Question

Which of the following is commutative for rational numbers?

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

Answer 1

The correct option is B Addition and multiplication

The commutative property of rational numbers states that when any two rational numbers are added or multiplied in any order it does not change the result. But in the case of subtraction and division if the order of the numbers is changed then the result will also change.

For example take any two rational numbers. Say $\frac{2}{3}\&\frac{1}{3}$
Now if we add them,
$\frac{2}{3}+\frac{1}{3}=\frac{1}{3}+\frac{2}{3}=1$
Order does not matter, result is same.

If we multiply them,
$\frac{2}{3}\times \frac{1}{3}=\frac{1}{3}\times \frac{2}{3}=\frac{2}{9}$
Order does not matter, result is same in multiplication also.

But if we subtract,
$\frac{2}{3}-\frac{1}{3}=\frac{1}{3}$
$\frac{1}{3}+\frac{2}{3}=-\frac{1}{3}$
We got the different results for different order.

And if we divide,
$\frac{2}{3}÷\frac{1}{3}=2$
$\frac{1}{3}÷\frac{2}{3}=\frac{1}{2}$
We got the different results for different order.

As we can see we get the same result for addition and multiplication.
Hence, option 'b' is correct.