# The Associative Property: Definition and Examples

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• 0:06 I Call Shotgun
• 0:41 Who's in Charge of the…
• 1:18 The Associative Property
• 4:07 Lesson Summary

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Lesson Transcript
Instructor: Jennifer Beddoe
There are three basic number properties that help to form the backbone of algebra. One of those properties is the associative property. This lesson will define the associative property and give some examples of how it works.

## I Call Shotgun

How many times have you been out with friends and heard, or yelled, that statement: 'I call shotgun!'? The unquestioned right to sit in the front seat and have room to stretch your legs and de facto control of the radio. At the next stop, someone else may call out for their turn in the front seat.

I bet the thought never crossed your mind that sitting in different seats in the vehicle did not change the makeup of the people that were with you. They are all the same, no matter where they are sitting. Bob is still Bob wherever he is riding, and Jody is still herself, even if she's no longer in control of what music you are listening to.

## Who's in Charge of the Math Radio?

So, who's in charge of the math radio? There is a mathematical rule governing that very question! OK, it's not presented in those terms, but it means the same. And the answer is the same as when you are out with your friends. But first, let's do a bit of background.

In mathematics, there are three basic principles for how equations work. They form the backbone of all higher math. These properties are:

â€¢ The commutative property

â€¢ The associative property

â€¢ The distributive property

They all govern different aspects of how you can manipulate and solve mathematical equations correctly.

## The Associative Property

The associative property is the focus for this lesson. It states that terms in an addition or multiplication problem can be grouped in different ways, and the answer remains the same. In other words, it doesn't matter which terms are in the back seat and which are in the front - the makeup of the equation is the same, just like it was in the car in the introduction.

Let's look a little bit at how that works. If you have an addition problem such as (3 + 6) + 13, you can also write it as 3 + (6 + 13), and, when you solve the problem, the answer will be the same either way: 22. Remember that the parenthesis signify the portion of the problem that should be completed first.

So, the associative property states that it doesn't matter which portion of the problem you do first, the answer will be the same. Again, this only works with addition and multiplication problems, and not if they are mixed. With mixed operations, you need to always follow the order of operations, which is: multiplication and division then addition and subtraction.

However, if your problem contains only addition or only multiplication, you can group them in any way and still get the same answer.

Look at this next example: (2 * 5) * 7 is the same as 2 * (5 * 7). It doesn't matter if you multiply the 2 and 5 first or the 5 and 7 first, the answer is still 70.

Let's try it both ways:

(2 * 5) * 7 = 10 * 7, or 70.

2 * (5 * 7) = 2 * 35, which is also 70.

The associative property can work with subtraction, but only if you convert your subtraction problem to an addition problem. If you remember, subtraction is the opposite of addition. Because of this, you can turn any subtraction problem into an addition problem. This means that 6 - 3 is equal to 6 + (-3).

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