Dividing by 2-digits: 6250÷25

Welcome to the presentation on level 4 division. So what makes level 4 division harder than level 3 division is instead of having a one-digit number being divided into a multi-digit number, we're now going to have a two-addition 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 4 problems you'll see are actually a little harder than this. But let's say I had 25 goes into 6,250. So the best way to think about this is you say, OK, I have 25. Does 25 go into 6? Well, no. Clearly 6 is smaller than 25, so 25 does not go into 6. So then ask yourself, well, then if 25 doesn't go into 6, does 25 go into 62? Well, sure. 62 is larger than 25, so 25 will go into 62? Well, let's think about it. 25 times 1 is 25. 25 times 2 is 50. So it goes into 62 at least two times. And 25 times 3 is 75. So that's too much. So 25 goes into 62 two times. And there's really no mechanical way to go about figuring this out. You have to kind of think about, OK, how many times do I think 25 will go into 62? And sometimes you get it wrong. Sometimes you'll put a number here. Say if I didn't know, I would've put a 3 up here and then I would've said 3 times 25 and I would've gotten a 75 here. And then that would have been too large of a number, so I would have gone back and changed it to a 2. Likewise, if I had done a 1 and I had done 1 tmes 25, when I subtracted it out, the difference I would've gotten would be larger than 25. And then I would know that, OK, 1 is too small. I have to increase it to 2. 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, every time I go through the step it's kind of like- I kind of have to guess what the numbers is as opposed to kind of a method. And that's true; everyone has to do that. So anyway, so 25 goes into 62 two times. Now let's multiply 2 times 25. Well, 2 times 5 is 10. And then 2 times 2 plus 1 is 5. And we know that 25 times 2 is 50 anyway. Then we subtract. 2 minus 0 is 2. 6 minus 5 is 1. And now we bring down the 5. So the rest of the mechanics are pretty much just like a level 3 division problem. Now we ask ourselves, how many times does 25 go into 125? Well, the way I think about it is 25-- it goes into 100 about four times, so it will go into 125 one more time. It goes into it five times. If you weren't sure you could try 4 and then you would see that you would have too much left over. Or if you tried 6 you would see that you would actually get 6 times 25 is a number larger than 125. So you can't use 6. So if we say 25 goes into 125 five times then we just multiply 5 times 5 is 25. 5 times 2 is 10 plus 2, 125. So it goes in exact. So 125 minus 125 is clearly 0. Then we bring down this 0. And 25 goes into 0 zero times. 0 times 25 is 0. Remainder is 0. So we see that 25 goes into 6,250 exactly 250 times. Let's do another problem. Let's say I had-- let me pick an interesting number. Let's say I had 15 and I want to know how many times it goes into 2,265. Well, we just do the same thing we did before. We say OK, does 15 go into 2? No. So does 15 go into 22? Sure. 15 goes into 22 one time. Notice we wrote the 1 above the 22. If it go had gone into 2 we would've written the 1 here. But 15 goes into 22 one time. 1 times 15 is 15. 22 minus 15-- we could do the whole carrying thing-- 1, 12. 12 minus 5 is 7. 1 minus 1 is 0. 22 minus 15 is 7. Bring down the 6. OK, now how many times does 15 go into 76? Once again, there isn't a real easy mechanical way to do it. You can kind of eyeball it and estimate. Well, 15 times 2 is 30. 15 times 4 is 60. 15 times 5 is 75. That's pretty close, so let's say 15 goes into 76 five times. So 5 times 5 once again, I already figured it out in my head, but I'll just do it again. 5 times 1 is 5. Plus 7. Oh, sorry. 5 times 5 is 25. 5 times 1 is 5. Plus 2 is 7. Now we just subtract. 76 minus 75 is clearly 1. Bring down that 5. Well, 15 goes into 15 exactly one time. 1 times 15 is 15. Subtract it and we get a remainder of 0. So 15 goes into 2,265 exactly 151 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 67 going into 5,978. 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 67 goes into 5 zero times. 67 goes into 59 zero times. 67 goes into 597-- so let's see. 67 is almost 70 and 597 is almost 600. So if it was 70 goes into-- 70 times 9 to 630. Because 7 times 9 is 63. So I'm going to just eyball 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. 8 times 7-- well that's 56. And then 8 times 6 is 48. Plus 2 is 53. 7 minus 6 is 1. 9 minus 9 is 6. 5 minus 5 is 0. 61. So good. I got it right because if I got a number here that was larger than-- 67 or larger, than that means that this number up here wasn't large enough. But here, I got a number that's positive because 536 is less than 597. And it's less than 67, so I did that step right. So now we bring down this 8. Now this one might be a little bit trickier this time. Once again, we have almost 70 and here we have almost 630. So maybe it will go into it 9 times. Well, let's give it a try and see if it does. 9 times 7 is 63. 9 times 6 is 54. Plus 6 is 60. Good. So it did actually go into it nine times because 603 is less than 618. 8 minus 3 is 5. 1 minus 0 is 1. And 6 minus 6 is 0. We have a remainder of 15, which is smaller than 67. 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 67 goes into 5,978 89 times. And when it goes into it 89 times, you're left with a remainder of 15. hopefully you're ready now to try some level 4 division problems. Have fun.