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