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Dividing a two digit number into a larger number. Created by Sal Khan.
Video transcript
Welcome to the presentation on level four division. So what makes level four division harder than level three division is instead of having a one-digit number being divided into a multi-digit number, we're now going to have a two-digit number divided into a multi-digit number. So let's get started with some practice problems. So let's start with what I would say is a relatively straightforward example. The level four problems you'll see are actually a little harder than this. But let's say I had twenty-five goes into six thousand two hundred fifty. So the best way to think about this is you say, okay, I have twenty-five. Does twenty-five go into six? Well, no. Clearly six is smaller than twenty-five, so twenty-five does not go into six. So then ask yourself well, then if twenty-five doesn't go into six, does twenty-five go into sixty-two? Well, sure. Sixty-two is larger than twenty-five, so twenty-five will go into sixty-two. Well, let's think about it. Twenty-five times one is twenty-five. Twenty-five times two is fifty. So it goes into sixty-two at least two times. And twenty-five times three is seventy-five. So that's too much. So twenty-five goes into sixty-two two times. And there's really no mechanical way to go about figuring this out. You have to kind of think about, okay, how many times do I think twenty-five will go into sixty-two? And sometimes you get it wrong. Sometimes you'll put a number here. Say if I didn't know, I would've put a three up here and then I would've said three times twenty-five and I would've gotten a seventy-five here. And then that would have been too large of a number, so I would have gone back and changed it to a two. Likewise, if I had done a one and I had done one times twenty-five, when I subtracted it out, the difference I would've gotten would be larger than twenty-five. And then I would know that, okay, one is too small. I have to increase it to two. I hope I didn't confuse you too much. I just want you to know that you shouldn't get nervous if you're like, boy, you know every time I go through the step it's kind of like-- I kind of have to guess what the number is as opposed to kind of a method. And that's true. Everyone has to do that. So anyway, so twenty-five goes into sixty-two two times. Now let's multiply two times twenty-five. Well, two times five is ten. And then two times two plus one is five. And we know that twenty-five times two is fifty anyway. Then we subtract. Two minus zero is two. Six minus five is one. And now we bring down the five. So the rest of the mechanics are pretty much just like a level three division problem. Now we ask ourselves, how many times does twenty-five go into one hundred twenty-five? Well, the way I think about it is, twenty-five-- it goes into one hundred about four times-- so it will go into one hundred twenty-five one more time. It goes into it five times. If you weren't sure you could try four and then you would see that you would have too much left over. Or if you tried six you would see that you would actually get-- six times twenty-five is a number larger than one hundred twenty-five. So you can't use six. So if we say twenty-five goes into one hundred twenty-five five times, then we just multiply five times five is twenty-five. Five times two is ten plus two. One hundred twenty five. So it goes in exact. So one hundred twenty-five minus one hundred twenty-five is clearly zero. Then we bring down this zero. And twenty-five goes into zero zero times. Zero times twenty-five is zero. Remainder is zero. So we see that twenty-five goes into six thousand two hundred fifty exactly two hundred fifty times. Let's do another problem. Let's say I had-- let me pick an interesting number. Let's say I had fifteen, and I want to know how many times it goes into two thousand two hundred sixty-five. Well, we just do the same thing we did before. We say okay, does fifteen go into two? No. So, does fifteen go into twenty-two? Sure. Fifteen goes into twenty-two one time. Notice we wrote the one above the twenty-two. If it go had gone into two we would've written the one here. But fifteen goes into twenty-two one time. One times fifteen is fifteen. Right? Twenty-two minus fifteen-- we could do the whole carrying thing-- one, twelve. Twelve minus five is seven. One minus one is zero. Twenty-two minus fifteen is seven. Bring down the six. Okay, now how many times does fifteen go into seventy-six? Once again, there isn't a real easy mechanical way to do it. You can kind of eyeball it and estimate. Well, fifteen times two is thirty. Fifteen times four is sixty. Fifteen times five is seventy-five. That's pretty close, so let's say fifteen goes into seventy-six five times. So five times five once again, I already figured it out in my head, but I'll just do it again. Five times one is five. Plus seven. Oh, sorry. Five times five is twenty-five. Five times one is five. Plus two is seven. Now we just subtract. Seventy-six minus seventy-five is clearly one. Bring down that five. Well, fifteen goes into fifteen exactly one time. One times fifteen is fifteen. Subtract it and we get a remainder of zero. So fifteen goes into two thousand two hundred sixty-five exactly one hundred fifty-one times. So just think about what we're doing here and why it's a little bit harder than when you have a one-digit number here. Is that you have to kind of think about, well, how many times does this two-digit number go into this larger number? And since you don't know two-digit multiplication tables-- very few people do-- you have to do a little bit of guesswork. Sometimes you can look at this first digit and look at the first digit here and make an estimate. But sometimes it's trial and error. You'll try and when you multiply it out, you might get it wrong on the first try. Let's do another problem. And actually, I'm going to pick numbers at random, so it might not have an easy remainder. But I think you'll get the point. I won't teach you decimals now, so I'll just leave the remainder if there is one. Let's say I had sixty-seven going into five thousand nine hundred seventy-eight. So I just picked these numbers randomly out of my head, so I'll show you that I also sometimes have to do a little bit of guesswork to figure out how many times one of these two-digit numbers go into a larger number. So sixty-seven goes into five zero times. Sixty-seven goes into fifty-nine zero times. Sixty-seven goes into five hundred ninety-seven-- so let's see. Sixty-seven is almost seventy and five hundred ninety-seven is almost six hundred. So if it was seventy goes into-- seventy times nine is six hundred thirty. Right? Because seven times nine is sixty-three. So I'm going to just eyeball approximate. I'm going to say that it goes into it eight times. I might be wrong. And you can always check, but well, we're going to actually check in this step essentially. Eight times seven-- well that's fifty-six. And then eight times six is forty-eight. Plus two is fifty-three. Seven minus six is one. Nine minus three is six. Five minus five is zero. Sixty-one. So, good. I got it right. Because if I got a number here that was larger than-- that was sixty-seven or larger, then that means that this number up here wasn't large enough. But here, I got a number that's positive, because five hundred thirty-six is less than five hundred ninety-seven. And it's less than sixty-seven, so I did that step right. So, now we bring down this eight. Now this one might be a little bit trickier this time. Once again, we have almost seventy and here we have almost six hundred thirty. So maybe it will go into it nine times. Well, let's give it a try and see if it does. Nine times seven is sixty-three. Nine times six is fifty-four. Plus six is sixty. Good! So it did actually go into it nine times because six hundred three is less than six hundred eighteen. Eight minus three is five. One minus zero is one. And six minus six is zero. We have a remainder of fifteen, which is smaller than sixty-seven. So I'm not going to teach you decimals right now, so we can just leave that remainder. So what we could say is that sixty-seven goes into five thousand nine hundred seventy-eight eighty-nine times. And when it goes into it eighty-nine times, you're left with a remainder of fifteen. Hopefully you're ready now to try some level four division problems. Have fun!