Question

The commutative property for rational numbers does not hold for which of the following mathematical operations?

• A. Subtraction and division.
• B. Addition and subtraction.
• C. Multiplication and addition.
• D. Division and multiplication.

Answer 1

The correct option is A Subtraction and division.

Let us take $\frac{-1}{4}$ and $\frac{2}{7}$ as examples of rational numbers and check each operation.

Addition = $\frac{-1}{4}$ + $\frac{2}{7}$ = $\frac{1}{28}$ and
$\frac{2}{7}$ + ($\frac{-1}{4}$) = $\frac{1}{28}$

Subtraction = $\frac{-1}{4}$ - $\frac{2}{7}$ = $\frac{-15}{28}$ and
$\frac{2}{7}$ - ($\frac{-1}{4}$) = $\frac{15}{28}$

Multiplication = $\frac{-1}{4}$ $\times$ $\frac{2}{7}$ = $\frac{-1}{14}$ and
$\frac{2}{7}$ $\times$ ($\frac{-1}{4}$) = $\frac{-1}{14}$

Division = $\frac{-1}{4}$ $÷$ $\frac{2}{7}$ = $\frac{-7}{8}$ and
$\frac{2}{7}$ $÷$ ($\frac{-1}{4}$) = $\frac{-8}{7}$

As we can see that the commutative property does not hold under subtraction and division for rational numbers.