Question

why Division is not closed for rational number

Answer 1

A set of Rational numbers are always closed under all of the operations of addition, subtraction, multiplication, division. ... rational number is any numberwhich can be expressed in the form of p/q where p and q are integers. zero can be expressed as 0÷2, 0÷3, 0÷4 etc.

Answer 2

First you should know that Any number Divided by 0 is not a number...

Number / 0 = Not defined ( not a number )

Rational numbers are closed under addition , Suntraction and multiplication...means if we take any two rational numbers then their sum , difference and product is again a rational number...

For example :
a = 4 ( rational number ) , b = 0 ( rational number )

=> a +b = 4+0 = 4 is a rational number
=> a-b = 4 - 0 = 4 is a rational number
=> a × b = 4 × 0 = 0 is a rational number

But a / b = 4 / 0 is not defined or not a rational number
as per definition of rational number...( in rational number denominator should be non zero...)

So Division is not closed for rational numbers...(Note : If you gake denominator other than zero , then Division operation will be closed....but here we have to check for all rational number...Because of zero , closure property fails....)

Hope this help.......