Multiplying multi-digit numbers: 6,742x23

- [Instructor] In this video, we're going to try to compute 6742 times 23. So like always, pause this video and try to compute it for yourself. All right, now let's work on this together. And I'm going to do it using what's often known as the standard algorithm. Algorithm is just a fancy word for a series of steps, a process for doing something. So we have 6742 times 23. And so I'm gonna write the 23 in the same place values. So that's two 10s, so I'm gonna write it under the four 10s over there. And then three ones. I'll write it under the two ones. And it's important to realize this isn't the only way to multiply numbers. In fact, we've studied other methods for doing it in other videos. And it's important to realize what's really going on and how these different methods are all, on some level, doing the same thing, maybe just writing them different or doing them in different orders. So the way that we would tackle it using the standard algorithm, probably the way that your parents first learned to multiply multi-digit numbers like this is we'll take all of the numbers in 6742, all of the various places, and multiply it by three. And then we're gonna multiply it times two 10s. And then we're gonna add everything up. So let's first multiply it times three. So we have two times three, that is six. Then we have four times three. And what people often say is, "Four times three is 12, write the two, "and then carry the one." But what really just happened is you said four 10s times three is 12 10s. 12 10s can be written as two 10s plus 100. Then we say seven times three is 21. And then you'll say, "Oh, I have to add that other one, "so I get 22." But once again, what just happened? We said seven hundreds times three is 2100 plus another hundred is 22 hundreds, which can be expressed as two hundreds and two thousands. And then, last but not least, six times three is 18 plus two is 20. But remember, we're talking about thousands. So this is 20 thousands. So then we will move on to the two 10s right over here. So two times two 10s is four 10s. Now some folks might be tempted to put the four over there, but that's not four 10s. Four 10s would be right over here. And so it's common practice as you move to the next place value over, as you get to this two, that people will just put a zero here just so they don't make that mistake. All right, now let's keep going. What is four times two? Well that's eight. We'll just write the eight right over there. Why did that work? Well we're having four 10s times two 10s, well that's going to be eight times 10 times 10, eight hundreds. And then we say what is seven times two. That is 14, which of course we can write the four and then we can carry the one, so to speak. And I'll cross these out so I don't get confused. And then six times two is going to be equal to 12, plus this one that we had carried, is 13. So there we go. And then we just have to add everything up. And we are going to get six plus zero ones is six. Two 10s plus four 10s is six 10s. Two hundreds plus eight hundreds is 10 hundreds, which you could do as zero hundreds and one thousand. One thousand plus zero thousands plus four thousands is five thousands. Two 10 thousands plus three 10 thousands is going to be five 10 thousands. And then we just have one hundred thousand right over there. So we've got 155,066. And we are done.