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The Commutative Property: Definition and Examples

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  • 0:05 The Long Commute
  • 0:41 A Mathematical Commute
  • 1:05 The Commutative Property
  • 3:00 So What?
  • 3:22 Lesson Summary
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Lesson Transcript
Instructor: Jennifer Beddoe
There are three major properties that deal with the addition and multiplication of numbers. One of those properties is the commutative property. This lesson will define and give examples of the commutative property and how it works.

The Long Commute

If you commute to school or work, you know that sometimes the traffic can drive you crazy. Maybe, like me, you have four of so different routes you can take to work that all are about the same distance and take roughly the same amount of time (depending on if you catch the lights right or not).

Obviously, you have decided on each of these routes to your destination because each of them will get you where you want to go. There probably is no chance that you will drive in a pattern that will not get you to school (even if you would like to take the day off). That is the whole point of the commute - to get you there, regardless of the pattern you take to get you there.

A Mathematical Commute

Right now you might be sitting there thinking, what on earth does this have to do with math? Keep listening, and you will find out.

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

• The commutative property

• The associative property

• The distributive property

The Commutative Property

This lesson focuses on the commutative property. It states that you can swap terms in an equation and still get the same answer. Just like your commute where you can take different routes to get to the same place, in addition and multiplication, you can swap the order of your terms and still get the same answer.

Let's look at a simple example: 2 + 5 = 7.

When you swap the terms, in this case the 2 and 5, you will still get the same answer: 5 + 2 = 7.

It works for multiplication as well. 4 * 6 = 24 is the same as 6 * 4 = 24.

As my high school algebra teacher said: the commutative property means that 'order doesn't matter' (for addition and multiplication).

It also doesn't matter how long your problem is. 5 + 3 + 9 + 12 is the same as 12 + 3 + 5 + 9. The answer is 29 both times.

Or 2 * 7 * 5 * 1 is the same as 7 * 2 * 1 * 5. Again, the answer will be 70, no matter what order the numbers are in.

The commutative property can also work with subtraction, if you are very careful. 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 the same as 6 + (-3).

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