The Commutative Property

Introducing terms such as the commutative property of arithmetic to kids in basic mathematics is in general the time we start to completely lose and confuse them!  This is because we start to use language that they are not familiar with.

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If we break these terms down to language they are familiar with understanding comes soon after. HOWEVER, once understanding is there, the proper terms must be used at the right times, as this is how mathematics is communicated!

So what is the Commutative Property of numbers?

When we discuss this in basic arithmetic, or further on in Basic Algebra, we are simply referring to the order in which numbers appear and are operated upon.  

If we operate on the numbers in one order, then change the order and operate again - if we get the same answer the operation is said to be commutative.  And that is simply it!

Let's look at each operation in turn.

Addition

Steps to be taken

Action

Result

Addition problem

Change Order

Are the answers the same?

Addition IS Commutative

ie - the order in which you add numbers does not change the result.

3 + 5 

5 + 3

8 = 8

8

8

Yes

Subtraction

Steps to be taken

Action

Result

Subtraction problem

Change Order

Are the answers the same?

Subtraction is NOT Commutative

ie - the order in which you add numbers does not change the result.

9 - 3

3 - 9

6 is not equal to -6

6

-6

NO

Multiplication

Steps to be taken

Action

Result

Multiplication problem

Change Order

Are the answers the same?

Multiplication IS Commutative

ie - the order in which you add numbers does not change the result.

3 x 5

5 x 3

15 = 15

15

15 

YES

Division

Steps to be taken

Action

Result

Division problem

Change Order

Are the answers the same?

Division Is NOT Commutative

ie - the order in which you add numbers does not change the result.

9/3

3/9

3 is not equal to 1/3

3

1/3

NO

Your child must understand the commutative property and the other properties of arithmetic if they want to enjoy (yes enjoy!) Basic Algebra!

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