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Associative law of addition

Associative Law of Addition. Created by Sal Khan and Monterey Institute for Technology and Education.

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Video transcript

Use the associative law of addition to write the expression. We have a 77 plus 2 in parentheses, plus 3, in a different way. Simplify both expressions to show they have identical results. So this associative law of addition, which sounds very fancy and complicated, literally means that you can associate these three numbers in different ways or you can add them in different orders. Now let me just make that clear. So the way they wrote it right here, they wrote it 77 plus 2 in parentheses, and then they wrote plus 3. These parentheses mean do the 77 plus 2 before you add the 3. So if you were to evaluate this, you would evaluate what's in the parentheses first. So you would say, well, 77 plus 2, that's 79, so everything in the parentheses just evaluates to 79. And then you still have that plus 3. And 79 plus 3 is 82, so this is equal to 82. That's if you just evaluate it the way that they gave it to us. Now, the associative law of addition tells us it doesn't matter whether we add 77 and 2 first or whether we add 2 and 3 first. We can associate them differently. So this is going to be the exact same thing. This is the exact same thing as-- we could write it this way. Let me write them all. 77 plus 2 plus 3. If we have no parentheses here, this is actually the same thing as this over here, because we'd go 77 plus 2 is 79 plus 3 is 82. But the associative law tells as, well, you know what? I could do 77 plus 2 plus 3. I could add this first and then add it to 77, and it's going to be the exact same thing as if I added these two guys first and then add the 3. Let's verify that for ourselves. So 2 plus 3 is 5, so this evaluates to 77 plus 5. And 77 plus 5, once again, is 82. So it doesn't matter how you associate the numbers. Either way, you get 82. And that's the associative law of addition.