Question

Are the rational numbers closed under addition?

Answer 1

Yes, rational numbers are closed under addition.

Explanation:

Rational numbers are number that can be expressed in the form of fraction
`(x)/(y)`, where x and y are integers and y ≠ 0.

Now, the closure property of addition of rational number states that if we add two rational number, then the sum of these two rational number will also be a rational number.

Let a and b be two rational number, then,

a+b = c, where c is the sum of and b

c is also a rational number.

Thus, rational numbers are closed under addition.

This can be explained with the help of a example.

`(1)/(7) + (2)/(7)` =
`(2)/(7)`

It is clear that
`(1)/(7), (2)/(7), (3)/(7)` are rational numers.

Thus, rational numbers are closed under addition.