Karin has taught middle and high school Health and has a master's degree in social work.
The Commutative Property of Addition
First of all, addition is the process of adding something to something else. In math, it is the process of adding two or more numbers or amounts together. We call the resulting number a sum.
The commutative property of addition, also called the order property of addition, states that when two numbers are added, the sum is the same even if you switch the order of the numbers being added. Those two numbers being added are called addends. Let's look at a simple example:
2 + 4 = 4 + 2
Even if we switch the order of the addends (2 and 4), we still get 6, so 2 plus 4 equals 4 plus 2!
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Using the Property in Real Life
Imagine that you had two jellybeans: a red one and a green one. It won't matter if you eat the green jellybean before the red one or the red one before the green one; the result is still that you ate two jellybeans. This is a real life example of the commutative property of addition at work!
But, sometimes the order of doing things does make a difference. For example, if you put on your socks after your shoes, you would look pretty silly and be quite uncomfortable, no? This is an example of a time where order does matter and makes a big difference on the outcome. So this would not be similar to how the commutative property of addition works.
In the first example in this lesson, two numbers were used to illustrate the commutative property of addition. You can use numerous numbers and the property will still work. It is just important that you are using the same numbers on each side!
Let's look at the following examples:
1 + 3 = 3 + 1
Here, we are saying that one plus three equals three plus one. Because we are working with solely numbers here, we can attest this statement as being true. Both sides of the equation give us 4, and it does not matter that the one and three were switched.
Here are a couple more examples of the commutative property of addition in use:
2 + 5 + 7 = 5 + 7 + 2
13 + 15 + 19 + 25 = 15 + 25 + 13 + 19
We could keep going with examples, but hopefully you get the point by now!
Application of Algebraic Expressions
The above examples entailed numerical expressions. The commutative property of addition also works with algebraic expressions. Algebraic expressions are expressions that contain numbers, variables (like x and y) and operations (addition, subtraction, division, multiplication). For the purpose of this lesson, we are specifically talking about algebraic expressions using the operation of addition.
Algebraic expressions with the same variables and numbers being added in a different order are also examples of the commutative property of addition. Let's look at the following examples:
5 + a = a + 5
In this example, we are saying that five plus a number is equal to a number plus five.
2d + 8 + 5b = 5b + 8 + 2d
In the above example, we are saying that 2d plus 8 plus 5b equals 5b plus 8 plus 2d
The commutative property of addition states that when two numbers are added, the sum is the same even if you switch the order of the numbers being added. The commutative property of addition works with numerical expressions, like 4 + 5 = 5 + 4, and with algebraic expressions, like a + 5 = 5 + a.
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Commutative Property of Addition: Definition & Example
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