Question

Rational numbers are not closed under which operation?

• A. Addition
• B. Subtraction
• C. Multiplication
• D. Division

Answer 1

The correct option is D

Division

When we add, subtract or multiply any two rational numbers, the result will always be a rational number.
For example: Consider two rational numbers $\frac{4}{3}$ and $\frac{5}{4}$
Addition: $\frac{4}{3}$ + $\frac{5}{4}$ = $\frac{31}{12}$
Subtraction: $\frac{4}{3}$ - $\frac{5}{4}$ = $\frac{1}{12}$
Multiplication: $\frac{4}{3}$ $\times$ $\frac{5}{4}$ = $\frac{5}{3}$
In division, when we take two rational numbers other than zero, we will get rational number in result. But when we take 0 as one of the rational numbers, division by 0 is not defined and hence it doesn't satisfy the condition of closure property. So only in division, rational numbers do not follow the closure property.