Properties of Addition

In this section, we will learn about the properties of addition. We begin with some basic vocabulary (addend, sum) that goes with an addition problem. When two or more numbers are being added together, these numbers are referred to as addends; the result of the addition problem is known as the sum.
Example 1: Identify the parts of: 2 + 6 = 8
The 2 and 6 are being added together, these parts are known as addends.
The 8 is the result of the addition, this part is known as the sum.
Next, we focus on the properties of addition. These include:

Commutative Property of Addition

States that addends can be put in any order and the result will be the same. Simply put, we can change the order of the numbers being added and obtain the same answer.

Example 2: Rewrite 1 + 3 using the commutative property of addition
To solve this problem, we simply change the order of the addends:
1 + 3 -> 3 + 1
In each case, the result is 4.
1 + 3 = 4
3 + 1 = 4.
Changing the order of the addends (numbers being added) does not change the sum (result of the addition problem).

Associative Property of Addition

States that we can group the addition of three or more numbers in any order without changing the sum.

Example 3: Rewrite 2 + (7 + 5) using the associative property of addition
To solve this problem, we simply regroup or change which addends are enclosed in parentheses:
2 + (7 + 5) -> (2 + 7) + 5
In each case, the result is 14.
2 + (7 + 5) = 2 + 12 = 14
(2 + 7) + 5 = 9 + 5 = 14.
Changing the way we group the addends (numbers being added) does not change the sum (result of the addition problem).