Question

Rational numbers are not closed under division.Example: 2 ÷ 0 is not defined.

But in the case of multiplaction also, 1/8 x 0 is 0 which is not a rational number. So as per this logic, rational nos should not be closed under multiplaction also. But why is it not so?

Answer 1

Answer :

We know rational numbers expressed in the form of $\frac{p}{q}$ , where q $\ne$ 0 ,
And as given "​In the case of multiplication, we get

$\frac{1}{8}$ $\times$ 0 = $\frac{0}{8}$ = 0

And we can express 0 in form of $\frac{p}{q}$ , where q $\ne$ 0, but p can be = 0,
as $\frac{0}{q}$

So,

0 is a rational number .

And rational numbers are closed under multiplication .