# Properties of Addition – Definition with Examples

» Properties of Addition – Definition with Examples

There are four properties of the addition of whole numbers.

• Closure Property
• Commutative Property
• Associative Property

Before we start with the properties, let us revise what are whole numbers.

Whole numbers

Natural numbers (Counting numbers), including 0, form the set of whole numbers

## Closure Property:

The sum of the addition of two or more whole numbers is always a whole number.

Whole Number + Whole Number = Whole Number

For example, 2 + 4 = 6

Here, both 2 and 4 whole numbers and their sum is 6, which also is a whole number.

## Commutative Property

When we add two or more whole numbers, their sum is the same regardless of the order of the addends.

Example 1: 2 + 4 = 4 + 2 = 6

The sum of both 2 + 4 and 4 + 2 is 6. That means, we can add whole numbers in any order.

## Associative Property

When three or more numbers are added, the sum is the same regardless of the grouping of the addends.

For example (4 + 2) + 3 = (4 + 3) + 2

Here, the addends are 2, 4 and 3. So, as per the associative property, the sum of the three numbers will remain the same, no matter how we group them. So, (2 + 4) = 3 = (4 + 3) + 2 = 9

On adding zero to any number, the sum remains the original number. Adding 0 to a number does not change the value of the number.

For example, 3 + 0 = 3   