Home > Pre-Algebra > Whole Numbers > Determine Property of Addition

#### Introduction

Addition is one of the simplest math functions, and one of the first you learn. Addition has three properties - or rules - that you must follow when you add one or more numbers. These are:

• The cumulative property
• The associative property
• The identity property

## Lesson

There are three properties of addition. Each of them works in a slightly different way, although they can all be combined.

### Commutative Property

The commutative property of addition means that the order you add numbers doesn't make a difference to the final sum.

For example: 8 + 3 + 2 = 13 3 + 8 + 2 = 13 2 + 3 + 8 = 13

Whatever order we put the numbers, we still get the same result.

### Associative Property

The associative property of addition means that however you group numbers (with parenthesis) the end result will not make a difference to the final sum.

For example:

5 + 3 + 9 + 8 = 25 (5 + 3) + 9 + 8 = 25 5 + (3 + 9 = 8) = 25

Also, because of the commutative property, we can shuffle the order as well and it won't change the result:

9 + (3 + 8) + 5 = 25

### Identity Property

The identity property of addition means that whatever number you add to 0, the end result will be the number you added to 0.

For example:

8 + 0 = 8 0 + 73 = 73 5,78987 + 0 = 5,78987

## Examples

51 + 0 = 51
The sum of any number and zero is the original number
This is called the Additive Identity Property
(27 + 47) + 21 = 27 + (47 + 21)
When three or more numbers are added, the sum is the same regardless of the grouping of the numbers
This is called the Associative Property of Addition
31 + 35 = 35 + 31
When two numbers are added, the sum is the same regardless of the order of the numbers
This is called the Commutative Property of Addition