Video:What Is the Associative Property?

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Transcript:What Is the Associative Property?

Hi, I'm Rebecca Pierce for About.com, and today we're going to be talking about the associative property.

Definition of the Associative Property

The associative property is important because it can be used in multiple areas of math from the simplest algebra to more complex analysis.

The associative property states that when you are adding a succession of numbers, it does not matter which numbers you add first. This also works for multiplication.

The Associative Property for Addition

So let's start with addition; and let's start in simple terms : a + b + c. And in the associative property we often use parenthesis to indicate which part of the addition we are going to do first. So with a + b + c we can have: (a + b) + c = a + (b + c).

So as an example of this, let's say that we have: 3 + 5 + 6. So going with the a + b + c that we talked about earlier, let's have: (3 + 5) + 6 = 8 + 6 = 14. So the associative property would tell us that that's equal to: 3 + (5 + 6) [so that means we do five plus six first] = 3 + 11 = 14.

The Associative Property for Multiplication

So now let's look at multiplication. Let's go to the general terms: a x b x c. So let's start with (a x b) x c = a x (b x c). So let's look at an example of this. Let's say we have: 3 x 5 x 6. (3 x 5) x 6 [so that means we do the three times five first] = 15 x 6 = 90.

And if we do it the second way, we have: 3 x (5 x 6) [that means that we do five times six first] = 3 x 30 = 90.

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