The product of two rational numbers is always a _____.

Answer 1

Find the product of two rational numbers.

Rational number: a rational number is a number that can be expressed as a fraction of two integers, that is in the form ${\displaystyle \frac{p}{q}}$, where $p,q\in \mathbb{R}$ and $q\ne 0$

Let ${\displaystyle \frac{p_1}{q_1}}$ and ${\displaystyle \frac{p_2}{q_2}}$ be two rational numbers.

So the product of these two numbers is ${\displaystyle \frac{p_1}{q_1}}\times {\displaystyle \frac{p_2}{q_2}}={\displaystyle \frac{p_1{p}_2}{q_1{q}_2}}$ where $p_1{p}_2$ and $q_1{q}_2$ are integers.

As, the above product is a rational number.
Hence, the product of two rational numbers is always a rational number .