Art of Problem Solving: Commutative Property of Addition

Art of Problem Solving: Commutative Property of Addition


[introductory music] Today we’re going to talk about rules. I know, I know, I know…you don’t like rules. But you’re thinking about home rules. And home
rules are always about what you CAN’T do. Math rules are better because they’re about
what you CAN do. Now I’m going to start with one of the simplest rules of addition. The
Commutative Property. I’m going to start with an example. I’ll count some hats here. I’ve got two floppy hats and three fuzzy hats. That sounds like 2+3 hats. Of course, there
are also three fuzzy hats and two floppy hats. So, that’s 3 plus 2 hats. Well, it doesn’t
matter which order I count the hats in. There are the same number of hats either way. So, these two have to be equal. And there’s nothing special about 2 and 3. You could write
4+5 is 5+4, 9 plus a million is a million plus 9. We don’t want to have to write down all those equations as rules. What we want to do is write down just one equation that
stands for all the possible equations that tell us it doesn’t matter what order you add the two numbers in. And to do that, I’m going to use variables. A variable is a letter that
stands for a number. So I’m going to write “a plus b” – and each of these letters is
a variable that stands for some number, and we can choose whatever number we want to to
put in there, like 2 and 3. And what the commutative property tells us is that it doesn’t matter
what order I add them in — a plus b is the same thing as b plus a. Nice and simple, and it makes sense. And that’s one of the great things about math rules. Math rules make sense, ’cause rules that don’t make sense, those are bad rules. But, uh, don’t tell your parents
you heard that from me.

2 thoughts on “Art of Problem Solving: Commutative Property of Addition

  1. I'm not sure why, but I am scandalized by the fact that you make the plus sign by drawing the horizontal line first, then the vertical.

  2. Wonderful video! Although Khan Academy videos are good, this video is way better than any Khan Academy video I've ever seen.

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