Associative Property of Multiplication

The associative property of multiplication states that when multiplying three or more real numbers, the product is always the same regardless of their regrouping.

In English to associate means to join or to connect.

In math, the associative property of multiplication allows us to group factors in different ways to get the same product.

For example:

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

= 2 x (15) and = 6 x (5)

= 30 = 30

This means that 2 x (3 x 5) = (2 x 3) x 5

The product is the same, only the grouping is different.

Example: Is (2 x 6) x 7 = 2 x (6 x 7) a true statement?

Answer: Yes, because you can regroup the factors and get the same product.

(2 x 5) x 7 = 2 x (35)

=(10) x 7 and = 70

= 70

2 x (5 x 7)

Example: Is 5 x (3 x 8) = (5 x 3) x 8 a true statement?

Answer: Yes, because you can regroup the numbers and get the same product.

4 x (3 x 7) = 84 and

= 4 x (21) (4 x 3) x 7

= (12) x 7 = 84

Example: Use the associative property of multiplication to rewrite (5 x 4) x 3 In order to rewrite the expression, take the parenthesis off of the first two factors and put them around the last two factors.

Answer: 5 x (4 x 3)

Example: Use the associative property of multiplication to rewrite (6 x 2) x 7

In order to rewrite the expression, take the parenthesis off of the first two factors and put them around the last two factors.

Answer: 6 x (2 x 7)

Example: What is the missing number in 9 x (4 x 5) = (9 x ___) x 5?

Answer: 4

Because with the associative property of multiplication we can regroup the numbers and 9 x (4 x 5) = (9 x 4) x 5.

Example: What is the missing number in (7 x 8) x 3 = ___ x (8 x 3)?

Answer: 7

Because we can regroup the factors, and (7 x 8) x 3 = 7 x (8 x 3).

Now that you know that the numbers can be regrouped, you can regroup the factors to multiply in the order that you want.


Related Links:
Math
algebra
Commutative Property of Multiplication
Distributive Property


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