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Multiplying by multiples of 10

Sal decomposes multiples of ten to multiply. Created by Sal Khan.

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Video transcript

Let's see if we can figure out 3 times 60. Well, there's a couple of ways you could think about it. You could literally view this as 60 three times. So you could view this as 60 plus 60 plus 60. And you might be able to compute this in your head. 60 plus 60 is 120, plus another 60 is 180. And you'd be done. But another way to think about this is that 3 times 60 is the same thing as 3 times-- instead of thinking of it as 60, you could think of 60 as 6 times 10. 3 times 6 times 10. Now, when you're multiplying three numbers like this, it doesn't matter what order you multiply them in. So we could multiply the 3 times 6 first and get 18 and then multiply that times 10. And 18 times 10 is just going to be 180. It's going to be 18 with another zero. So this is going to be 180. Now, the more practice you get here, you'll realize, hey, I could have just said 3 times 6 is 18, but I have to worry about this 0 right over here. So I'm going to put one more zero at the end. It's going to be 180. Same answer that we got right over there. Let's do another one of these. So let's say we want to multiply 50 times 7. And I encourage you to pause the video and think about it yourself, and then unpause it and see what I do. So 50, well, there's a couple of ways you could think about it. One, you could literally try to add 50 seven times. Adding 7 fifty times would take forever, but you could literally say 50 plus 50 plus 50 plus 50-- let's see, that's four-- plus 50 plus 50. Let's see, that is six. I'll do one more right over here. 50 right over here. So this is 50 seven times. If you add together 50 plus 50 is 100, 150, 200, 250, 300, 350. So you could do it that way. But you could imagine that there is an easier way to do it. You just need to realize that 50 is the same thing as 10 times 5. So we could write this as 10 times 5, and then we're multiplying that times 7. Once again, the order that we multiply does not matter. So we can multiply the 5 times the 7 first. We know that that is 35, and we're going to multiply that times 10. 10 times 35, well, we're just going to stick a zero at the end of the 35. It's going to be equal to 350. Now I want to do that zero in that same color. It's going to be 350. Now, you might realize, hey, look, I could have just looked at this 5 right over here, multiplied the 5 times the 7, and have gotten the 35. And then, not forgetting that it's actually not a 5, it's a 50. So I have to multiply by 10 again, or I have to throw that 0 at the end of it to get that 0 right over here. So 50 times 7 is 350.