# Video: Associative Operations

Tim Burnham

We explain the associative laws of addition and multiplication and go through a series of examples to show how they work. We also show how subtraction and division are not associative.

05:29

### Video Transcript

In this video, we’re gonna talk about associativity and how the operations of addition and multiplication are associative but subtraction and division aren’t. The associative law of addition says that when you’ve got an expression that applies addition more than once, the result doesn’t depend upon how the pairs of terms are grouped. So for example, if you have one plus two plus three, it doesn’t matter whether you add the one and the two first and then add that to the three or whether you take one and then add the result of two plus three. Whichever way you do it, you’ll still get the answer six. So in general, 𝑎 plus 𝑏 plus 𝑐 gives the same result as 𝑎 plus 𝑏 plus 𝑐, and that gives the same result as 𝑎 plus 𝑏 plus 𝑐. And this works for all values of 𝑎, 𝑏, and 𝑐 whether they’re integers, fractions, decimals, positive, negative numbers, doesn’t matter. Now I’m sure you’ve all used this property before, even if you haven’t thought of it in quite this way or use these words to describe it. The fact that addition is associative can make adding up a bit easier.