0:00:00.165,0:00:01.946
It never hurts to get a lot of practice.

0:00:01.961,0:00:02.845
So, in this video I'm just going to do

0:00:02.845,0:00:07.540
a bunch more of essentially what we call long division problems.

0:00:07.540,0:00:17.040
And so if you have four divided into two thousand two hundred ninety-two.

0:00:17.050,0:00:20.280
And I don't know exactly why they call it long division,

0:00:20.280,0:00:23.580
and we saw this in the last video a little bit.

0:00:23.580,0:00:25.548
I didn't call it long division then,

0:00:25.548,0:00:28.486
but I think the reason why is it takes you a long time

0:00:28.486,0:00:31.890
or it takes a long piece of your paper.

0:00:31.890,0:00:35.102
As you go along, you kind of have this thing,

0:00:35.102,0:00:37.270
this long tail that develops on the problem.

0:00:37.280,0:00:39.663
So all of those are, at least, reasons in my head

0:00:39.663,0:00:41.060
why it's called long division.

0:00:41.060,0:00:44.588
But we saw in the last video there's a way to tackle any division problem

0:00:44.588,0:00:46.746
while just knowing your multiplication tables

0:00:46.746,0:00:49.810
up to maybe ten times ten or twelve times twelve.

0:00:49.820,0:00:52.034
But just as a bit of review, this is the same thing

0:00:52.034,0:00:57.854
as two thousand two hundred ninety-two divided by four.

0:00:57.854,0:00:59.368
And it's actually the same thing--

0:00:59.368,0:01:01.385
you probably haven't seen this notation before--

0:01:01.385,0:01:06.644
as two thousand two hundred ninety-two divided by four.

0:01:06.644,0:01:09.006
These-- This, this, and this--

0:01:09.006,0:01:12.780
are all equivalent statements on some level.

0:01:12.790,0:01:14.930
And you could say, hey Sal, that looks like a fraction.

0:01:14.930,0:01:17.040
In case you have seen fractions already.

0:01:17.040,0:01:18.550
And that is exactly what it is.

0:01:18.560,0:01:20.060
It is a fraction.

0:01:20.060,0:01:21.865
But anyway, I'll just focus on this format

0:01:21.865,0:01:26.870
and in future videos we'll think about other ways to represent division.

0:01:26.870,0:01:28.460
So let's do this problem.

0:01:28.460,0:01:31.210
So four goes into two how many times?

0:01:31.210,0:01:34.580
It goes into two no times, so let's move on to--

0:01:34.590,0:01:35.320
let me switch colors--

0:01:35.320,0:01:37.250
Let's move on to the twenty-two.

0:01:37.260,0:01:40.100
Four goes into twenty-two how many times?

0:01:40.100,0:01:40.380
Let's see.

0:01:40.390,0:01:45.140
Four times five is equal to twenty.

0:01:45.140,0:01:49.590
Four times six is equal to twenty-four.

0:01:49.590,0:01:51.430
So six is too much.

0:01:51.430,0:01:55.405
So four goes into twenty-two five times.

0:01:55.405,0:01:58.050
Five times four is twenty.

0:01:58.059,0:01:59.908
There's going to be a little bit of a leftover,

0:01:59.908,0:02:02.166
And then we subtract.

0:02:02.166,0:02:03.843
Twenty-two minus twenty?

0:02:03.843,0:02:05.692
Well that's just two.

0:02:05.692,0:02:08.710
And then you bring down this nine.

0:02:08.720,0:02:11.148
And you saw in the last video exactly what this means, right?

0:02:11.148,0:02:13.706
When you wrote this five up here, notice you wrote hundreds place.

0:02:13.706,0:02:15.595
So this is really a five hundred.

0:02:15.595,0:02:17.856
But in this video I'm just going to focus more on the process,

0:02:17.856,0:02:19.860
and you can think more about what it actually means

0:02:19.870,0:02:21.650
in terms of where I'm writing the numbers.

0:02:21.650,0:02:24.358
But I think the process is going to be crystal clear,

0:02:24.358,0:02:25.780
hopefully, by the end of this video.

0:02:25.780,0:02:27.030
So we brought down the nine.

0:02:27.030,0:02:29.960
Four goes into twenty-nine how many times?

0:02:29.970,0:02:31.370
It goes into it at least six times.

0:02:31.380,0:02:32.740
What's four times seven?

0:02:32.750,0:02:34.840
Four times seven is twenty-eight.

0:02:34.840,0:02:36.610
So it goes into it at least seven times.

0:02:36.610,0:02:38.760
What's four times eight?

0:02:38.770,0:02:41.770
Four times eight is thirty-two, so it can't go into it eight times.

0:02:41.770,0:02:43.210
So it's going to go into it seven.

0:02:43.210,0:02:46.390
Four goes into twenty-nine seven times.

0:02:46.400,0:02:49.700
Seven times four is twenty-eight.

0:02:49.710,0:02:51.684
Twenty-nine minus twenty-eight,

0:02:51.684,0:02:56.370
to get our remainder for this step in the problem, is one.

0:02:56.370,0:02:59.520
And now we're going to bring down this two.

0:02:59.530,0:03:03.760
We're going to bring it down and you get a twelve.

0:03:03.770,0:03:04.750
Four goes into twelve?

0:03:04.750,0:03:05.170
That's easy.

0:03:05.180,0:03:06.680
Four times three is twelve.

0:03:06.680,0:03:09.080
Four goes into twelve three times.

0:03:09.080,0:03:11.390
Three times four is twelve.

0:03:11.400,0:03:13.360
Twelve minus twelve is zero.

0:03:13.360,0:03:14.730
We have no remainder.

0:03:14.740,0:03:20.390
So four goes into two thousand two hundred ninety-two exactly five hundred seventy-three times.

0:03:20.400,0:03:26.500
So this two thousand two hundred ninety-two divided by four we can say is equal to five hundred seventy-three.

0:03:26.500,0:03:32.240
Or we could say that this thing right here is equal to five hundred and seventy-three.

0:03:32.250,0:03:34.680
Let's do a couple of more.

0:03:34.680,0:03:39.080
Let's do a few more problems.

0:03:39.090,0:03:40.960
So I'll do that red color.

0:03:40.960,0:03:50.800
Let's say we had seven going into six thousand four hundred seventy-five.

0:03:50.810,0:03:52.200
Maybe it's called long division

0:03:52.200,0:03:54.350
because you write it nice and long up here and you have this line.

0:03:54.360,0:03:55.610
I don't know.

0:03:55.610,0:03:58.160
There's multiple reasons why it could be called long division.

0:03:58.160,0:04:00.760
So you say seven goes into six zero times.

0:04:00.770,0:04:03.660
So we need to keep moving forward.

0:04:03.660,0:04:06.050
So then we go to sixty-four.

0:04:06.060,0:04:09.160
Seven goes into sixty-four how many times?

0:04:09.160,0:04:11.040
Let's see.

0:04:11.050,0:04:15.300
Seven times seven is?

0:04:15.300,0:04:16.800
Well, that's way too small.

0:04:16.800,0:04:18.060
Let me think about it a little bit.

0:04:18.060,0:04:20.610
Well seven times nine is sixty-three.

0:04:20.620,0:04:21.390
That's pretty close.

0:04:21.390,0:04:23.350
And then seven times ten is going to be too big.

0:04:23.360,0:04:25.126
Seven times ten is seventy.

0:04:25.126,0:04:25.982
So that's too big.

0:04:25.982,0:04:29.681
So seven goes into sixty-four nine times.

0:04:29.711,0:04:32.680
Nine times seven is sixty-three.

0:04:32.690,0:04:38.040
Sixty-four minus sixty-three, to get our remainder at this stage, is one.

0:04:38.050,0:04:41.230
Bring down the seven.

0:04:41.240,0:04:43.110
Seven goes into seventeen how many times?

0:04:43.120,0:04:45.240
Well, seven times two is fourteen.

0:04:45.240,0:04:47.000
And then seven times three is twenty-one.

0:04:47.000,0:04:48.590
So three is too big.

0:04:48.600,0:04:51.490
So seven goes into seventeen two times.

0:04:51.500,0:04:54.350
Two times seven is fourteen.

0:04:54.350,0:04:57.610
Seventeen minus fourteen is three.

0:04:57.620,0:05:03.527
And now we bring down the five.

0:05:03.527,0:05:05.336
And seven goes into thirty-five--

0:05:05.350,0:05:07.810
That's in our seven multiplication tables-- five times.

0:05:07.810,0:05:14.093
Five times seven is thirty-five.

0:05:14.093,0:05:15.465
And there you go.

0:05:15.465,0:05:17.990
So the remainder is zero.

0:05:17.990,0:05:20.120
So all the examples I did so far had no remainders.

0:05:20.120,0:05:22.230
Let's do one that maybe might have a remainder.

0:05:22.240,0:05:23.694
And to ensure it has a remainder,

0:05:23.694,0:05:24.860
I'll just make up the problem.

0:05:24.870,0:05:27.300
It's much easier to make problems that have remainders

0:05:27.310,0:05:29.510
than the ones that don't have remainders.

0:05:29.510,0:05:37.016
So let's say I want to divide three into--

0:05:37.016,0:05:40.343
I'm going to divide it into

0:05:40.343,0:05:47.365
let's say, one seven three five zero nine two.

0:05:47.365,0:05:49.480
This will be a nice, beastly problem.

0:05:49.490,0:05:50.940
So if we can do this we can handle everything.

0:05:50.940,0:05:54.210
So it's one million seven hundred thirty-five thousand ninety-two.

0:05:54.220,0:05:56.514
That's what we're dividing three into.

0:05:56.529,0:05:58.721
So, three goes into--

0:05:58.721,0:06:00.390
And actually, I'm not sure if this will have a remainder.

0:06:00.390,0:06:03.136
In the future video I'll show you

0:06:03.136,0:06:06.260
how to figure out whether something is divisible by three.

0:06:06.260,0:06:07.150
Actually, we can do it right now.

0:06:07.160,0:06:08.780
We can just add up all these digits.

0:06:08.790,0:06:10.920
One plus seven is eight.

0:06:10.930,0:06:13.180
Eight plus three is eleven.

0:06:13.180,0:06:15.680
Eleven plus five is sixteen.

0:06:15.680,0:06:20.240
Sixteen plus nine is twenty-five.

0:06:20.250,0:06:22.190
Twenty-five plus two is twenty-seven.

0:06:22.190,0:06:24.660
So actually, this number is divisible by three.

0:06:24.670,0:06:27.420
So if you add up all of the digits, you get twenty-seven.

0:06:27.420,0:06:28.878
And then you can add up those digits--

0:06:28.878,0:06:30.545
Two plus seven is nine.

0:06:30.545,0:06:32.120
So that is divisible by three.

0:06:32.120,0:06:34.050
That's a trick that only works for three.

0:06:34.060,0:06:35.880
So this number actually is divisible by three.

0:06:35.890,0:06:37.698
So let me change it a little bit,

0:06:37.698,0:06:41.260
so it's not divisible by three.

0:06:41.260,0:06:44.867
Let me make this into a one.

0:06:44.867,0:06:46.940
Now this number will not be divisible by three.

0:06:46.940,0:06:50.425
I definitely want a number where I'll end up with a remainder.

0:06:50.425,0:06:53.090
Just so you see what it looks like.

0:06:53.100,0:06:54.570
So let's do this one.

0:06:54.570,0:06:57.010
Three goes into one zero times.

0:06:57.020,0:06:57.889
So we can just move forward.

0:06:57.889,0:06:59.368
You could write a zero here,

0:06:59.368,0:07:00.878
and multiply that out.

0:07:00.878,0:07:03.207
But that just makes it a little bit messy in my head.

0:07:03.207,0:07:04.368
So we just move one to the right.

0:07:04.383,0:07:06.880
Three goes into seventeen how many times?

0:07:06.880,0:07:11.050
Well, three times five is equal to fifteen.

0:07:11.060,0:07:13.930
And three times six is equal to eighteen and that's too big.

0:07:13.930,0:07:18.010
So three goes into seventeen right here five times.

0:07:18.010,0:07:20.570
Five times three is fifteen.

0:07:20.570,0:07:22.000
And we subtract.

0:07:22.010,0:07:27.010
Seventeen minus fifteen is two.

0:07:27.010,0:07:31.410
And now we bring down this three.

0:07:31.420,0:07:33.480
Three goes into twenty-three how many times?

0:07:33.480,0:07:36.740
Well, three times seven is equal to twenty-one.

0:07:36.750,0:07:38.350
And three times eight is too big.

0:07:38.350,0:07:40.010
That's equal to twenty-four.

0:07:40.010,0:07:44.070
So three goes into twenty-three seven times.

0:07:44.080,0:07:46.850
Seven times three is twenty-one.

0:07:46.860,0:07:47.910
Then we subtract.

0:07:47.910,0:07:51.740
Twenty-three minus twenty-one is two.

0:07:51.750,0:07:53.420
Now we bring down the next number.

0:07:53.420,0:07:54.570
We bring down the five.

0:07:54.570,0:07:57.350
I think you can appreciate why it's called long division now.

0:07:57.360,0:08:00.050
We bring down this five.

0:08:00.060,0:08:02.040
Three goes into twenty-five how many times?

0:08:02.040,0:08:04.506
Well three times eight gets you pretty close

0:08:04.506,0:08:06.153
and three times nine is too big.

0:08:06.153,0:08:08.230
So it goes into it eight times.

0:08:08.240,0:08:10.170
Eight times three is twenty-four.

0:08:10.170,0:08:12.210
I'm going to run out of space.

0:08:12.220,0:08:14.170
You subtract, you get one.

0:08:14.180,0:08:16.810
Twenty-five minus twenty-four is one.

0:08:16.810,0:08:20.146
Now we can bring down this zero.

0:08:20.146,0:08:23.059
You bring down this zero, just like that.

0:08:23.059,0:08:25.254
And you get three goes into ten how many times?

0:08:25.254,0:08:25.840
That's easy.

0:08:25.850,0:08:26.940
It goes into it three times.

0:08:26.940,0:08:28.000
Three times three is nine.

0:08:28.010,0:08:30.070
That's about as close to ten as we can get.

0:08:30.080,0:08:32.870
Three times three is nine.

0:08:32.870,0:08:33.612
Ten minus nine--

0:08:33.612,0:08:36.150
I'm going to have to scroll up and down here a little bit--

0:08:36.150,0:08:37.712
Ten minus nine is one,

0:08:37.712,0:08:39.681
and then we can bring down the next number.

0:08:39.681,0:08:41.420
I'm running out of colors.

0:08:41.420,0:08:44.750
I can bring down that nine.

0:08:44.750,0:08:46.590
Three goes into nineteen how many times?

0:08:46.600,0:08:48.880
Well, six is about as close as we can get.

0:08:48.880,0:08:49.861
That gets us to eighteen.

0:08:49.861,0:08:51.867
So three times six.

0:08:51.867,0:08:53.659
Three goes into nineteen six times.

0:08:53.659,0:08:56.390
Six times three-- let me scroll down.

0:08:56.400,0:08:59.520
Six times three is eighteen.

0:08:59.530,0:09:01.560
Nineteen minus eighteen-- we subtract it up here too.

0:09:01.570,0:09:04.360
Nineteen minus eighteen is one and then we're almost done.

0:09:04.370,0:09:06.120
I can revert back to the pink.

0:09:06.120,0:09:09.900
We bring down this one right there.

0:09:09.910,0:09:11.830
Three goes into eleven how many times?

0:09:11.840,0:09:15.670
Well, that's three times because three times four is too big.

0:09:15.670,0:09:17.170
Three times four is twelve, so that's too big.

0:09:17.170,0:09:18.890
So it goes into it three times.

0:09:18.890,0:09:22.260
So three goes into eleven three times.

0:09:22.260,0:09:26.180
Three times three is nine.

0:09:26.190,0:09:30.590
And then we subtract and we get a two.

0:09:30.600,0:09:32.669
And there's nothing left to bring down.

0:09:32.669,0:09:34.675
Right? When we look up here there's nothing left to bring down.

0:09:34.675,0:09:35.750
So we're done!

0:09:35.750,0:09:37.896
So we're left with the remainder of two,

0:09:37.896,0:09:40.410
after doing this entire problem.

0:09:40.410,0:09:45.313
So the answer, three goes into one million seven hundred thirty-five thousand ninety-one--

0:09:45.313,0:09:52.940
it goes into it five hundred seventy-eight thousand three hundred sixty-three remainder two.

0:09:52.950,0:09:57.190
And that remainder two was what we got all the way down there.

0:09:57.190,0:09:58.417
So hopefully you now appreciate

0:09:58.417,0:10:01.140
that you can tackle pretty much any division problem.

0:10:01.140,0:10:02.940
And you also, through this exercise,

0:10:02.955,0:10:06.110
can appreciate why it's called long division.