Question

Are the rational numbers closed under multiplication?

Answer 1

Yes, The rational numbers are closed under multiplication.

Explanation:

A rational number is a number which can be expressed in the form of a fraction
`(x)/(y)`, where x and y are integers and y ≠ 0.

Now, closure property of multiplication states that if two rational numbers are multiplied then the product is also a rational number. Thus, if r and t are rational numbers, then

r×t = s, where s is the product of r and t

s is also a rational number.

Hence, the rational numbers are closed under multiplication.

This can be better explained with the help of an example
`(3)/(4) * (2)/(5) = (6)/(20)`,

It is clear that
`(6)/(20)` is a rational number.