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Associative law of multiplication

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

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Video transcript

Use the associative law of multiplication to write-- and here they have 12 times 3 in parentheses, and then they want us to multiply that times 10-- in a different way. Simplify both expressions to show they have identical results. So the way that they wrote it is-- let me just rewrite it. So they have 12 times 3 in parentheses, and then they multiply that times 10. Now whenever something is in parentheses, that means do that first. So this literally says let's do the 12 times 3 first. Now, what is 12 times 3? It's 36. So this evaluates to 36, and then we still have that times 10 over there. And we know the trick. Whenever we multiply something times a power of ten, we just add the number of zeroes that we have at the back of it, so this is going to be 360. This is going to be equal to 360. Now, the associative law of multiplication, once again, it sounds like a very fancy thing. All that means is it doesn't matter how we associate the multiplication or it doesn't matter how we put the parentheses, we're going to get the same answer, so let me write it down again. If we were to do 12 times 3 times 10, if we just wrote it like this without parentheses, if we just went left to right, that would essentially be exactly what we just did here on the left. But the associative law of multiplication says, you know what? We can multiply the 3 times 10 first and then multiply the 12, and we're going to get the exact same answer as if we multiplied the 12 times the 3 and then the 10. So let's just verify it for ourselves. So 3 times 10 is 30, and we still want to multiply the 12 times that. Now, what's 12 times 30? And we've seen this several times before. You can view it as a 12 times 3, which is 36, but we still have this 0 here. So that is also equal to 360. So it didn't matter how we associated the multiplication. You can do the 12 times 3 first or you can do the 3 times 10 first. Either way, they both evaluated to 360.