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Nov11

What is the Associative Property of Multiplication?

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a x (b x c) = (a x b) x c

Multiplication is an operation that has various properties. One of them is the associative property. This property tells us that how we group factors does not alter the result of the multiplication, no matter how many factors there may be. We begin with an example:

3 x 2 x 5

The associative property of multiplication says that if we first multiply 3 x 2 and multiply the result by 5, it would be the same as if we first multiplied 2 x 5 and afterward multiplied by 3.

(3 x 2) x 5 = 3 x (2 x 5)

Shall we check?

3 x 2 = 6

6 x 5 = 30

2 x 5 = 10

10 x 3 = 30

Do you see?  We have obtained the same result by multiplying in two different ways. This is the associative property of multiplication!

Let’s do it with another example:

2 x 3 x 4 x 5

We will multiply in a variety of ways to demonstrate the associative property of multiplication:

2 x 3 x 4 x 5

2 x 3 = 6

6 x 4 = 24

24 x 5 = 120

 

3 x 5 x 2 x 4

3 x 5 = 15

15 x 2 = 30 

30 x 4 = 120

 

5 x 2 x 4 x 3

5 x 2 = 10

10 x 4 = 40 

40 x 3 = 120

 

4 x 5 x 3 x 2

4 x 5 = 20 

20 x 3 = 60 

60 x 2 = 120

The associative property of multiplication is easy, right?

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