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The associate property will multipy and add groups of numbers.  No matter the grouped pair, the solution will be the same.

Comm
EXAMPLES & SOLUTIONS
Expressions:  Commutative Property

The commutative property allows you to change the order of numbers and receive the same result.

Commutative property is utilized while multiplying and adding.
They are needed to simplify expressions and equations.
Subtraction or division operators cannot be utilized with the commutative property. 
Commutative Property
Explanation of how to multiply with the commutative property

Rule:
Multiplying numbers in any order has the same result

Examples

             a * b  =   b * a
              8 * 2  =  2 * 8
            
       16   =   16

 a * b = b * a
 8 * 2  = 2 * 8

1

2

3

4

5

6

7

8

8 * 2  =  16

1

2

2 * 8 =  16

1

5

6

1

2

2

3

4

8

7

   8 * 2  =  2 * 8
       16  =  16

Commutative Property
Explanation of how to add with the commutative property

Rule:
Adding numbers in any order has the same result

Examples

      a + b + c  =   b +  c + a
     3 + 2  +  1   =  2 +  1 + 3
           
  5 + 1   =  3 + 3
                    6    =   6

       3                                           2    

3 + 2 = 5

     2                                           3    

2 + 3 = 5

3 + 2  2 + 3
       
=  5  

Fact:  Division is not allowed with the commutative property

Fact:  Subtraction is not allowed with the commutative property

                a / b            b / a
                8 / 2             2 / 8
                      4             0.25

  =  

  =  

  =  

                a -  b            b -  a
                3 - 2             2 - 3
                        1             -1

  =  

  =  

  =  

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