Question

Product of two rational numbers is always rational numbers, is it true. Justify your answer.

Answer 1

Answer :

We know rational number can be expressed as $\frac{p}{q}$ , Where q $\ne$ 0 and p and q are integers . Or have decimal digits terminating or non terminating but repeating .

SO,

We assume our Two rational number :

A = $\frac{a}{b}$ , Here b $\ne$ 0 and a and b are integers .
And
B = $\frac{c}{d}$ , Here d $\ne$ 0 and c and d are integers .

So,

A $\times$ B = $\frac{a}{b}$ $\times$ $\frac{c}{d}$ = $\frac{ac}{bd}$

And

Integers $\times$ Integers = Integers , So

ab and cd also integers , So

A $\times$ B also a rational number .

So,

We can say multiple of rational number also a rational number . ( Hence Proved )