# Video: Commutative Operations

We explain the commutative laws of addition and multiplication and go through a series of examples to show how it works. We also show how subtraction and division are not commutative.

04:17

### Video Transcript

In this video, we’re gonna talk about commutativity, or the commutative law of operations. Addition and multiplication are both operations that are commutative, but subtraction and division aren’t.

The commutative law of addition is when applying the operation of addition to two terms, you get the same result regardless of their order. For example, if I do three add five, I get eight. And if I do five plus three, I also get eight. And viewing that on a number line, that makes good sense. If I do three plus five, I start at zero. I’m gonna go for the three and then I’m gonna add five. So one, two, three, four, five, end up at eight. And if I do five plus three, I start off at five and I do one, two, three, I still end up at eight.

And more generally, if I add two numbers 𝑎 and 𝑏, I get 𝑎 plus 𝑏. But if I add them in the other order, 𝑏 plus 𝑎, I still get the result 𝑎 plus 𝑏. And that works for whatever values of 𝑎 and 𝑏 you use, whether that integers, fractions, decimals, positive, or negative numbers.