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.

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Video Transcript

In this video, weβre gonna talk about commutativity, or the commutative law of operations. Addition and multiplication are both operations that are commutative, but subtraction and division arenβ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. Iβm gonna go for the three and then Iβ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 π and π, I get π plus π. But if I add them in the other order, π plus π, I still get the result π plus π. And that works for whatever values of π and π you use, whether that integers, fractions, decimals, positive, or negative numbers.