The Associative Property in Mathematics: Addition and Multiplication Explained.

Associative Property

Changing the grouping of numbers will NOT change the value. For example: (7 + 4) + 8 = 7 + (4 + 8) also works with multiplication

The associative property is a concept in mathematics that describes the way in which numbers can be grouped together in an operation without changing the result. Specifically, the associative property states that when performing an operation on three or more numbers, the order in which the numbers are grouped will not affect the outcome. This applies to addition and multiplication.

For example, the associative property of addition states that:

(a + b) + c = a + (b + c)

This means that regardless of the order in which we group the values, the result will be the same. So, if we have the values 3, 4 and 5, we could group them in two ways:

(3 + 4) + 5 = 7 + 5 = 12

3 + (4 + 5) = 3 + 9 = 12

As you can see, the result is the same in both cases.

Similarly, the associative property of multiplication states that:

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

So, if we have the values 2, 3 and 4, we could group them in two ways:

(2 x 3) x 4 = 6 x 4 = 24

2 x (3 x 4) = 2 x 12 = 24

Once again, the result is the same in both cases.

It’s important to note that the associative property does not apply to subtraction or division, as changing the order of these operations will result in a different answer.

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