Question

The statement “Rational number are closed under division” is
A.True
B.False
C.Cannot determine
D.None

Answer 1

Hint: Rational numbers are those numbers which can be written in p/q form where p and q do not have common factors and q should not be equal to zero. Closed under division implies that if we divide two rational numbers then the resultant number will also be a rational number.

Complete step-by-step answer:
If we add two rational numbers then the resultant number is also rational which implies rational numbers are closed under addition.
For example- 1 + 2 =3
Here, 1 and 2 both are rational numbers, when we add them the resultant number is 3 which is also a rational number.

If we subtract two rational numbers then the resultant number is also rational which implies rational numbers are closed under subtraction.
For example- 2 - 1 = 1
Here, 1 and 2 both are rational numbers, when we subtract 1 from 2 then the resultant number is 1 which is also a rational number.

If we multiply two rational numbers then the resultant number is also rational which implies rational numbers are closed under multiplication.
For example- 1 * 2 =2
Here, 1 and 2 both are rational numbers, when we multiply them the resultant number is 2 which is also a rational number.

0 is a rational number because it can be written as 0/1. When we divide any rational number by 0 which is also a rational number, then the resultant number is not a rational (infinity is not defined).
Rational number is not closed under division.

Option (B) is correct.

Note:-Rational numbers are closed under division as long as the division is not by zero. Irrational numbers are not closed under addition, subtraction, multiplication or division.