# Commutative property explained

Learn what is the commutative property in math. All the numbers have some important properties, in that commutative property is one of them. First we will know what is the meaning of commutative property then we will apply it for different types of numbers. What is commutative property? Commutative property says that the numbers can be added or subtracted or multiplied or divided in any order. But we need to check that commutative property satisfies for all the numbers or not. We will learn the commutative property for Natural numbers, whole numbers, Integers and Rational numbers. For all these numbers we will see the commutative property under addition, subtraction, multiplication and division satisfies or not.

## Commutative property for Natural numbers:

Let “p” and “q” be the two natural numbers then p + q = q + p.

Subtraction:

Let “p” and “q” be the two natural numbers then p – q ≠ q – p.

Multiplication:

Let “p” and “q” be the two natural numbers then p × q = q × p.

Division:

Let “p” and “q” be the two natural numbers then p ÷ q ≠  q ÷  p.

Commutative property for natural numbers satisfies only under addition and multiplication.

### Commutative property for whole numbers:

Let “p” and “q” be the two whole numbers then p + q = q + p.

Subtraction:

Let “p” and “q” be the two whole numbers then p – q ≠  q – p.

Multiplication:

Let “p” and “q” be the two whole numbers then p × q = q × p.

Division:

Let “p” and “q” be the two whole numbers then p ÷  q ≠  q ÷  p.

Commutative property for whole numbers satisfies only under addition and multiplication.

#### Commutative property for Integers:

Let “p” and “q” be the two Integers then p + q = q + p.

Subtraction:

Let “p” and “q” be the two Integers then p – q ≠  q – p.

Multiplication:

Let “p” and “q” be the two Integers then p × q = q × p.

Division:

Let “p” and “q” be the two Integers then p ÷  q ≠  q ÷  p.

Commutative property for Integers satisfies only under addition and multiplication.

##### Commutative property for Rational numbers:

Let “p” and “q” be the two rational numbers then p + q = q + p.

Subtraction:

Let “p” and “q” be the two rational numbers then p – q ≠  q – p.

Multiplication:

Let “p” and “q” be the two rational numbers then p × q = q × p.

Division:

Let “p” and “q” be the two rational numbers then p ÷  q ≠  q ÷  p.

Commutative property for rational numbers satisfies only under addition and multiplication. 