WEBVTT 00:00:00.165 --> 00:00:01.946 It never hurts to get a lot of practice. 00:00:01.961 --> 00:00:02.845 So, in this video I'm just going to do 00:00:02.845 --> 00:00:07.540 a bunch more of essentially what we call long division problems. 00:00:07.540 --> 00:00:17.040 And so if you have four divided into two thousand two hundred ninety-two. 00:00:17.050 --> 00:00:20.280 And I don't know exactly why they call it long division, 00:00:20.280 --> 00:00:23.580 and we saw this in the last video a little bit. 00:00:23.580 --> 00:00:25.548 I didn't call it long division then, 00:00:25.548 --> 00:00:28.486 but I think the reason why is it takes you a long time 00:00:28.486 --> 00:00:31.890 or it takes a long piece of your paper. 00:00:31.890 --> 00:00:35.102 As you go along, you kind of have this thing, 00:00:35.102 --> 00:00:37.270 this long tail that develops on the problem. 00:00:37.280 --> 00:00:39.663 So all of those are, at least, reasons in my head 00:00:39.663 --> 00:00:41.060 why it's called long division. 00:00:41.060 --> 00:00:44.588 But we saw in the last video there's a way to tackle any division problem 00:00:44.588 --> 00:00:46.746 while just knowing your multiplication tables 00:00:46.746 --> 00:00:49.810 up to maybe ten times ten or twelve times twelve. 00:00:49.820 --> 00:00:52.034 But just as a bit of review, this is the same thing 00:00:52.034 --> 00:00:57.854 as two thousand two hundred ninety-two divided by four. 00:00:57.854 --> 00:00:59.368 And it's actually the same thing-- 00:00:59.368 --> 00:01:01.385 you probably haven't seen this notation before-- 00:01:01.385 --> 00:01:06.644 as two thousand two hundred ninety-two divided by four. 00:01:06.644 --> 00:01:09.006 These-- This, this, and this-- 00:01:09.006 --> 00:01:12.780 are all equivalent statements on some level. 00:01:12.790 --> 00:01:14.930 And you could say, hey Sal, that looks like a fraction. 00:01:14.930 --> 00:01:17.040 In case you have seen fractions already. 00:01:17.040 --> 00:01:18.550 And that is exactly what it is. 00:01:18.560 --> 00:01:20.060 It is a fraction. 00:01:20.060 --> 00:01:21.865 But anyway, I'll just focus on this format 00:01:21.865 --> 00:01:26.870 and in future videos we'll think about other ways to represent division. 00:01:26.870 --> 00:01:28.460 So let's do this problem. 00:01:28.460 --> 00:01:31.210 So four goes into two how many times? 00:01:31.210 --> 00:01:34.580 It goes into two no times, so let's move on to-- 00:01:34.590 --> 00:01:35.320 let me switch colors-- 00:01:35.320 --> 00:01:37.250 Let's move on to the twenty-two. 00:01:37.260 --> 00:01:40.100 Four goes into twenty-two how many times? 00:01:40.100 --> 00:01:40.380 Let's see. 00:01:40.390 --> 00:01:45.140 Four times five is equal to twenty. 00:01:45.140 --> 00:01:49.590 Four times six is equal to twenty-four. 00:01:49.590 --> 00:01:51.430 So six is too much. 00:01:51.430 --> 00:01:55.405 So four goes into twenty-two five times. 00:01:55.405 --> 00:01:58.050 Five times four is twenty. 00:01:58.059 --> 00:01:59.908 There's going to be a little bit of a leftover, 00:01:59.908 --> 00:02:02.166 And then we subtract. 00:02:02.166 --> 00:02:03.843 Twenty-two minus twenty? 00:02:03.843 --> 00:02:05.692 Well that's just two. 00:02:05.692 --> 00:02:08.710 And then you bring down this nine. 00:02:08.720 --> 00:02:11.148 And you saw in the last video exactly what this means, right? 00:02:11.148 --> 00:02:13.706 When you wrote this five up here, notice you wrote hundreds place. 00:02:13.706 --> 00:02:15.595 So this is really a five hundred. 00:02:15.595 --> 00:02:17.856 But in this video I'm just going to focus more on the process, 00:02:17.856 --> 00:02:19.860 and you can think more about what it actually means 00:02:19.870 --> 00:02:21.650 in terms of where I'm writing the numbers. 00:02:21.650 --> 00:02:24.358 But I think the process is going to be crystal clear, 00:02:24.358 --> 00:02:25.780 hopefully, by the end of this video. 00:02:25.780 --> 00:02:27.030 So we brought down the nine. 00:02:27.030 --> 00:02:29.960 Four goes into twenty-nine how many times? 00:02:29.970 --> 00:02:31.370 It goes into it at least six times. 00:02:31.380 --> 00:02:32.740 What's four times seven? 00:02:32.750 --> 00:02:34.840 Four times seven is twenty-eight. 00:02:34.840 --> 00:02:36.610 So it goes into it at least seven times. 00:02:36.610 --> 00:02:38.760 What's four times eight? 00:02:38.770 --> 00:02:41.770 Four times eight is thirty-two, so it can't go into it eight times. 00:02:41.770 --> 00:02:43.210 So it's going to go into it seven. 00:02:43.210 --> 00:02:46.390 Four goes into twenty-nine seven times. 00:02:46.400 --> 00:02:49.700 Seven times four is twenty-eight. 00:02:49.710 --> 00:02:51.684 Twenty-nine minus twenty-eight, 00:02:51.684 --> 00:02:56.370 to get our remainder for this step in the problem, is one. 00:02:56.370 --> 00:02:59.520 And now we're going to bring down this two. 00:02:59.530 --> 00:03:03.760 We're going to bring it down and you get a twelve. 00:03:03.770 --> 00:03:04.750 Four goes into twelve? 00:03:04.750 --> 00:03:05.170 That's easy. 00:03:05.180 --> 00:03:06.680 Four times three is twelve. 00:03:06.680 --> 00:03:09.080 Four goes into twelve three times. 00:03:09.080 --> 00:03:11.390 Three times four is twelve. 00:03:11.400 --> 00:03:13.360 Twelve minus twelve is zero. 00:03:13.360 --> 00:03:14.730 We have no remainder. 00:03:14.740 --> 00:03:20.390 So four goes into two thousand two hundred ninety-two exactly five hundred seventy-three times. 00:03:20.400 --> 00:03:26.500 So this two thousand two hundred ninety-two divided by four we can say is equal to five hundred seventy-three. 00:03:26.500 --> 00:03:32.240 Or we could say that this thing right here is equal to five hundred and seventy-three. 00:03:32.250 --> 00:03:34.680 Let's do a couple of more. 00:03:34.680 --> 00:03:39.080 Let's do a few more problems. 00:03:39.090 --> 00:03:40.960 So I'll do that red color. 00:03:40.960 --> 00:03:50.800 Let's say we had seven going into six thousand four hundred seventy-five. 00:03:50.810 --> 00:03:52.200 Maybe it's called long division 00:03:52.200 --> 00:03:54.350 because you write it nice and long up here and you have this line. 00:03:54.360 --> 00:03:55.610 I don't know. 00:03:55.610 --> 00:03:58.160 There's multiple reasons why it could be called long division. 00:03:58.160 --> 00:04:00.760 So you say seven goes into six zero times. 00:04:00.770 --> 00:04:03.660 So we need to keep moving forward. 00:04:03.660 --> 00:04:06.050 So then we go to sixty-four. 00:04:06.060 --> 00:04:09.160 Seven goes into sixty-four how many times? 00:04:09.160 --> 00:04:11.040 Let's see. 00:04:11.050 --> 00:04:15.300 Seven times seven is? 00:04:15.300 --> 00:04:16.800 Well, that's way too small. 00:04:16.800 --> 00:04:18.060 Let me think about it a little bit. 00:04:18.060 --> 00:04:20.610 Well seven times nine is sixty-three. 00:04:20.620 --> 00:04:21.390 That's pretty close. 00:04:21.390 --> 00:04:23.350 And then seven times ten is going to be too big. 00:04:23.360 --> 00:04:25.126 Seven times ten is seventy. 00:04:25.126 --> 00:04:25.982 So that's too big. 00:04:25.982 --> 00:04:29.681 So seven goes into sixty-four nine times. 00:04:29.711 --> 00:04:32.680 Nine times seven is sixty-three. 00:04:32.690 --> 00:04:38.040 Sixty-four minus sixty-three, to get our remainder at this stage, is one. 00:04:38.050 --> 00:04:41.230 Bring down the seven. 00:04:41.240 --> 00:04:43.110 Seven goes into seventeen how many times? 00:04:43.120 --> 00:04:45.240 Well, seven times two is fourteen. 00:04:45.240 --> 00:04:47.000 And then seven times three is twenty-one. 00:04:47.000 --> 00:04:48.590 So three is too big. 00:04:48.600 --> 00:04:51.490 So seven goes into seventeen two times. 00:04:51.500 --> 00:04:54.350 Two times seven is fourteen. 00:04:54.350 --> 00:04:57.610 Seventeen minus fourteen is three. 00:04:57.620 --> 00:05:03.527 And now we bring down the five. 00:05:03.527 --> 00:05:05.336 And seven goes into thirty-five-- 00:05:05.350 --> 00:05:07.810 That's in our seven multiplication tables-- five times. 00:05:07.810 --> 00:05:14.093 Five times seven is thirty-five. 00:05:14.093 --> 00:05:15.465 And there you go. 00:05:15.465 --> 00:05:17.990 So the remainder is zero. 00:05:17.990 --> 00:05:20.120 So all the examples I did so far had no remainders. 00:05:20.120 --> 00:05:22.230 Let's do one that maybe might have a remainder. 00:05:22.240 --> 00:05:23.694 And to ensure it has a remainder, 00:05:23.694 --> 00:05:24.860 I'll just make up the problem. 00:05:24.870 --> 00:05:27.300 It's much easier to make problems that have remainders 00:05:27.310 --> 00:05:29.510 than the ones that don't have remainders. 00:05:29.510 --> 00:05:37.016 So let's say I want to divide three into-- 00:05:37.016 --> 00:05:40.343 I'm going to divide it into 00:05:40.343 --> 00:05:47.365 let's say, one seven three five zero nine two. 00:05:47.365 --> 00:05:49.480 This will be a nice, beastly problem. 00:05:49.490 --> 00:05:50.940 So if we can do this we can handle everything. 00:05:50.940 --> 00:05:54.210 So it's one million seven hundred thirty-five thousand ninety-two. 00:05:54.220 --> 00:05:56.514 That's what we're dividing three into. 00:05:56.529 --> 00:05:58.721 So, three goes into-- 00:05:58.721 --> 00:06:00.390 And actually, I'm not sure if this will have a remainder. 00:06:00.390 --> 00:06:03.136 In the future video I'll show you 00:06:03.136 --> 00:06:06.260 how to figure out whether something is divisible by three. 00:06:06.260 --> 00:06:07.150 Actually, we can do it right now. 00:06:07.160 --> 00:06:08.780 We can just add up all these digits. 00:06:08.790 --> 00:06:10.920 One plus seven is eight. 00:06:10.930 --> 00:06:13.180 Eight plus three is eleven. 00:06:13.180 --> 00:06:15.680 Eleven plus five is sixteen. 00:06:15.680 --> 00:06:20.240 Sixteen plus nine is twenty-five. 00:06:20.250 --> 00:06:22.190 Twenty-five plus two is twenty-seven. 00:06:22.190 --> 00:06:24.660 So actually, this number is divisible by three. 00:06:24.670 --> 00:06:27.420 So if you add up all of the digits, you get twenty-seven. 00:06:27.420 --> 00:06:28.878 And then you can add up those digits-- 00:06:28.878 --> 00:06:30.545 Two plus seven is nine. 00:06:30.545 --> 00:06:32.120 So that is divisible by three. 00:06:32.120 --> 00:06:34.050 That's a trick that only works for three. 00:06:34.060 --> 00:06:35.880 So this number actually is divisible by three. 00:06:35.890 --> 00:06:37.698 So let me change it a little bit, 00:06:37.698 --> 00:06:41.260 so it's not divisible by three. 00:06:41.260 --> 00:06:44.867 Let me make this into a one. 00:06:44.867 --> 00:06:46.940 Now this number will not be divisible by three. 00:06:46.940 --> 00:06:50.425 I definitely want a number where I'll end up with a remainder. 00:06:50.425 --> 00:06:53.090 Just so you see what it looks like. 00:06:53.100 --> 00:06:54.570 So let's do this one. 00:06:54.570 --> 00:06:57.010 Three goes into one zero times. 00:06:57.020 --> 00:06:57.889 So we can just move forward. 00:06:57.889 --> 00:06:59.368 You could write a zero here, 00:06:59.368 --> 00:07:00.878 and multiply that out. 00:07:00.878 --> 00:07:03.207 But that just makes it a little bit messy in my head. 00:07:03.207 --> 00:07:04.368 So we just move one to the right. 00:07:04.383 --> 00:07:06.880 Three goes into seventeen how many times? 00:07:06.880 --> 00:07:11.050 Well, three times five is equal to fifteen. 00:07:11.060 --> 00:07:13.930 And three times six is equal to eighteen and that's too big. 00:07:13.930 --> 00:07:18.010 So three goes into seventeen right here five times. 00:07:18.010 --> 00:07:20.570 Five times three is fifteen. 00:07:20.570 --> 00:07:22.000 And we subtract. 00:07:22.010 --> 00:07:27.010 Seventeen minus fifteen is two. 00:07:27.010 --> 00:07:31.410 And now we bring down this three. 00:07:31.420 --> 00:07:33.480 Three goes into twenty-three how many times? 00:07:33.480 --> 00:07:36.740 Well, three times seven is equal to twenty-one. 00:07:36.750 --> 00:07:38.350 And three times eight is too big. 00:07:38.350 --> 00:07:40.010 That's equal to twenty-four. 00:07:40.010 --> 00:07:44.070 So three goes into twenty-three seven times. 00:07:44.080 --> 00:07:46.850 Seven times three is twenty-one. 00:07:46.860 --> 00:07:47.910 Then we subtract. 00:07:47.910 --> 00:07:51.740 Twenty-three minus twenty-one is two. 00:07:51.750 --> 00:07:53.420 Now we bring down the next number. 00:07:53.420 --> 00:07:54.570 We bring down the five. 00:07:54.570 --> 00:07:57.350 I think you can appreciate why it's called long division now. 00:07:57.360 --> 00:08:00.050 We bring down this five. 00:08:00.060 --> 00:08:02.040 Three goes into twenty-five how many times? 00:08:02.040 --> 00:08:04.506 Well three times eight gets you pretty close 00:08:04.506 --> 00:08:06.153 and three times nine is too big. 00:08:06.153 --> 00:08:08.230 So it goes into it eight times. 00:08:08.240 --> 00:08:10.170 Eight times three is twenty-four. 00:08:10.170 --> 00:08:12.210 I'm going to run out of space. 00:08:12.220 --> 00:08:14.170 You subtract, you get one. 00:08:14.180 --> 00:08:16.810 Twenty-five minus twenty-four is one. 00:08:16.810 --> 00:08:20.146 Now we can bring down this zero. 00:08:20.146 --> 00:08:23.059 You bring down this zero, just like that. 00:08:23.059 --> 00:08:25.254 And you get three goes into ten how many times? 00:08:25.254 --> 00:08:25.840 That's easy. 00:08:25.850 --> 00:08:26.940 It goes into it three times. 00:08:26.940 --> 00:08:28.000 Three times three is nine. 00:08:28.010 --> 00:08:30.070 That's about as close to ten as we can get. 00:08:30.080 --> 00:08:32.870 Three times three is nine. 00:08:32.870 --> 00:08:33.612 Ten minus nine-- 00:08:33.612 --> 00:08:36.150 I'm going to have to scroll up and down here a little bit-- 00:08:36.150 --> 00:08:37.712 Ten minus nine is one, 00:08:37.712 --> 00:08:39.681 and then we can bring down the next number. 00:08:39.681 --> 00:08:41.420 I'm running out of colors. 00:08:41.420 --> 00:08:44.750 I can bring down that nine. 00:08:44.750 --> 00:08:46.590 Three goes into nineteen how many times? 00:08:46.600 --> 00:08:48.880 Well, six is about as close as we can get. 00:08:48.880 --> 00:08:49.861 That gets us to eighteen. 00:08:49.861 --> 00:08:51.867 So three times six. 00:08:51.867 --> 00:08:53.659 Three goes into nineteen six times. 00:08:53.659 --> 00:08:56.390 Six times three-- let me scroll down. 00:08:56.400 --> 00:08:59.520 Six times three is eighteen. 00:08:59.530 --> 00:09:01.560 Nineteen minus eighteen-- we subtract it up here too. 00:09:01.570 --> 00:09:04.360 Nineteen minus eighteen is one and then we're almost done. 00:09:04.370 --> 00:09:06.120 I can revert back to the pink. 00:09:06.120 --> 00:09:09.900 We bring down this one right there. 00:09:09.910 --> 00:09:11.830 Three goes into eleven how many times? 00:09:11.840 --> 00:09:15.670 Well, that's three times because three times four is too big. 00:09:15.670 --> 00:09:17.170 Three times four is twelve, so that's too big. 00:09:17.170 --> 00:09:18.890 So it goes into it three times. 00:09:18.890 --> 00:09:22.260 So three goes into eleven three times. 00:09:22.260 --> 00:09:26.180 Three times three is nine. 00:09:26.190 --> 00:09:30.590 And then we subtract and we get a two. 00:09:30.600 --> 00:09:32.669 And there's nothing left to bring down. 00:09:32.669 --> 00:09:34.675 Right? When we look up here there's nothing left to bring down. 00:09:34.675 --> 00:09:35.750 So we're done! 00:09:35.750 --> 00:09:37.896 So we're left with the remainder of two, 00:09:37.896 --> 00:09:40.410 after doing this entire problem. 00:09:40.410 --> 00:09:45.313 So the answer, three goes into one million seven hundred thirty-five thousand ninety-one-- 00:09:45.313 --> 00:09:52.940 it goes into it five hundred seventy-eight thousand three hundred sixty-three remainder two. 00:09:52.950 --> 00:09:57.190 And that remainder two was what we got all the way down there. 00:09:57.190 --> 00:09:58.417 So hopefully you now appreciate 00:09:58.417 --> 00:10:01.140 that you can tackle pretty much any division problem. 00:10:01.140 --> 00:10:02.940 And you also, through this exercise, 00:10:02.955 --> 00:10:06.110 can appreciate why it's called long division.