What is Associative Property?
This video gives examples of the associative property. The associative property states that when adding or multiplying a series of numbers, it does not matter how the terms are ordered. Simplifying within the parentheses is the first step using the order of operations.
Free Associative Property Fact Sheet
Use the associative property fact sheet below to help you get a better understanding of how associative property work. You are encouraged to print or download the associative property fact sheet with the PDF link at the bottom of the page.
The associative property states that when adding or multiplying a series of numbers it does not matter how the terms are ordered. Remember that simplifying within the parentheses is the first step using the order of operations, so you can remember the associative property, (the rule for the associative property) because the numbers are grouped, or “associated” with one another.
Let’s look at a couple of examples. A plus B, plus C is equal to A, plus B, plus C. Again, we’re going to do what’s in the parentheses first. Let’s try this with 2 plus 3, plus 4 equals 2, plus 3, plus 4. Again, we’re going to follow our order of operations, or PEMDAS.
We’re going to start by adding 2 plus 3, 5, plus 4 is equal to 2, plus (and again, following order of operations) 3, plus 4 which is 7. 5 plus 4 is 9, and that does equal 2, plus 7 which is also 9. You can see it doesn’t matter which terms we add first, since we’re doing addition, it doesn’t matter what we do first. Let’s see what happens when we do the multiplication side. Again, I’m going to use 2 times 3, times 4 is equal to 2, times 3, times 4.
According to PEMDAS, we have to start inside our parentheses, so that’s 2 times, 3 times 4 is 12 is equal to (again, starting in our parentheses) 2 times 3 is 6, times 4. 2 times 12 is 24, and that does equal 6, times 4, which is also 24. Like the commutative property, the associative property is only true for addition and multiplication.
Let’s look what happens when we try to use it on subtraction and division. If we tried to use the associative property it would look like A minus B, minus C, but again, it’s not going to be equal to A, minus B, minus C. I’m going to use numbers like 8 minus 4, minus 2 does not equal 8, minus 4, minus 2.
Again, using order of operations, 8 minus 4 is 4, minus 2 does not equal 8, minus 4, minus 2 is 2. 4 minus 2 is 2, and that does not equal 8, minus 2, which is 6. As you can see, the associative property does not work on subtraction. Let’s use it on division now.
With division it would look like A divided by B, divided by C, again, will not equal A, divided by B, divided by C. I’m going to use the same numbers we used for subtraction, so 8 divided by 4, divided by 2 does not equal 8, divided by 4 divided by 2.
Let’s simplify (order of operations). 8 divided by 4, (must be done first) 2, divided by 2 does not equal (again, parentheses first) 8, divided by, 4 divided by 2 is 2. 2 divided by 2 is 1, and that does not equal 8, divided by 2 which is 4, and that’s the associative property.