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Assocate
EXAMPLES & SOLUTIONS
Expressions: Associative Property

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

Associate property is utilized while multiplying and adding.
The original order of numbers must remain the same, but the grouped pair can change.
Subtraction or division operators cannot be utilized with the associated property. 
Associative Properties
Explanation of how to multiply with the associative property

Rule:  Multiplying numbers with different pair groups results in the same answer.

Examples

  (a * b) * c  =   a * (b * c)
 (4 * 2 ) * 2   =  4 *  ( 2* 2)
             8 * 2 
 =  4 * 4
                   16   =   16

8 * 2  =  16

  (a * b) * c
  (4 * 2) * 2 

1

2

3

4

 4 * 2  =  8

1

2

* 2

1

2

3

4

5

6

7

8

1

2

 4 * 4  =  16

 a *(b * c) 
4 * (2 * 2)

2 * 2  =  4 

1

2

1

2

* 4

1

2

3

4

1

2

3

4

 (4 * 2 ) * 2    =  4 * ( 2 * 2)
             8 * 2 
   =  4 * 4
                 
 16   =   16

Associative Properties
Explanation of how to add with the associative property

Rule: 
Adding numbers with different pair groups results in same answer.

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

+

 3    +    2    =   5

1

5 + 1 = 6

+

2   +    1    =   3

3 + 3 = 6

   (3 + 2 ) +  1   =  3 +  ( 2 + 1)
               
  5 + 1  =  3 + 3
                        6

Fact:  Division is not allowed with the associate property

      (a / b)  / c        a / (b / c)
      (4 / 2)  / 2         2 / (2 / 2)
                   2 / 2         2 / 1
                          1          2

  =  

  =  

  =  

  =  

Fact:  Subtraction is not allowed with the associate property

     (a - b)  - c         a - (b - c)
       (3 - 2)  - 1          3 - (2 - 1)
                    1  - 1         3 - 1
                          0         2

  =  

  =  

  =  

  =  

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