Commutative Property

The commutative property is one of several properties in math that allow us to evaluate expressions or compute mental math in a quicker, easier way. This is a well known number property that is used very often in math.

This property was first given it's name by a Frenchman named Francois Servois in 1814. He used the french word "commutatif", which means "switchable".

Why the word "switchable"? The commutative property can be used with addition or multiplication and it says that you can add or multiply numbers in any order and you will still end up with the same answer.

Let's first take a closer look at the commutative property for addition.

Commutative Property of Addition

You can add numbers in any order and still have the same sum.

Algebraic Definition: a + b = b + a


5 + 3 = 8   and   3 + 5 = 8

6 + 8 + 4 = 18  and  8 + 4 + 6 = 18

So, not too bad! Just switch the numbers around in your addition problem and you have used this property.

Now let's take a quick look at the Commutative Property for Multiplication. It is utilized in exactly the same way.

Commutative Property of Multiplication

You can multiply numbers (factors) in any order and still end up with the same product.

Algebraic Definition: ab = ba


5(3) = 15    and     3(5) = 15

2(9)(5) = 90   and    5(2)(9) = 90

Same concept - just switch the numbers around in your multiplication problem and you will end up with the same product.

One thing we don't want to forget.....


The commutative property only works for multiplication and division.  It does NOT work for subtraction or division.

For example:

5 - 3 = 2     but     3 - 5 = -2

18/2 = 9    but    2/18 = 1/9

So, Why is this Property so Helpful?

Is your mental math strong? If not, let's see how this property can make you a mental math whiz! Take a look at the following example.

Mental Math Strategies Using the Commutative Property

Let's say that you are given the following problem to compute mentally. Try to compute this problem mentally, in the order that it is presented!

20 + 3 + 55 + 7

Yeah, this is tough because you have to think about the sum of 23 + 55 which is 78 and then add another 7 to get 85.

Now, let's experiment.

Same numbers, different order. Let's compute this mentally and see if we can work any faster.

20 + 55 + 3 + 7

Did it take a shorter amount of time? This is easier because you know that                20 + 55 is 75 and 3 + 7 is 10, so 75 + 10 = 85.

We used the commutative property to rewrite these numbers in a different order. I ended up with the same answer, but it was easier to add 20 +55 and then 7+3.

The commutative property helps to make your mental math much faster!

Work smarter not harder!! Make sure that you make yourself more efficient with mental math.

The commutative property is an extremely helpful property used in math.

The associative property and distributive property are the two other number properties that are also used very often in math.

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