Question

The rational numbers are not closed under .

• 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.

$\text{Consider two rational numbers}\frac{-4}{5}\text{and}\frac{7}{5}.$

$\text{Addition:}\frac{-4}{5}+\frac{7}{5}=\frac{3}{5},\text{which is a rational number.}$

$\text{Subtraction:}\frac{-4}{5}-\frac{7}{5}=\frac{-11}{5},\text{which is a rational number.}$

$\text{Multiplication:}\frac{-4}{5}\times \frac{7}{5}=\frac{-28}{25},\text{which is a rational number.}$

$\text{Division:}\frac{-4}{5}÷\frac{7}{5}=\frac{-4}{7},\text{which is also a rational number.}$

$\text{If we consider the numbers,}\frac{-4}{5}\text{and}0\frac{-4}{5}÷0\text{is not defined.}\text{Rational numbers are not closed under}\text{division.}$

So only in case of division, rational numbers do not follow the closure property.