Properties Of Addition - Definition with Examples

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Properties of Addition?

There are four properties of addition of whole numbers.

  • Closure Property

  • Commutative Property

  • Associative Property

  • Additive Identity 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. 

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

closure property of whole number

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

commutative property of whole number example 1
 

commutative property of whole number example 2

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

associative property example 1
 
associative property example 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
 

Additive Identity Property

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

additive identity property example 1
 
additive identity property example 2
 

  Fun Facts

  • Addition of two whole numbers except for zero will always give a bigger number.

  • When you add numbers (except 0) on a number line, the result will always shift you to the right.
 
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