Question

The division of a rational number by a non zero rational number always gives a rational number.

• A. True
• B. False

Answer 1

The correct option is A

True

Let there be two rational numbers $\frac{a}{b}$ and $\frac{p}{q}$, where $a,b,p$ and $q\ne 0$

We have to check whether $\frac{a}{b}÷\frac{p}{q}$ is a rational number or not.

To divide one rational number by the other non-zero rational number, we divide the first rational number by the reciprocal of the other.

So, $\frac{a}{b}÷\frac{p}{q}=\frac{a}{b}\times \frac{q}{p}$

Since, it is a multiplication of two rational numbers, it is always rational.

Thus, division of a rational number by a non zero rational number always gives a rational number.