The associative property allows grouping of numbers in mathematical operations without changing the answer. It applies to addition and multiplication, and can be useful in simplifying calculations. It does not apply to subtraction or division.
The associative property of mathematics refers to the ability to group certain numbers together in specific mathematical operations, in any kind of order without changing the answer. Most commonly, children begin by studying the associative property of addition and then move on to studying the associative property of multiplication. With both of these operations, changing the order of the numbers added or the numbers multiplied will not result in a change in the sum or product.
Some confuse the associative property with the commutative property, but the commutative property tends to apply to only two numbers. Conversely, the associative property is often used to express the immutable nature of sums or products when three or more numbers are used. The property can also be discussed in relation to how parentheses are used in mathematics. Placing parentheses around some of the numbers that will be added does not change the results.
Consider the following examples:
1 + 2 + 3 +4 = 10. This will remain true even if the numbers are grouped differently.
(1 + 3) + (2 + 4) and (1 + 2 + 3) + 4 both equal ten. You don’t have to consider the order of these numbers or their grouping as the act of adding means they will still have the same sum total.
In the associative property of multiplication, the same basic idea holds. AXBXC = (AB)C or (AC)B. No matter how you lump these numbers together, the product stays constant.
Especially in multiplication, the associative property can prove to be very useful. Take for example the basic formula for calculating the area of a triangle: 1/2bh or half the base times the height. Now consider that the height is 4 inches and the base is 13 inches. It’s easier to take half the height (4/2 = 2) than half the base (13/2 = 6.5). It is much easier to solve the resulting 2 X 13 problem than to solve 6.5 X 4.
We can do this when we understand the associative property because we will know that it doesn’t matter in which order we multiply these numbers. This can take the work out of some complicated calculations and make math work a little easier. Note that this property doesn’t work when you use division or subtraction. Changing the order and grouping with these operations will affect the results.
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