Dividing numbers: long division with remainders

WEBVTT
Kind: captions
Language: en

00:00:00.000 --> 00:00:02.590
It never hurts to get a lot of
practice, so in this video I'm

00:00:02.590 --> 00:00:05.660
just going to do a bunch more
of essentially, what we call

00:00:05.660 --> 00:00:07.550
long division problems.

00:00:07.550 --> 00:00:17.050
And so if you have
4 goes into 2,292.

00:00:17.050 --> 00:00:20.290
And I don't know exactly why
they call it long division,

00:00:20.290 --> 00:00:23.590
and we saw this in the
last video a little bit.

00:00:23.590 --> 00:00:26.430
I didn't call it long division
then, but I think the reason

00:00:26.430 --> 00:00:30.250
why is it takes you a long
time or it takes a long

00:00:30.250 --> 00:00:31.890
piece of your paper.

00:00:31.890 --> 00:00:36.240
As you go along, you kind of
have this thing, this long tail

00:00:36.240 --> 00:00:37.280
that develops on the problem.

00:00:37.280 --> 00:00:39.740
So all of those are, at least,
reasons in my head why

00:00:39.740 --> 00:00:41.060
it's called long division.

00:00:41.060 --> 00:00:43.690
But we saw in the last video
there's a way to tackle any

00:00:43.690 --> 00:00:46.510
division problem while just
knowing your multiplication

00:00:46.510 --> 00:00:49.820
tables up to maybe 10
times 10 or 12 times 12.

00:00:49.820 --> 00:00:52.230
But just as a bit of review,
this is the same thing

00:00:52.230 --> 00:00:58.000
as 2,292 divided by 4.

00:00:58.000 --> 00:00:59.930
And it's actually the same
thing, and you probably haven't

00:00:59.930 --> 00:01:07.640
seen this notation before,
as 2,292 divided by 4.

00:01:07.640 --> 00:01:10.970
This, this, and this are
all equivalent statements

00:01:10.970 --> 00:01:12.790
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 --> 00:01:17.050
in case you have seen
fractions already.

00:01:17.050 --> 00:01:18.560
And that is exactly what it is.

00:01:18.560 --> 00:01:20.060
It is a fraction.

00:01:20.060 --> 00:01:22.650
But anyway, I'll just focus on
this format and in future

00:01:22.650 --> 00:01:26.880
videos we'll think about other
ways to represent division.

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So let's do this problem.

00:01:28.470 --> 00:01:31.220
So 4 goes into 2
how many times?

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It goes into 2 no times,
so let's move on to-- let

00:01:34.600 --> 00:01:35.330
me just switch colors.

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So let's move on to the 22.

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4 goes into 22 how many times?

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Let's see.

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4 times 5 is equal to 20.

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4 times 6 is equal to 24.

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So 6 is too much.

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So 4 goes into 22 five times.

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5 times 4 is 20.

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There's going to be a
little bit of a leftover.

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And then we subtract
22 minus 20.

00:02:03.850 --> 00:02:05.720
Well that's just 2.

00:02:05.720 --> 00:02:08.730
And then you bring down this 9.

00:02:08.730 --> 00:02:11.370
And you saw in the last video
exactly what this means.

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When you wrote this 5 up
here-- notice we wrote

00:02:13.000 --> 00:02:13.880
in the 100's place.

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So this is really a 500.

00:02:15.590 --> 00:02:17.220
But in this video I'm just
going to focus more on the

00:02:17.220 --> 00:02:19.880
process, and you can think more
about what it actually means

00:02:19.880 --> 00:02:21.660
in terms of where I'm
writing the numbers.

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But I think the process
is going to be crystal

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clear hopefully, by
the end of this video.

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So we brought down the 9.

00:02:27.040 --> 00:02:29.980
4 goes into 29 how many times?

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It goes into at
least six times.

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What's 4 times 7?

00:02:32.750 --> 00:02:34.840
4 times 7 is 28.

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So it goes into it at
least seven times.

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What's 4 times 8?

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4 times 8 is 32, so it can't go
into it eight times so it's

00:02:41.770 --> 00:02:43.220
going to go into it seven.

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4 goes into 29
nine seven times.

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7 times 4 is 28.

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29 minus 28 to get our
remainder for this step

00:02:53.930 --> 00:02:56.380
in the problem is 1.

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And now we're going to
bring down this 2.

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We're going to bring it
down and you get a 12.

00:03:03.770 --> 00:03:04.760
4 goes into 12?

00:03:04.760 --> 00:03:05.180
That's easy.

00:03:05.180 --> 00:03:06.680
4 times 3 is 12.

00:03:06.680 --> 00:03:09.080
4 goes into 12 three times.

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3 times 4 is 12.

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12 minus 12 is 0.

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We have no remainder.

00:03:14.740 --> 00:03:20.400
So 4 goes into 2,292
exactly 573 times.

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So this 2,292 divided by 4
we can say is equal to 573.

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Or we could say that this thing
right here is equal to 573.

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Let's do a couple of more.

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Let's do a few more problems.

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So I'll do that red color.

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Let's say we had 7
going into 6,475.

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Maybe it's called long division
because you write it nice and

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long up here and you
have this line.

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I don't know.

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There's multiple reasons why it
could be called long division.

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So you say 7 goes
into 6 zero times.

00:04:00.770 --> 00:04:03.670
So we need to keep
moving forward.

00:04:03.670 --> 00:04:06.060
So then we go to 64.

00:04:06.060 --> 00:04:09.170
7 goes into 64 how many times?

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Let's see.

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7 times 7 is?

00:04:15.300 --> 00:04:16.800
Well, that's way too small.

00:04:16.800 --> 00:04:18.070
Let me think about
it a little bit.

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Well 7 times 9 is 63.

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That's pretty close.

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And then 6 times 10 is
going to be too big.

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7 times 10 is 70.

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So that's too big.

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So 7 goes into 64 nine times.

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9 times 7 is 63.

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64 minus 63 to get our
remainder of this stage 1.

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Bring down the 7.

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7 goes into 17 how many times?

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Well, 7 times 2 is 14.

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And then 7 times 3 is 21.

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So 3 is too big.

00:04:48.600 --> 00:04:51.500
So 7 goes into 17 two times.

00:04:51.500 --> 00:04:54.350
2 times 7 is 14.

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17 minus 14 is 3.

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And now we bring down the 5.

00:05:03.700 --> 00:05:05.350
And 7 goes into 35?

00:05:05.350 --> 00:05:07.820
That's in our 7 multiplication
tables, five times.

00:05:07.820 --> 00:05:08.920
5 times 7 is 35.

00:05:14.200 --> 00:05:15.370
And there you go.

00:05:15.370 --> 00:05:17.990
So the remainder is zero.

00:05:17.990 --> 00:05:20.130
So all the examples I did
so far had no remainders.

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Let's do one that maybe
might have a remainder.

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And to ensure it has a
remainder I'll just

00:05:23.950 --> 00:05:24.870
make up the problem.

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It's much easier to make
problems that have remainders

00:05:27.310 --> 00:05:29.520
than the ones that
don't have remainders.

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So let's say I want to divide 3
into-- I'm going to divide it

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into, let's say 1,735,092.

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This will be a nice,
beastly problem.

00:05:49.490 --> 00:05:50.950
So if we can do this we
can handle everything.

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So it's 1,735,092.

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That's what we're
dividing 3 into.

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And actually, I'm not sure if
this will have a remainder.

00:06:00.530 --> 00:06:04.290
In the future video I'll show
you how to figure out whether

00:06:04.290 --> 00:06:06.270
something is divisible by 3.

00:06:06.270 --> 00:06:07.160
Actually, we can
do it right now.

00:06:07.160 --> 00:06:08.790
We can just add up
all these digits.

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1 plus 7 is 8.

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8 plus 3 is 11.

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11 5 five is 16.

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16 plus 9 is 25.

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25 plus 2 is 27.

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So actually, this number
is divisible by 3.

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So if you add up all of
the digits, you get 27.

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And then you can add up those
digits-- 2 plus 7 is 9.

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So that is divisible by 9.

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That's a trick that
only works for 3.

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So this number actually
is divisible by 3.

00:06:35.900 --> 00:06:37.990
So let me change it a
little bit, so it's

00:06:37.990 --> 00:06:41.270
not divisible by 3.

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Let me make this into a 1.

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Now this number will
not be divisible by 3.

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I definitely want a
number where I'll end

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up with a remainder.

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Just so you see what
it looks like.

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So let's do this one.

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3 goes into 1 zero times.

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So we can just move forward.

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You could write a 0 here and
multiply that out, but that

00:07:01.000 --> 00:07:03.070
just makes it a little
bit messy in my head.

00:07:03.070 --> 00:07:04.400
So we just move
one to the right.

00:07:04.400 --> 00:07:06.890
3 goes into 17 how many times?

00:07:06.890 --> 00:07:11.060
Well, 3 times 5 is equal to 15.

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And 3 times 6 is equal to
18 and that's too big.

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So 3 goes into 17 right
here five times.

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5 times 3 is 15.

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And we subtract.

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17 minus 15 is 2.

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And now we bring down this 3.

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3 goes into 23 how many times?

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Well, 3 times 7 is equal to 21.

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And 3 times 8 is too big.

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That's equal to 24.

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So 3 goes into 23 seven times.

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7 times 3 is 21.

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Then we subtract.

00:07:47.910 --> 00:07:51.750
23 minus 21 is 2.

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Now we bring down
the next number.

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We bring down the 5.

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I think you can appreciate why
it's called long division now.

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We bring down this 5.

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3 goes into 25 how many times?

00:08:02.040 --> 00:08:06.270
Well, 3 times 8 gets you pretty
close and 3 times 9 is too big.

00:08:06.270 --> 00:08:08.240
So it goes into it eight times.

00:08:08.240 --> 00:08:10.175
8 times 3 is 24.

00:08:10.175 --> 00:08:12.220
I'm going to run out of space.

00:08:12.220 --> 00:08:14.180
You subtract, you get 1.

00:08:14.180 --> 00:08:16.820
25 minus 24 is 1.

00:08:16.820 --> 00:08:19.116
Now we can bring down this 0.

00:08:23.110 --> 00:08:25.260
And you get 3 goes into
10 how many times?

00:08:25.260 --> 00:08:25.850
That's easy.

00:08:25.850 --> 00:08:26.950
It goes into it three times.

00:08:26.950 --> 00:08:28.020
3 times 3 is 9.

00:08:28.020 --> 00:08:30.090
That's about as close
to 10 as we can get.

00:08:30.090 --> 00:08:32.880
3 times 3 is 9.

00:08:32.880 --> 00:08:34.930
10 minus 9, I'm going to
have to scroll up and

00:08:34.930 --> 00:08:36.160
down here a little bit.

00:08:36.160 --> 00:08:39.850
10 minus 9 is 1, and then we
can bring down the next number.

00:08:39.850 --> 00:08:41.430
I'm running out of colors.

00:08:41.430 --> 00:08:44.760
I can bring down that 9.

00:08:44.760 --> 00:08:46.600
3 goes into 19 how many times?

00:08:46.600 --> 00:08:48.890
Well, 6 is about as
close as we can get.

00:08:48.890 --> 00:08:51.830
That gets us to 18.

00:08:51.830 --> 00:08:53.400
3 goes into 19 six times.

00:08:53.400 --> 00:08:56.410
6 times 3-- let me scroll down.

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6 times 3 is 18.

00:08:59.540 --> 00:09:01.570
19 minus 18-- we subtract
it up here too.

00:09:01.570 --> 00:09:04.370
19 minus 18 is 1 and
then we're almost done.

00:09:04.370 --> 00:09:06.130
I can revert back to the pink.

00:09:06.130 --> 00:09:09.920
We bring down this
1 right there.

00:09:09.920 --> 00:09:11.840
3 goes into 11 how many times?

00:09:11.840 --> 00:09:15.680
Well, that's three times
because 3 times 4 is too big.

00:09:15.680 --> 00:09:17.180
3 times 4 is 12, so
that's too big.

00:09:17.180 --> 00:09:18.900
So it goes into it three times.

00:09:18.900 --> 00:09:22.270
So 3 goes into 11 three times.

00:09:22.270 --> 00:09:26.190
3 times 3 is 9.

00:09:26.190 --> 00:09:30.600
And then we subtract
and we get a 2.

00:09:30.600 --> 00:09:32.910
And there's nothing
left to bring down.

00:09:32.910 --> 00:09:34.500
When we look up here there's
nothing left to bring

00:09:34.500 --> 00:09:35.750
down, so we're done.

00:09:35.750 --> 00:09:38.450
So we're left with the
remainder of 2 after doing

00:09:38.450 --> 00:09:40.420
this entire problem.

00:09:40.420 --> 00:09:46.190
So the answer, 3 goes into
1,735,091-- it goes into

00:09:46.190 --> 00:09:52.950
it 578,363 remainder 2.

00:09:52.950 --> 00:09:57.190
And that remainder 2 was what
we got all the way down there.

00:09:57.190 --> 00:09:59.740
So hopefully you now appreciate
and you can tackle pretty

00:09:59.740 --> 00:10:01.150
much any division problem.

00:10:01.150 --> 00:10:03.740
And you also, through this
exercise, can appreciate why

00:10:03.740 --> 00:10:06.110
it's called long division.


Introduction to long division

WEBVTT
Kind: captions
Language: en

00:00:00.740 --> 00:00:03.400
Let's now see if we can
divide into larger numbers.

00:00:03.400 --> 00:00:06.660
And just as a starting point,
in order to divide into larger

00:00:06.660 --> 00:00:09.920
numbers, you at least need to
know your multiplication tables

00:00:09.920 --> 00:00:12.950
from the 1-multiplication
tables all the way to, at

00:00:12.950 --> 00:00:14.540
least, the 10-multiplication.

00:00:14.540 --> 00:00:17.080
So all the way up to 10 times
10, which you know is 100.

00:00:17.080 --> 00:00:20.270
And then, starting at 1 times 1
and going up to 2 times 3, all

00:00:20.270 --> 00:00:22.320
the way up to 10 times 10.

00:00:22.320 --> 00:00:24.350
And, at least when I was
in school, we learned

00:00:24.350 --> 00:00:25.340
through 12 times 12.

00:00:25.340 --> 00:00:28.100
But 10 times 10 will
probably do the trick.

00:00:28.100 --> 00:00:29.770
And that's really just
the starting point.

00:00:29.770 --> 00:00:32.550
Because to do multiplication
problems like this, for

00:00:32.550 --> 00:00:34.150
example, or division
problems like this.

00:00:34.150 --> 00:00:39.640
Let's say I'm taking 25 and
I want to divide it by 5.

00:00:39.640 --> 00:00:42.980
So I could draw 25 objects and
then divide them into groups of

00:00:42.980 --> 00:00:46.050
5 or divide them into 5 groups
and see how many elements

00:00:46.050 --> 00:00:47.590
are in each group.

00:00:47.590 --> 00:00:49.900
But the quick way to do is
just to think about, well

00:00:49.900 --> 00:00:52.930
5 times what is 25, right?

00:00:52.930 --> 00:00:58.100
5 times question mark
is equal to 25.

00:00:58.100 --> 00:00:59.860
And if you know your
multiplication tables,

00:00:59.860 --> 00:01:02.070
especially your
5-multiplication tables,

00:01:02.070 --> 00:01:06.280
you know that 5 times 5
is equal to 25.

00:01:06.280 --> 00:01:08.480
So something like this, you'll
immediately just be able to

00:01:08.480 --> 00:01:12.230
say, because of your knowledge
of multiplication, that 5

00:01:12.230 --> 00:01:14.840
goes into 25 five times.

00:01:14.840 --> 00:01:16.320
And you'd write the
5 right there.

00:01:16.320 --> 00:01:18.580
Not over the 2, because you
still want to be careful

00:01:18.580 --> 00:01:20.040
of the place notation.

00:01:20.040 --> 00:01:21.650
You want to write the
5 in the ones place.

00:01:21.650 --> 00:01:25.480
It goes into it 5 ones times,
or exactly five times.

00:01:25.480 --> 00:01:26.190
And the same thing.

00:01:26.190 --> 00:01:31.770
If I said 7 goes into 49.

00:01:31.770 --> 00:01:33.250
That's how many times?

00:01:33.250 --> 00:01:36.910
Well you say, that's like
saying 7 times what-- you could

00:01:36.910 --> 00:01:38.850
even, instead of a question
mark, you could put a blank

00:01:38.850 --> 00:01:43.130
there --7 times what
is equal to 49?

00:01:43.130 --> 00:01:45.760
And if you know your
multiplication tables, you know

00:01:45.760 --> 00:01:50.090
that 7 times 7 is equal to 49.

00:01:50.090 --> 00:01:52.160
All the examples I've
done so far is a number

00:01:52.160 --> 00:01:53.150
multiplied by itself.

00:01:53.150 --> 00:01:55.030
Let me do another example.

00:01:55.030 --> 00:02:01.840
Let me do 9 goes into
54 how many times?

00:02:01.840 --> 00:02:03.840
Once again, you need to
know your multiplication

00:02:03.840 --> 00:02:05.100
tables to do this.

00:02:05.100 --> 00:02:09.290
9 times what is equal to 54?

00:02:09.290 --> 00:02:10.966
And sometimes, even if you
don't have it memorized, you

00:02:10.966 --> 00:02:14.720
could say 9 times 5 is 45.

00:02:14.720 --> 00:02:19.470
And 9 times 6 would be 9 more
than that, so that would be 54.

00:02:19.470 --> 00:02:22.380
So 9 goes into 54 six times.

00:02:22.380 --> 00:02:24.390
So just as a starting point,
you need to have your

00:02:24.390 --> 00:02:27.930
multiplication tables from 1
times 1 all the way up the

00:02:27.930 --> 00:02:29.250
10 times 10 memorized.

00:02:29.250 --> 00:02:33.320
In order to be able to do at
least some of these more basic

00:02:33.320 --> 00:02:36.700
problems relatively quickly.

00:02:36.700 --> 00:02:39.060
Now, with that out of the way,
let's try to do some problems

00:02:39.060 --> 00:02:41.600
that's might not fit
completely cleanly into your

00:02:41.600 --> 00:02:43.990
multiplication tables.

00:02:43.990 --> 00:02:47.190
So let's say I want to
divide-- I am looking

00:02:47.190 --> 00:02:54.800
to divide 3 into 43.

00:02:54.800 --> 00:02:58.440
And, once again, this is larger
than 3 times 10 or 3 times 12.

00:02:58.440 --> 00:02:58.930
Actually, look.

00:02:58.930 --> 00:03:00.950
Well, let me do
another problem.

00:03:00.950 --> 00:03:04.260
Let me do 3 into 23.

00:03:04.260 --> 00:03:07.150
And, if you know your 3-times
tables, you realize that

00:03:07.150 --> 00:03:10.060
there's 3 times nothing
is exactly 23.

00:03:10.060 --> 00:03:10.910
I'll do it right now.

00:03:10.910 --> 00:03:13.280
3 times 1 is 3.

00:03:13.280 --> 00:03:15.690
3 times 2 is 6.

00:03:15.690 --> 00:03:16.870
Let me just write them all out.

00:03:16.870 --> 00:03:24.690
3 times 3 is 9, 12, 15,
18, 21, 24, right?

00:03:24.690 --> 00:03:27.700
There's no 23 in the
multiples of 3.

00:03:27.700 --> 00:03:29.700
So how do you do this
division problem?

00:03:29.700 --> 00:03:32.880
Well what you do is you think
of what is the largest multiple

00:03:32.880 --> 00:03:34.440
of 3 that does go into 23?

00:03:34.440 --> 00:03:36.640
And that's 21.

00:03:36.640 --> 00:03:39.170
And 3 goes into 21
how many times?

00:03:39.170 --> 00:03:44.150
Well you know that 3
times 7 is equal to 21.

00:03:44.150 --> 00:03:48.520
So you say, well 3 will
go into 23 seven times.

00:03:48.520 --> 00:03:50.570
But it doesn't go into
it cleanly because

00:03:50.570 --> 00:03:53.850
7 times 3 is 21.

00:03:53.850 --> 00:03:55.750
So there's a
remainder left over.

00:03:55.750 --> 00:04:00.170
So if you take 23 minus 21,
you have a remainder of 2.

00:04:00.170 --> 00:04:08.010
So you could write that 23
divided by 3 is equal to 7

00:04:08.010 --> 00:04:10.780
remainder-- maybe I'll just,
well, write the whole

00:04:10.780 --> 00:04:15.010
word out --remainder 2.

00:04:15.010 --> 00:04:17.050
So it doesn't have to go
in completely cleanly.

00:04:17.050 --> 00:04:19.790
And, in the future, we'll learn
about decimals and fractions.

00:04:19.790 --> 00:04:22.470
But for now, you just say, well
it goes in cleanly 7 times,

00:04:22.470 --> 00:04:24.290
but that only gets us to 21.

00:04:24.290 --> 00:04:26.110
But then there's 2 left over.

00:04:26.110 --> 00:04:28.830
So you can even work with the
division problems where it's

00:04:28.830 --> 00:04:31.940
not exactly a multiple of the
number that you're dividing

00:04:31.940 --> 00:04:33.310
into the larger number.

00:04:33.310 --> 00:04:37.720
But let's do some practice
with even larger numbers.

00:04:37.720 --> 00:04:40.520
And I think you'll
see a pattern here.

00:04:40.520 --> 00:04:47.720
So let's do 4 going into--
I'm going to pick a pretty

00:04:47.720 --> 00:04:51.800
large number here --344.

00:04:51.800 --> 00:04:55.340
And, immediately when you see
that you might say, hey Sal, I

00:04:55.340 --> 00:04:57.850
know up to 4 times
10 or 4 times 12.

00:04:57.850 --> 00:04:59.850
4 times 12 is 48.

00:04:59.850 --> 00:05:01.340
This is a much larger number.

00:05:01.340 --> 00:05:03.690
This is way out of bounds
of what I know in my

00:05:03.690 --> 00:05:05.420
4-multiplication tables.

00:05:05.420 --> 00:05:07.610
And what I'm going to show you
right now is a way of doing

00:05:07.610 --> 00:05:10.910
this just knowing your
4-multiplication tables.

00:05:10.910 --> 00:05:12.920
So what you do is you
say 4 goes into this

00:05:12.920 --> 00:05:16.800
3 how many times?

00:05:16.800 --> 00:05:18.910
And you're actually saying
4 goes into this 3 how

00:05:18.910 --> 00:05:20.430
many hundred times?

00:05:20.430 --> 00:05:22.590
So this is-- Because
this is 300, right?

00:05:22.590 --> 00:05:24.880
This is 344.

00:05:24.880 --> 00:05:30.180
But 4 goes into 3 no hundred
times, or 4 goes into-- I guess

00:05:30.180 --> 00:05:32.810
the best way to think of
it --4 goes 3 0 times.

00:05:32.810 --> 00:05:34.470
So you can just move on.

00:05:34.470 --> 00:05:36.260
4 goes into 34.

00:05:36.260 --> 00:05:41.460
So now we're going
to focus on the 34.

00:05:41.460 --> 00:05:43.900
So 4 goes into 34
how many times?

00:05:43.900 --> 00:05:46.900
And here we can use our
4-multiplication tables.

00:05:46.900 --> 00:05:51.950
4-- Let's see, 4 times
8 is equal to 32.

00:05:51.950 --> 00:05:56.210
4 times 9 is equal to 36.

00:05:56.210 --> 00:05:59.630
So 4 goes into 34-- 30-- 9
is too many times, right?

00:05:59.630 --> 00:06:01.500
36 is larger than 34.

00:06:01.500 --> 00:06:03.740
So 4 goes into 34 eight times.

00:06:03.740 --> 00:06:06.000
There's going to be a
little bit left over.

00:06:06.000 --> 00:06:09.050
4 goes in the 34 eights times.

00:06:09.050 --> 00:06:10.860
So let's figure out
what's left over.

00:06:10.860 --> 00:06:15.000
And really we're saying 4 goes
into 340 how many ten times?

00:06:15.000 --> 00:06:17.800
We're actually saying 4 goes
into 340 eighty times.

00:06:17.800 --> 00:06:20.040
Because notice we wrote
this 8 in the tens place.

00:06:20.040 --> 00:06:23.020
But just for our ability to do
this problem quickly, you just

00:06:23.020 --> 00:06:26.400
say 4 goes into 34 eight times,
but make sure you write the 8

00:06:26.400 --> 00:06:28.770
in the tens place right there.

00:06:28.770 --> 00:06:30.100
8 times 4.

00:06:30.100 --> 00:06:30.970
We already know what that is.

00:06:30.970 --> 00:06:34.140
8 times 4 is 32.

00:06:34.140 --> 00:06:36.290
And then we figure
out the remainder.

00:06:36.290 --> 00:06:38.160
34 minus 32.

00:06:38.160 --> 00:06:40.400
Well, 4 minus 2 is 2.

00:06:40.400 --> 00:06:42.030
And then these 3's cancel out.

00:06:42.030 --> 00:06:43.300
So you're just left with a 2.

00:06:43.300 --> 00:06:46.120
But notice we're in the
tens column, right?

00:06:46.120 --> 00:06:48.710
This whole column right here,
that's the tens column.

00:06:48.710 --> 00:06:55.120
So really what we said is 4
goes into 340 eighty times.

00:06:55.120 --> 00:06:58.350
80 times 4 is 320, right?

00:06:58.350 --> 00:07:00.850
Because I wrote the 3 in
the hundreds column.

00:07:00.850 --> 00:07:04.000
And then there is-- and I don't
want to make this look like a--

00:07:04.000 --> 00:07:06.320
I don't want to make this look
like a-- Let me clean

00:07:06.320 --> 00:07:07.110
this up a little bit.

00:07:07.110 --> 00:07:09.010
I didn't want to make that line
there look like a-- when I was

00:07:09.010 --> 00:07:10.510
dividing the columns
--to look like a 1.

00:07:10.510 --> 00:07:12.380
But then there's a remainder
of 2, but I wrote the

00:07:12.380 --> 00:07:14.270
2 in the tens place.

00:07:14.270 --> 00:07:15.740
So it's actually a
remainder of 20.

00:07:15.740 --> 00:07:16.990
But let me bring down this 4.

00:07:16.990 --> 00:07:18.660
Because I didn't want to
just divide into 340.

00:07:18.660 --> 00:07:20.290
I divided into 344.

00:07:20.290 --> 00:07:22.290
So you bring down the 4.

00:07:22.290 --> 00:07:24.440
Let me switch colors.

00:07:24.440 --> 00:07:26.670
And then-- So another
way to think about it.

00:07:26.670 --> 00:07:31.250
We just said that 4 goes into
344 eighty times, right?

00:07:31.250 --> 00:07:33.050
We wrote the 8 in
the tens place.

00:07:33.050 --> 00:07:35.550
And then 8 times 4 is 320.

00:07:35.550 --> 00:07:38.170
The remainder is now 24.

00:07:38.170 --> 00:07:40.800
So how many times
does 4 go into 24?

00:07:40.800 --> 00:07:41.620
Well we know that.

00:07:41.620 --> 00:07:46.000
4 times 6 is equal to 24.

00:07:46.000 --> 00:07:49.090
So 4 goes into 24 six times.

00:07:49.090 --> 00:07:50.550
And we put that in
the ones place.

00:07:50.550 --> 00:07:53.480
6 times 4 is 24.

00:07:53.480 --> 00:07:54.560
And then we subtract.

00:07:54.560 --> 00:07:56.270
24 minus 24.

00:07:56.270 --> 00:07:58.490
That's-- We subtract at
that stage, either case.

00:07:58.490 --> 00:07:59.530
And we get 0.

00:07:59.530 --> 00:08:01.050
So there's no remainder.

00:08:01.050 --> 00:08:05.850
So 4 goes into 344 exactly
eighty-six times.

00:08:05.850 --> 00:08:09.180
So if your took 344 objects and
divided them into groups of

00:08:09.180 --> 00:08:10.900
4, you would get 86 groups.

00:08:10.900 --> 00:08:12.950
Or if you divided them
into groups of 86, you

00:08:12.950 --> 00:08:13.880
would get 4 groups.

00:08:13.880 --> 00:08:15.640
Let's do a couple
more problems.

00:08:15.640 --> 00:08:18.440
I think you're getting
the hang of it.

00:08:18.440 --> 00:08:21.180
Let me do 7-- I'll
do a simple one.

00:08:21.180 --> 00:08:24.790
7 goes into 91.

00:08:24.790 --> 00:08:28.710
So once again, well, this is
beyond 7 times 12, which

00:08:28.710 --> 00:08:31.340
is 84, which you know from
our multiplication tables.

00:08:31.340 --> 00:08:34.650
So we use the same system we
did in the last problem.

00:08:34.650 --> 00:08:37.750
7 goes into 9 how many times?

00:08:37.750 --> 00:08:41.220
7 goes into 9 one time.

00:08:41.220 --> 00:08:44.640
1 times 7 is 7.

00:08:44.640 --> 00:08:48.330
And you have 9 minus 7 is 2.

00:08:48.330 --> 00:08:51.190
And then you bring down the 1.

00:08:51.190 --> 00:08:51.770
21.

00:08:51.770 --> 00:08:53.590
And remember, this might seem
like magic, but what we really

00:08:53.590 --> 00:08:58.530
said was 7 goes into 90 ten
times-- 10 because we wrote the

00:08:58.530 --> 00:09:02.840
1 in the tens place --10
times 7 is 70, right?

00:09:02.840 --> 00:09:05.000
You can almost put a
0 there if you like.

00:09:05.000 --> 00:09:08.410
And 90 with the remainder--
And 91 minus 70 is 21.

00:09:08.410 --> 00:09:12.640
So 7 goes into 91 ten
times remainder 21.

00:09:12.640 --> 00:09:15.780
And then you say 7 goes into
21-- Well you know that.

00:09:15.780 --> 00:09:17.590
7 times 3 is 21.

00:09:17.590 --> 00:09:20.170
So 7 goes into 21 three times.

00:09:20.170 --> 00:09:22.710
3 times 7 is 21.

00:09:22.710 --> 00:09:24.550
You subtract these
from each other.

00:09:24.550 --> 00:09:26.340
Remainder 0.

00:09:26.340 --> 00:09:32.000
So 91 divided by 7
is equal to 13.

00:09:32.000 --> 00:09:32.640
Let's do another one.

00:09:32.640 --> 00:09:34.940
And I won't take that little
break to explain the

00:09:34.940 --> 00:09:35.860
places and all of that.

00:09:35.860 --> 00:09:36.800
I think you understand that.

00:09:36.800 --> 00:09:39.800
I want, at least, you to get
the process down really

00:09:39.800 --> 00:09:41.580
really well in this video.

00:09:41.580 --> 00:09:44.990
So let's do 7-- I keep
using the number 7.

00:09:44.990 --> 00:09:46.510
Let me do a different number.

00:09:46.510 --> 00:09:56.560
Let me do 8 goes into
608 how many times?

00:09:56.560 --> 00:09:59.440
So I go 8 goes into
6 how many times?

00:09:59.440 --> 00:10:00.740
It goes into it 0 time.

00:10:00.740 --> 00:10:01.980
So let me keep moving.

00:10:01.980 --> 00:10:05.360
8 goes into 60 how many times?

00:10:05.360 --> 00:10:06.820
Let me write down the 8.

00:10:06.820 --> 00:10:09.110
Let me draw a line here so
we don't get confused.

00:10:09.110 --> 00:10:11.340
Let me scroll down
a little bit.

00:10:11.340 --> 00:10:13.760
I need some space
above the number.

00:10:13.760 --> 00:10:15.580
So 8 goes into 60
how many times?

00:10:15.580 --> 00:10:19.590
We know that 8 times
7 is equal to 56.

00:10:19.590 --> 00:10:23.330
And that 8 times 8
is equal to 64.

00:10:23.330 --> 00:10:25.640
So 8 goes into-- 64 is too big.

00:10:25.640 --> 00:10:26.770
So it's not this one.

00:10:26.770 --> 00:10:30.000
So 8 goes into 60 seven times.

00:10:30.000 --> 00:10:31.540
And there's going to be
a little bit left over.

00:10:31.540 --> 00:10:34.600
So 8 goes into 60 seven times.

00:10:34.600 --> 00:10:37.790
Since we're doing the whole 60,
we put the 7 above the ones

00:10:37.790 --> 00:10:41.030
place in the 60, which is the
tens place in the whole thing.

00:10:41.030 --> 00:10:44.970
7 times 8, we know, is 56.

00:10:44.970 --> 00:10:47.100
60 minus 56.

00:10:47.100 --> 00:10:48.030
That's 4.

00:10:48.030 --> 00:10:48.990
We could do that in our heads.

00:10:48.990 --> 00:10:50.270
Or if we wanted, we can borrow.

00:10:50.270 --> 00:10:51.510
That be a 10.

00:10:51.510 --> 00:10:53.380
That would be a 5.

00:10:53.380 --> 00:10:54.890
10 minus 6 is 4.

00:10:54.890 --> 00:10:57.130
Then you bring down this 8.

00:10:59.980 --> 00:11:02.750
8 goes into 48 how many times?

00:11:02.750 --> 00:11:06.260
Well what's 8 times 6?

00:11:06.260 --> 00:11:09.210
Well, 8 times 6 is exactly 48.

00:11:09.210 --> 00:11:13.170
So 8 times-- 8 goes
into 48 six times.

00:11:13.170 --> 00:11:17.180
6 times 8 is 48.

00:11:17.180 --> 00:11:18.180
And you subtract.

00:11:18.180 --> 00:11:19.500
We subtracted up here as well.

00:11:19.500 --> 00:11:22.020
48 minus 48 is 0.

00:11:22.020 --> 00:11:25.260
So, once again, we get
a remainder of 0.

00:11:25.260 --> 00:11:27.660
So hopefully, that gives you
the hang of how to do these

00:11:27.660 --> 00:11:28.790
larger division problems.

00:11:28.790 --> 00:11:31.150
And all we really need to know
to be able to do these, to

00:11:31.150 --> 00:11:34.780
tackle these, is our
multiplication tables up to

00:11:34.780 --> 00:11:38.150
maybe 10 times 10
or 12 times 12.


Division 1

WEBVTT
Kind: captions
Language: en

00:00:00.730 --> 00:00:04.390
I think you've probably heard
the word divide before, where

00:00:04.390 --> 00:00:06.730
someone tells you to
divide something up.

00:00:06.730 --> 00:00:11.450
Divide the money between you
and your brother or between

00:00:11.450 --> 00:00:12.650
you and your buddy.

00:00:12.650 --> 00:00:14.640
And it essentially means
to cut up something.

00:00:14.640 --> 00:00:16.720
So let me write down
the word divide.

00:00:20.510 --> 00:00:24.370
Let's say that I
have 4 quarters.

00:00:24.370 --> 00:00:27.500
Do my best to draw
the quarters.

00:00:27.500 --> 00:00:32.320
If I have 4 quarters
just like that.

00:00:32.320 --> 00:00:36.030
That's my rendition of George
Washington on the quarters.

00:00:36.030 --> 00:00:38.820
And let's say there's two of
us and we're going to divide

00:00:38.820 --> 00:00:40.550
the quarters between us.

00:00:40.550 --> 00:00:42.520
So this is me right here.

00:00:42.520 --> 00:00:45.870
Let me try my best to draw me.

00:00:45.870 --> 00:00:48.760
So that's me right there.

00:00:48.760 --> 00:00:51.160
Let's see, I have
a lot of hair.

00:00:51.160 --> 00:00:56.090
And then this is
you right there.

00:00:56.090 --> 00:00:57.300
Do my best.

00:00:57.300 --> 00:00:59.270
So you're bald.

00:00:59.270 --> 00:01:00.315
You have side burns.

00:01:03.760 --> 00:01:07.000
Maybe you have a little
bit of a beard.

00:01:07.000 --> 00:01:09.090
I want to get too
focused on the drawing.

00:01:09.090 --> 00:01:12.240
So that's you, that's me, and
we're going to divide these 4

00:01:12.240 --> 00:01:15.520
quarters between the 2 of us.

00:01:15.520 --> 00:01:22.230
So notice, we have 4 quarters
and we're going to divide

00:01:22.230 --> 00:01:23.580
between the 2 of us.

00:01:23.580 --> 00:01:26.540
There are 2 of us.

00:01:26.540 --> 00:01:28.740
And I want to stress
the number 2.

00:01:28.740 --> 00:01:31.880
So we're going to divide
4 quarters by 2.

00:01:31.880 --> 00:01:34.480
We're going to divide it
between the 2 of us.

00:01:34.480 --> 00:01:36.900
And you've probably done
something like this.

00:01:36.900 --> 00:01:37.540
What happens?

00:01:37.540 --> 00:01:40.230
Well, each of us are
going to get 2 quarters.

00:01:40.230 --> 00:01:41.290
So let me divide it.

00:01:41.290 --> 00:01:43.180
We're going to
divide it into 2.

00:01:43.180 --> 00:01:46.460
Essentially what I did do is
I take the 4 quarters and I

00:01:46.460 --> 00:01:48.785
divide it into 2 equal groups.

00:01:51.820 --> 00:01:53.930
And that's what division is.

00:01:53.930 --> 00:01:57.620
We cut up this group of
quarters into 2 equal groups.

00:01:57.620 --> 00:02:01.550
So when you divide 4 quarters
into 2 groups, so this was

00:02:01.550 --> 00:02:03.230
4 quarters right there.

00:02:08.030 --> 00:02:09.760
And you want to divide
it into 2 groups.

00:02:09.760 --> 00:02:11.770
This is group 1.

00:02:11.770 --> 00:02:16.530
Group 1 right here.

00:02:16.530 --> 00:02:19.380
And this is group 2 right here.

00:02:19.380 --> 00:02:21.890
How many numbers
are in each group?

00:02:21.890 --> 00:02:23.990
Or how many quarters
are in each group?

00:02:23.990 --> 00:02:26.870
Well, in each group I
have 1, 2 quarters.

00:02:26.870 --> 00:02:28.660
Let me use a brighter color.

00:02:28.660 --> 00:02:31.260
I have 1, 2 quarters
in each group.

00:02:31.260 --> 00:02:34.040
1 quarter and 2 quarters
in each group.

00:02:34.040 --> 00:02:36.630
So to write this out
mathematically, I think this is

00:02:36.630 --> 00:02:40.070
something that you've done,
probably as long as you've been

00:02:40.070 --> 00:02:43.020
splitting money between you and
your siblings and your buddies.

00:02:43.020 --> 00:02:44.420
Actually, let me scroll over
a little bit, so you can

00:02:44.420 --> 00:02:47.330
see my entire picture.

00:02:47.330 --> 00:02:50.360
How do we write this
mathematically?

00:02:50.360 --> 00:02:55.270
We can write that 4
divided by-- so this 4.

00:02:55.270 --> 00:02:56.980
Let me use the right colors.

00:02:56.980 --> 00:03:04.020
So this 4, which is this 4,
divided by the 2 groups, these

00:03:04.020 --> 00:03:07.500
are the 2 groups: group 1 and
this is group 2 right here.

00:03:07.500 --> 00:03:11.030
So divided into 2 groups
or into 2 collections.

00:03:11.030 --> 00:03:17.200
4 divided by 2 is equal to--
when you divide 4 into 2

00:03:17.200 --> 00:03:20.530
groups, each group is going
to have 2 quarters in it.

00:03:20.530 --> 00:03:23.010
It's going to be equal to 2.

00:03:23.010 --> 00:03:25.050
And I just wanted to use this
example because I want to show

00:03:25.050 --> 00:03:27.180
you that division is something
that you've been

00:03:27.180 --> 00:03:29.260
using all along.

00:03:29.260 --> 00:03:32.560
And another important, I guess,
takeaway or thing to realize

00:03:32.560 --> 00:03:35.020
about this, is on some level
this is the opposite

00:03:35.020 --> 00:03:36.330
of multiplication.

00:03:36.330 --> 00:03:43.210
If I said that I had 2 groups
of 2 quarters I would multiply

00:03:43.210 --> 00:03:49.550
the 2 groups times the 2
quarters each and I would say

00:03:49.550 --> 00:03:53.000
I would then have 4 quarters.

00:03:53.000 --> 00:03:55.930
So on some level these are
saying the same thing.

00:03:55.930 --> 00:03:58.230
But just to make it a little
bit more concrete in our

00:03:58.230 --> 00:04:01.400
head, let's do a couple
of more examples.

00:04:01.400 --> 00:04:03.600
Let's do a bunch
of more examples.

00:04:03.600 --> 00:04:09.250
So let's write down, what is
6 divided by-- I'm trying to

00:04:09.250 --> 00:04:10.900
keep it nice and color coded.

00:04:10.900 --> 00:04:14.800
6 divided by 3, what
is that equal to?

00:04:14.800 --> 00:04:17.150
Let's just draw 6 objects.

00:04:17.150 --> 00:04:18.590
They can be anything.

00:04:18.590 --> 00:04:23.030
Let's say I have
6 bell peppers.

00:04:23.030 --> 00:04:25.050
I won't take too much
trouble to draw them.

00:04:25.050 --> 00:04:27.260
Well, that's not what a
bell pepper looks like,

00:04:27.260 --> 00:04:28.210
but you get the idea.

00:04:28.210 --> 00:04:34.370
So 1, 2, 3, 4, 5, 6.

00:04:34.370 --> 00:04:36.030
And I'm going to
divide it by 3.

00:04:36.030 --> 00:04:38.500
And one way that we can think
about that is that means I want

00:04:38.500 --> 00:04:42.690
to divide my 6 bell peppers
into 3 equal groups

00:04:42.690 --> 00:04:43.730
of bell peppers.

00:04:43.730 --> 00:04:46.230
You could kind of think of it
if 3 people are going to share

00:04:46.230 --> 00:04:48.970
these bell peppers, how
many do each of them get?

00:04:48.970 --> 00:04:50.840
So let's divide it
into 3 groups.

00:04:50.840 --> 00:04:52.770
So that's our 6 bell peppers.

00:04:52.770 --> 00:04:54.580
I'm going to divide
it into 3 groups.

00:04:54.580 --> 00:04:57.210
So the best way to divide it
into 3 groups is I can have 1

00:04:57.210 --> 00:05:02.470
group right there, 2 groups, or
the second group right there,

00:05:02.470 --> 00:05:04.910
and then, the third group.

00:05:04.910 --> 00:05:10.350
And then each group will have
exactly how many bell peppers?

00:05:10.350 --> 00:05:12.120
They'll have 1, 2.

00:05:12.120 --> 00:05:13.510
1, 2.

00:05:13.510 --> 00:05:15.140
1, 2 bell peppers.

00:05:15.140 --> 00:05:20.060
So 6 divided by 3
is equal to 2.

00:05:20.060 --> 00:05:23.030
So the best way or one way to
think about it is that you

00:05:23.030 --> 00:05:26.790
divided the 6 into 3 groups.

00:05:26.790 --> 00:05:29.880
Now you could view that a
slightly different way,

00:05:29.880 --> 00:05:31.900
although it's not completely
different, but it's a good

00:05:31.900 --> 00:05:33.110
way to think about it.

00:05:33.110 --> 00:05:38.150
You could also think of
it as 6 divided by 3.

00:05:38.150 --> 00:05:41.690
And once again, let's
say I have raspberries

00:05:41.690 --> 00:05:42.850
now-- easier to draw.

00:05:42.850 --> 00:05:47.460
1, 2, 3, 4, 5, 6.

00:05:47.460 --> 00:05:50.060
And here, instead of
dividing it into 3

00:05:50.060 --> 00:05:51.600
groups like we did here.

00:05:51.600 --> 00:05:54.290
This was 1 group, 2
group, 3 groups.

00:05:54.290 --> 00:05:57.180
Instead of dividing into 3
groups, what I want to do is

00:05:57.180 --> 00:06:00.690
say well, if I'm dividing
6 divided by 3, I want to

00:06:00.690 --> 00:06:02.710
divide it into groups of 3.

00:06:02.710 --> 00:06:04.260
Not into 3 groups.

00:06:04.260 --> 00:06:05.960
I want to divide it
into groups of 3.

00:06:05.960 --> 00:06:09.490
So how many groups of
3 am I going to have?

00:06:09.490 --> 00:06:12.930
Well, let me draw
some groups of 3.

00:06:12.930 --> 00:06:16.040
So that is one group of 3.

00:06:16.040 --> 00:06:17.910
And that is two groups of 3.

00:06:21.750 --> 00:06:26.920
So if I take 6 things and I
divide them into groups of 3, I

00:06:26.920 --> 00:06:29.950
will end up with 1, 2 groups.

00:06:29.950 --> 00:06:33.230
So that's another way to
think about division.

00:06:33.230 --> 00:06:34.550
And this is an
interesting thing.

00:06:34.550 --> 00:06:37.400
When you think about these two
relations, you'll see a

00:06:37.400 --> 00:06:42.120
relationship between 6 divided
by 3 and 6 divided by 3.

00:06:42.120 --> 00:06:43.720
Let me do that right here.

00:06:43.720 --> 00:06:49.960
What is 6 divided by 2 when
you think of it in this

00:06:49.960 --> 00:06:51.740
context right here?

00:06:51.740 --> 00:06:55.250
6 divided by 2, when you
do it like that-- let me

00:06:55.250 --> 00:06:58.780
draw 1, 2, 3, 4, 5, 6.

00:06:58.780 --> 00:07:01.440
When we think about 6 divided
by 2 in terms of dividing it

00:07:01.440 --> 00:07:05.140
into 2 groups, what we can end
up is we could have 1 group

00:07:05.140 --> 00:07:09.520
like this and then 1 group
like this, and each group

00:07:09.520 --> 00:07:11.500
will have 3 elements.

00:07:11.500 --> 00:07:12.710
It'll have 3 things in it.

00:07:12.710 --> 00:07:14.730
So 6 divided by 2 is 3.

00:07:14.730 --> 00:07:16.400
Or you could think of
it the other way.

00:07:16.400 --> 00:07:22.560
You could say that 6 divided
by 2 is-- you're taking 6

00:07:22.560 --> 00:07:26.420
objects: 1, 2, 3, 4, 5, 6.

00:07:26.420 --> 00:07:29.810
And your dividing it into
groups of 2 where each

00:07:29.810 --> 00:07:31.200
group has 2 elements.

00:07:31.200 --> 00:07:32.920
And that on some level is
an easier thing to do.

00:07:32.920 --> 00:07:36.640
If each group has 2 elements,
well, that's the 1 right there.

00:07:36.640 --> 00:07:38.690
They don't even have
to be nicely ordered.

00:07:38.690 --> 00:07:41.700
This could be one group right
there and that could be the

00:07:41.700 --> 00:07:42.990
other group right there.

00:07:42.990 --> 00:07:44.580
I don't have to draw
them all stacked up.

00:07:44.580 --> 00:07:45.920
These are just groups of 2.

00:07:45.920 --> 00:07:47.390
But how many groups do I have?

00:07:47.390 --> 00:07:49.250
I have 1, 2, 3.

00:07:49.250 --> 00:07:51.070
I have 3 groups.

00:07:51.070 --> 00:07:55.460
But notice something, it's no
coincidence that 6 divided by 3

00:07:55.460 --> 00:08:00.690
is 2 and 6 divided by 2 is 3.

00:08:00.690 --> 00:08:03.280
Let me write that down.

00:08:03.280 --> 00:08:10.290
We get 6 divided by 3 is
equal to 2 and 6 divided

00:08:10.290 --> 00:08:13.290
by 2 is equal to 3.

00:08:13.290 --> 00:08:16.400
And the reason why you see this
relation where you can kind of

00:08:16.400 --> 00:08:22.500
swap this 2 and this 3 is
because 2 times 3

00:08:22.500 --> 00:08:23.350
is equal to 6.

00:08:26.160 --> 00:08:28.490
Let's say I have 2 groups of 3.

00:08:28.490 --> 00:08:29.840
Let me draw 2 groups of 3.

00:08:29.840 --> 00:08:33.430
So that's 1 group of 3 and then
here's another group of 3.

00:08:37.350 --> 00:08:40.790
So 2 groups of 3 is equal to 6.

00:08:40.790 --> 00:08:44.360
2 times 3 is equal to 6.

00:08:44.360 --> 00:08:46.770
Or you could think of
it the other way if I

00:08:46.770 --> 00:08:48.090
have 3 groups of 2.

00:08:48.090 --> 00:08:50.900
So that's 1 group
of 2 right there.

00:08:50.900 --> 00:08:53.840
I have another group
of 2 right there.

00:08:53.840 --> 00:08:56.450
And then I have a 3
group of 2 right there.

00:08:56.450 --> 00:08:57.960
What is that equal to?

00:08:57.960 --> 00:09:01.240
3 groups of 2-- 3 times 2.

00:09:01.240 --> 00:09:03.260
That's also equal to 6.

00:09:03.260 --> 00:09:04.840
So 2 times 3 is equal to 6.

00:09:04.840 --> 00:09:06.060
3 times 2 is equal to 6.

00:09:06.060 --> 00:09:07.830
We saw this in the
multiplication video that

00:09:07.830 --> 00:09:09.530
the order doesn't matter.

00:09:09.530 --> 00:09:12.490
But that's the reason why if
you want to divide it, if you

00:09:12.490 --> 00:09:14.630
want to go the other way-- if
you have 6 things and you

00:09:14.630 --> 00:09:18.990
want to divide it into
groups of 2, you get 3.

00:09:18.990 --> 00:09:21.120
If you have 6 and you want
to divide into groups

00:09:21.120 --> 00:09:23.070
of 3, you get 2.

00:09:23.070 --> 00:09:24.360
Let's do a couple
of more problems.

00:09:24.360 --> 00:09:26.440
I think it'll really
make sense about what

00:09:26.440 --> 00:09:28.340
division is all about.

00:09:33.980 --> 00:09:35.870
Let's do an interesting one.

00:09:35.870 --> 00:09:40.600
Let's do 9 divided by 4.

00:09:40.600 --> 00:09:43.360
So if we think about 9 divided
by 4, let me draw 9 objects.

00:09:43.360 --> 00:09:51.170
1, 2, 3, 4, 5, 6, 7, 8, 9.

00:09:51.170 --> 00:09:54.370
Now when you divide by 4, for
this problem, I'm thinking

00:09:54.370 --> 00:09:57.140
about dividing it
into groups of 4.

00:09:57.140 --> 00:09:59.120
So if I want to divide it
into groups of 4, let

00:09:59.120 --> 00:10:00.000
me try doing that.

00:10:00.000 --> 00:10:02.670
So here is one group of 4.

00:10:02.670 --> 00:10:04.820
I just picked any of
them right like that.

00:10:04.820 --> 00:10:06.570
That's one group of 4.

00:10:06.570 --> 00:10:11.100
Then here's another
group of 4 right there.

00:10:11.100 --> 00:10:13.330
And then I have this
left over thing.

00:10:13.330 --> 00:10:17.220
Maybe we could call it a
remainder, where I can't put

00:10:17.220 --> 00:10:18.450
this one into a group of 4.

00:10:18.450 --> 00:10:21.870
When I'm dividing by 4
I can only cut up the

00:10:21.870 --> 00:10:24.090
9 into groups of 4.

00:10:24.090 --> 00:10:28.610
So the answer here, and this is
a new concept for you maybe, 9

00:10:28.610 --> 00:10:32.580
divided by 4 is going
to be 2 groups.

00:10:32.580 --> 00:10:35.340
I have one group here and
another group here, and then

00:10:35.340 --> 00:10:36.670
I have a remainder of 1.

00:10:36.670 --> 00:10:38.970
I have 1 left over that I
wasn't able to do with.

00:10:41.670 --> 00:10:45.890
Remainder-- that
says remainder 1.

00:10:45.890 --> 00:10:49.410
9 divided by 4 is
2 remainder 1.

00:10:49.410 --> 00:10:53.010
If I asked you what 12 divided
by 4 is, so let me do 12.

00:10:53.010 --> 00:11:00.910
1, 2, 3, 4, 5, 6, 7,
8, 9, 10, 11, 12.

00:11:00.910 --> 00:11:01.980
So let me write that down.

00:11:01.980 --> 00:11:06.010
12 divided by 4.

00:11:06.010 --> 00:11:08.860
So I want to divide these
12 objects-- maybe

00:11:08.860 --> 00:11:10.480
they're apples or plums.

00:11:10.480 --> 00:11:12.520
And divide them
into groups of 4.

00:11:12.520 --> 00:11:14.830
So let me see if I can do that.

00:11:14.830 --> 00:11:19.340
So this is one group
of 4 just like that.

00:11:19.340 --> 00:11:23.340
This is another group
of 4 just like that.

00:11:23.340 --> 00:11:24.190
And this is pretty
straightforward.

00:11:24.190 --> 00:11:28.000
And then I have a third
group of 4 just like that.

00:11:28.000 --> 00:11:30.640
And there's nothing left
over like I had before.

00:11:30.640 --> 00:11:35.210
I can exactly divide 12
objects into 3 groups of 4.

00:11:35.210 --> 00:11:38.190
1, 2, 3 groups of 4.

00:11:38.190 --> 00:11:44.520
So 12 divided by
4 is equal to 3.

00:11:44.520 --> 00:11:47.110
And we can do the exercise that
we saw on the previous video.

00:11:47.110 --> 00:11:49.235
What is 12 divided by 3?

00:11:49.235 --> 00:11:51.840
Let me do a new color.

00:11:51.840 --> 00:11:55.200
12 divided by 3.

00:11:55.200 --> 00:11:57.470
Now based on what we've learn
so far we say, that should just

00:11:57.470 --> 00:12:00.930
be 4 because 3 times 4 is 12.

00:12:00.930 --> 00:12:02.770
But let's prove
it to ourselves.

00:12:02.770 --> 00:12:09.420
So 1, 2, 3, 4, 5, 6,
7, 8, 9, 20, 11, 12.

00:12:09.420 --> 00:12:12.180
Let's divide it
into groups of 3.

00:12:12.180 --> 00:12:14.030
And I'm going to make them a
little strange looking just

00:12:14.030 --> 00:12:15.730
so you see that you don't
always have to do it into

00:12:15.730 --> 00:12:17.730
nice, clean columns.

00:12:17.730 --> 00:12:19.870
So that's a group
of 3 right there.

00:12:19.870 --> 00:12:21.680
12 divided by 3.

00:12:21.680 --> 00:12:27.720
Let's see, here is another
group of 3 just like that.

00:12:27.720 --> 00:12:33.010
And then, maybe I'll take
this group of 3 like that.

00:12:33.010 --> 00:12:34.330
And I'll take this group of 3.

00:12:34.330 --> 00:12:37.120
There was obviously a much
easier way of dividing it up

00:12:37.120 --> 00:12:39.146
then doing these weird l-shaped
things, but I want to show

00:12:39.146 --> 00:12:40.110
you it doesn't matter.

00:12:40.110 --> 00:12:42.100
You're just dividing
it into groups of 3.

00:12:42.100 --> 00:12:43.780
And how many groups do we have?

00:12:43.780 --> 00:12:45.550
We have one group.

00:12:45.550 --> 00:12:49.720
Then we have our second
group right here.

00:12:49.720 --> 00:12:53.450
And then we have our
third group right there.

00:12:53.450 --> 00:12:56.610
And then we have-- let me
do it in a new color.

00:12:56.610 --> 00:12:59.110
And then we have our
fourth group right there.

00:12:59.110 --> 00:13:01.900
So we have exactly 4 groups.

00:13:01.900 --> 00:13:03.720
And when I say there was an
easier way to divide it, the

00:13:03.720 --> 00:13:08.980
easier way was obviously, maybe
not obviously-- if I want to

00:13:08.980 --> 00:13:12.750
divide these into groups of 3 I
could have just done 1,

00:13:12.750 --> 00:13:16.740
2, 3, 4 groups of 3.

00:13:16.740 --> 00:13:19.260
Either of these I'm
dividing the 12 objects

00:13:19.260 --> 00:13:20.710
into packets of 3.

00:13:20.710 --> 00:13:21.790
You can imagine them that way.

00:13:21.790 --> 00:13:26.110
Let's do another one that
maybe has a remainder.

00:13:26.110 --> 00:13:26.675
Let's see.

00:13:29.410 --> 00:13:36.350
What is 14 divided by 5?

00:13:36.350 --> 00:13:39.580
So let's draw 14 objects.

00:13:39.580 --> 00:13:47.390
1, 2, 3, 4, 5, 6, 7, 8,
9, 10, 11, 12, 13 14.

00:13:47.390 --> 00:13:48.330
14 objects.

00:13:48.330 --> 00:13:51.850
And I'm going to divide
it into groups of 5.

00:13:51.850 --> 00:13:55.510
Well, the easiest thing is
there's one group right there,

00:13:55.510 --> 00:13:57.930
two groups right there.

00:13:57.930 --> 00:14:00.570
But then this last one, I
only have 4 left, so I can't

00:14:00.570 --> 00:14:01.990
make another group of 5.

00:14:01.990 --> 00:14:05.680
So the answer here is I can
make 2 groups of 5 and I'm

00:14:05.680 --> 00:14:10.070
going to have a remainder--
r for remainder-- of 4.

00:14:10.070 --> 00:14:11.680
2 remainder 4.

00:14:11.680 --> 00:14:15.320
Now, once you get enough
practice, you're not always

00:14:15.320 --> 00:14:17.810
going to be wanting to draw
these circles and dividing

00:14:17.810 --> 00:14:18.470
them up like that.

00:14:18.470 --> 00:14:20.660
Although that would
not be incorrect.

00:14:20.660 --> 00:14:23.790
So another way to think about
this type of problem is to

00:14:23.790 --> 00:14:27.710
say, well, 14 divided by 5,
how do I figure that out?

00:14:27.710 --> 00:14:29.750
Actually, another way
of writing this and no

00:14:29.750 --> 00:14:31.310
harm in showing you.

00:14:31.310 --> 00:14:35.550
I could say 14 divided by 5 is
the same thing as 15 divided

00:14:35.550 --> 00:14:38.640
by-- this sign right--
divided by 5.

00:14:38.640 --> 00:14:40.060
And what you do is you
say, well, let's see.

00:14:40.060 --> 00:14:42.750
How many times does
5 go into 14?

00:14:42.750 --> 00:14:43.360
Well, let's see.

00:14:43.360 --> 00:14:45.340
5 times and you kind
of do multiplication

00:14:45.340 --> 00:14:45.980
tables in your head.

00:14:45.980 --> 00:14:48.950
5 times 1 is equal to 5.

00:14:48.950 --> 00:14:51.860
5 times 2 is equal to 10.

00:14:51.860 --> 00:14:55.960
So that's still less than 14,
so 5 goes at least two times.

00:14:55.960 --> 00:14:59.140
5 times 3 is equal to 15.

00:14:59.140 --> 00:15:01.650
Well that's bigger than 14,
so I have to go back here.

00:15:01.650 --> 00:15:03.980
So 5 only goes two times.

00:15:03.980 --> 00:15:05.630
So it goes 2 times.

00:15:05.630 --> 00:15:08.530
2 times 5 is 10.

00:15:08.530 --> 00:15:09.690
And then you subtract.

00:15:09.690 --> 00:15:12.160
You say 14 minus 10 is 4.

00:15:12.160 --> 00:15:15.090
And that's the same
remainder as right here.

00:15:15.090 --> 00:15:18.150
Well, I could divide 5 into
14 exactly two times, which

00:15:18.150 --> 00:15:19.670
would get us 2 groups of 5.

00:15:19.670 --> 00:15:21.090
Which is essentially just 10.

00:15:21.090 --> 00:15:23.320
And we still have
the 4 left over.

00:15:28.100 --> 00:15:30.950
Let me do a couple of more just
to really make sure you get

00:15:30.950 --> 00:15:33.180
this stuff really, really,
really, really well.

00:15:35.890 --> 00:15:37.560
Let me write it in
that notation.

00:15:37.560 --> 00:15:41.660
Let's say I do 8 divided by 2.

00:15:41.660 --> 00:15:44.590
And I could also write
this as 8-- so I want

00:15:44.590 --> 00:15:45.560
to know what that is.

00:15:45.560 --> 00:15:46.790
That's a question mark.

00:15:46.790 --> 00:15:52.100
I could also write this
as 8 divided by 2.

00:15:52.100 --> 00:15:54.650
And the way I do either of
these, I'll draw the circles in

00:15:54.650 --> 00:15:57.840
the second, but the way I do it
without drawing the circles, I

00:15:57.840 --> 00:16:01.250
say, well, 2 times
1 is equal to 2.

00:16:01.250 --> 00:16:04.160
So that definitely goes into 8,
but maybe I can think of a

00:16:04.160 --> 00:16:07.170
larger number that goes into--
that when I multiply it

00:16:07.170 --> 00:16:09.070
by 2 still goes into 8.

00:16:09.070 --> 00:16:11.360
2 times 2 is equal to 4.

00:16:11.360 --> 00:16:13.070
That's still less than 8.

00:16:13.070 --> 00:16:15.710
So 2 times 3 is equal to 6.

00:16:15.710 --> 00:16:17.230
Still less than 8.

00:16:17.230 --> 00:16:21.430
2 times-- oh, something
weird happened to my pen.

00:16:21.430 --> 00:16:25.130
2 times 4 is exactly
equal to 8.

00:16:25.130 --> 00:16:27.500
So 2 goes into 8 four times.

00:16:27.500 --> 00:16:29.750
So I could say 2 goes
into 8 four times.

00:16:29.750 --> 00:16:33.200
Or 8 divided by 2
is equal to 4.

00:16:33.200 --> 00:16:35.030
We can even draw our circles.

00:16:35.030 --> 00:16:38.490
1, 2, 3, 4, 5, 6, 7, 8.

00:16:38.490 --> 00:16:40.080
I drew them messy on purpose.

00:16:40.080 --> 00:16:42.950
Let's divide them
into groups of 2.

00:16:42.950 --> 00:16:48.240
I have one group of 2, two
groups of 2, three groups

00:16:48.240 --> 00:16:51.010
of 2, four groups of 2.

00:16:51.010 --> 00:16:54.170
So if I have 8 objects, divide
them into groups of 2,

00:16:54.170 --> 00:16:55.460
you have four groups.

00:16:55.460 --> 00:16:59.210
So 8 divided by 2 is 4.

00:16:59.210 --> 00:17:01.460
Hopefully you found
that helpful.


Alternate mental subtraction method

WEBVTT
Kind: captions
Language: en

00:00:00.700 --> 00:00:03.600
I want to show you a way that,
at least, I find more useful to

00:00:03.600 --> 00:00:05.400
subtract numbers in my head.

00:00:05.400 --> 00:00:08.000
And I do it this way-- it's
not necessarily faster on

00:00:08.000 --> 00:00:10.730
paper, but it allows you to
remember what you're doing.

00:00:10.730 --> 00:00:12.810
Because if you start borrowing
and stuff it becomes very hard

00:00:12.810 --> 00:00:14.580
to remember what's
actually going on.

00:00:14.580 --> 00:00:16.290
So let's try out a
couple of problems.

00:00:16.290 --> 00:00:27.270
Let's have 9,456 minus 7,589.

00:00:27.270 --> 00:00:29.640
So the way I do
this in my head.

00:00:29.640 --> 00:00:35.040
I say that 9,456 minus
7,589-- you have to

00:00:35.040 --> 00:00:36.560
remember the two numbers.

00:00:36.560 --> 00:00:40.910
So the first thing I do is
I say, well, what's 9,456

00:00:40.910 --> 00:00:44.140
minus is just 7,000?

00:00:44.140 --> 00:00:48.220
That's pretty easy because I
just take 9,000 minus 7,000.

00:00:48.220 --> 00:00:51.750
So what I can do is I'll
cross out this and I'll

00:00:51.750 --> 00:00:53.720
subtract 7,000 from it.

00:00:53.720 --> 00:00:58.030
And I'm going to get 2,456.

00:00:58.030 --> 00:01:05.330
So in my head I tell myself
that 9,456 minus 7,589 is the

00:01:05.330 --> 00:01:08.600
same thing as-- if I just
subtract out the 7,000--

00:01:08.600 --> 00:01:13.150
as 2,456 minus 589.

00:01:13.150 --> 00:01:15.140
I took the 7,000 out
of the picture.

00:01:15.140 --> 00:01:19.110
I essentially subtracted it
from both of these numbers.

00:01:19.110 --> 00:01:25.510
Now, if I want to do 2,456
minus 589 what I do is I

00:01:25.510 --> 00:01:28.820
subtract 500 from both
of these numbers.

00:01:28.820 --> 00:01:31.340
So if I subtract 500 from
this bottom number,

00:01:31.340 --> 00:01:32.990
this 5 will go away.

00:01:32.990 --> 00:01:36.230
And if I subtract 500 from this
top number, what happens?

00:01:36.230 --> 00:01:39.510
What's 2,456 minus 500?

00:01:39.510 --> 00:01:41.170
Or an easier way to
think about it?

00:01:41.170 --> 00:01:42.650
What's 24 minus 5?

00:01:42.650 --> 00:01:44.010
Well, that's 19.

00:01:44.010 --> 00:01:48.870
So it's going to be 1,956.

00:01:48.870 --> 00:01:50.820
Let me scroll up a little bit.

00:01:50.820 --> 00:01:52.240
So it's 1,956.

00:01:52.240 --> 00:01:57.540
So my original problem has now
been reduced to 1,956 minus 89.

00:01:57.540 --> 00:02:01.340
Now I can subtract 80 from both
that number and that number.

00:02:01.340 --> 00:02:04.840
So if I subtract 80 from this
bottom number the 8 disappears.

00:02:04.840 --> 00:02:07.100
898 minus 80 is just 9.

00:02:07.100 --> 00:02:09.470
And I subtract 80 from this top
number, I can just think of,

00:02:09.470 --> 00:02:12.480
well, what's 195 minus 8?

00:02:12.480 --> 00:02:15.170
Well, 195 minus 8, let's see.

00:02:15.170 --> 00:02:18.060
15 minus 8 is 17.

00:02:18.060 --> 00:02:25.300
So 195 minus 8 is going
to be 187 and then you

00:02:25.300 --> 00:02:26.600
still have the 6 there.

00:02:26.600 --> 00:02:32.050
So essentially I said,
1,956 minus 80 is 1,876.

00:02:32.050 --> 00:02:35.990
And now my problem has been
reduced to 1,876 minus 9.

00:02:35.990 --> 00:02:37.430
And then we can do
that in our head.

00:02:37.430 --> 00:02:39.630
What's 76 minus 9?

00:02:39.630 --> 00:02:40.340
That's what?

00:02:40.340 --> 00:02:41.840
67.

00:02:41.840 --> 00:02:47.860
So our final answer is 1,867.

00:02:47.860 --> 00:02:50.890
And as you can see this isn't
necessarily faster than the way

00:02:50.890 --> 00:02:52.370
we've done it in other videos.

00:02:52.370 --> 00:02:55.040
But the reason why I like it
is that at any stage, I just

00:02:55.040 --> 00:02:56.580
have to remember two numbers.

00:02:56.580 --> 00:02:59.030
I have to remember my
new top number and my

00:02:59.030 --> 00:02:59.880
new bottom number.

00:02:59.880 --> 00:03:03.490
My new bottom number is always
just some of the leftover

00:03:03.490 --> 00:03:05.180
digits of the original
bottom number.

00:03:05.180 --> 00:03:08.060
So that's how I like to
do things in my head.

00:03:08.060 --> 00:03:10.490
Now, just to make sure that we
got the right answer and maybe

00:03:10.490 --> 00:03:13.060
to compare and contrast
a little bit.

00:03:13.060 --> 00:03:15.020
Let's do it the
traditional way.

00:03:15.020 --> 00:03:25.030
9,456 minus 7,589.

00:03:25.030 --> 00:03:28.280
So the standard way of doing
it, I like to do all my

00:03:28.280 --> 00:03:31.180
borrowing before I do any of my
subtraction so that I can stay

00:03:31.180 --> 00:03:35.110
in my borrowing mode, or you
can think of it as regrouping.

00:03:35.110 --> 00:03:37.740
So I look at all of my numbers
on top and see, are they all

00:03:37.740 --> 00:03:39.190
larger than the numbers
on the bottom?

00:03:39.190 --> 00:03:40.590
And I start here at the right.

00:03:40.590 --> 00:03:43.610
6 is definitely not larger
than 9, so I have to borrow.

00:03:43.610 --> 00:03:46.680
So I'll borrow 10 or I'll
borrow 1 from the 10's place,

00:03:46.680 --> 00:03:48.010
which ends up being 10.

00:03:48.010 --> 00:03:53.090
So the 6 becomes a 16 and
then the 5 becomes a 4.

00:03:53.090 --> 00:03:54.120
Then I go to the 10's place.

00:03:54.120 --> 00:03:58.000
4 needs to be larger than
8, so let me borrow 1

00:03:58.000 --> 00:03:59.420
from the 100's place.

00:03:59.420 --> 00:04:03.290
So then that 4 becomes a 14
or fourteen 10's because

00:04:03.290 --> 00:04:04.310
we're in the 10's place.

00:04:04.310 --> 00:04:07.200
And then this 4 becomes a 3.

00:04:07.200 --> 00:04:10.095
Now these two columns or places
look good, but right here I

00:04:10.095 --> 00:04:12.120
have a 3, which is
less than a 5.

00:04:12.120 --> 00:04:14.380
Not cool, so I have
to borrow again.

00:04:14.380 --> 00:04:18.810
That 3 becomes a 13 and
then that 9 becomes an 8.

00:04:18.810 --> 00:04:21.520
And now I'm ready to subtract.

00:04:21.520 --> 00:04:24.440
So you get 16 minus 9 is 7.

00:04:24.440 --> 00:04:27.190
14 minus 8 is 16.

00:04:27.190 --> 00:04:29.570
13 minus 5 is 8.

00:04:29.570 --> 00:04:31.030
8 minus 7 is 1.

00:04:31.030 --> 00:04:33.840
And lucky for us, we
got the right answer.

00:04:33.840 --> 00:04:34.640
I want to make it very clear.

00:04:34.640 --> 00:04:36.580
There's no better
way to do this.

00:04:36.580 --> 00:04:39.780
This way is actually kind of
longer and it takes up more

00:04:39.780 --> 00:04:43.180
space on your paper than this
way was, but this for me,

00:04:43.180 --> 00:04:44.500
is very hard to remember.

00:04:44.500 --> 00:04:47.690
It's very hard for me to keep
track of what I borrowed and

00:04:47.690 --> 00:04:50.020
what the other number
is and et cetera.

00:04:50.020 --> 00:04:51.970
But here, at any point
in time, I just have to

00:04:51.970 --> 00:04:53.670
remember two numbers.

00:04:53.670 --> 00:04:56.560
And the two numbers get
simpler every step that I

00:04:56.560 --> 00:04:58.640
go through this process.

00:04:58.640 --> 00:05:00.190
So this is why I think
that this is a little

00:05:00.190 --> 00:05:01.380
bit easier in my head.

00:05:01.380 --> 00:05:04.140
But this might be, depending on
the context, easier on paper.

00:05:04.140 --> 00:05:06.630
But at least here you didn't
have to borrow or regroup.

00:05:06.630 --> 00:05:09.420
Well, hopefully you find
that a little bit useful.


Subtraction 3:  Introduction to Borrowing or Regrouping

WEBVTT
Kind: captions
Language: en

00:00:00.720 --> 00:00:03.730
I think we're just about ready
to learn how to subtract pretty

00:00:03.730 --> 00:00:06.130
much any number from
any other number.

00:00:06.130 --> 00:00:08.750
So let's just review a little
bit of what we know already.

00:00:08.750 --> 00:00:14.560
So if I were to ask you what
16 minus 4 is, I could draw

00:00:14.560 --> 00:00:17.790
16 apples and then take
away 4 of the apples.

00:00:17.790 --> 00:00:20.340
Or I could actually draw a
number line, and actually let

00:00:20.340 --> 00:00:23.740
me do it here just to start off
the video to get warmed up.

00:00:23.740 --> 00:00:25.140
I could draw the number
line and maybe that's

00:00:25.140 --> 00:00:28.210
16, maybe that's 17.

00:00:28.210 --> 00:00:35.160
It's 15, 14, 13, 12, let me
go down all the way to 11.

00:00:35.160 --> 00:00:37.590
I could keep going but
I've run out of space.

00:00:37.590 --> 00:00:41.720
Now, if I don't know in my head
what 16 minus 4 is, and it's a

00:00:41.720 --> 00:00:44.960
pretty good one to eventually
know in your head, you could

00:00:44.960 --> 00:00:46.920
start in your number line or
you could imagine the number

00:00:46.920 --> 00:00:49.730
line in your brain and you
could go down by 4's.

00:00:49.730 --> 00:00:58.350
16 minus 1 is 15 minus 2 is 14
minus 3 is 13 minus 4 is 12.

00:00:58.350 --> 00:00:59.560
And you would have the answer.

00:00:59.560 --> 00:01:02.120
16 minus 4 is 12.

00:01:02.120 --> 00:01:07.860
Now an even easier way to do
this problem is just to focus

00:01:07.860 --> 00:01:10.490
on the places of the digits.

00:01:10.490 --> 00:01:12.820
Now let me be clear what
I mean when I say that.

00:01:12.820 --> 00:01:13.580
Let me re-write it.

00:01:13.580 --> 00:01:17.680
16 minus 4, and I've gone
over this a little bit

00:01:17.680 --> 00:01:19.520
in the addition videos.

00:01:19.520 --> 00:01:22.340
This is the ones place.

00:01:22.340 --> 00:01:24.870
The 6 is in the ones place.

00:01:24.870 --> 00:01:26.900
The 4 is in the ones place.

00:01:26.900 --> 00:01:31.480
The 1, right here, this right
here, or there was something

00:01:31.480 --> 00:01:35.880
down here, this column,
that is the tens place.

00:01:35.880 --> 00:01:37.450
Now what do we mean by that?

00:01:37.450 --> 00:01:44.620
Well 16 is the same
thing as 10 plus 6.

00:01:44.620 --> 00:01:48.100
So when we write it, this
1 literally means one 10.

00:01:48.100 --> 00:01:51.170
If you think of it in money
it means one $10 bill.

00:01:51.170 --> 00:01:55.430
If I had a 2 there, if I had
26, that means two $10 bills.

00:01:55.430 --> 00:01:58.040
Two $10 bills would mean $20.

00:01:58.040 --> 00:02:01.730
So that's two $10 bills
and then six $1 bills.

00:02:01.730 --> 00:02:04.350
You can view this as a
$1 bill place, that's

00:02:04.350 --> 00:02:05.950
the $10 bill place.

00:02:05.950 --> 00:02:15.260
If I had 357, you could view
this as three $100 bills, five

00:02:15.260 --> 00:02:19.880
$10 bills, and seven $1 bills,
and that's why this is called

00:02:19.880 --> 00:02:24.510
the hundredths, that's the
hundredths place, this is the

00:02:24.510 --> 00:02:28.290
tens place, and this
is the ones place.

00:02:28.290 --> 00:02:32.030
And we'll dig a little bit
deeper into this as we explore

00:02:32.030 --> 00:02:35.070
borrowing and regrouping more
in this video and in others.

00:02:35.070 --> 00:02:37.600
But I wanted to label these
places because what I want to

00:02:37.600 --> 00:02:41.030
show you is you don't even have
to think about 16 minus 4.

00:02:41.030 --> 00:02:43.600
You can actually just look at
just the ones place and think

00:02:43.600 --> 00:02:47.945
about 6 minus 4, and say 6
minus 4 -- well you could draw

00:02:47.945 --> 00:02:50.600
a number line or you could even
use your fingers if you have

00:02:50.600 --> 00:02:52.340
to, but you probably
have that memorized.

00:02:52.340 --> 00:02:56.010
You could probably visualize it
in your head, 6 minus 4 is 2.

00:02:59.260 --> 00:03:02.780
And then 1, then we go to the
tens place, 1 minus nothing --

00:03:02.780 --> 00:03:03.840
there's nothing over here.

00:03:03.840 --> 00:03:07.790
So 1 minus nothing is
1, and you get 12.

00:03:07.790 --> 00:03:10.300
Same answer, we were able
to simplify a little bit.

00:03:10.300 --> 00:03:13.010
Let's try another
problem like that.

00:03:13.010 --> 00:03:22.720
If I were to ask you
what 78 minus 37 is.

00:03:22.720 --> 00:03:26.440
So we start off in the ones
place and we say 8 minus 7 --

00:03:26.440 --> 00:03:30.340
that's 8 ones minus seven
ones, or just 8 minus 7.

00:03:30.340 --> 00:03:33.675
8 minus 7 is equal to 1.

00:03:37.000 --> 00:03:38.550
Then we go to the tens place.

00:03:38.550 --> 00:03:43.370
7 minus 3 -- now remember, this
is seven 10s, or seven $10

00:03:43.370 --> 00:03:46.490
bills, minus three $10 bills.

00:03:46.490 --> 00:03:50.210
If I had seven $10 bills and I
give away three of those $10

00:03:50.210 --> 00:03:54.570
dollar bills, then I'll
have four $10 bills, or 7

00:03:54.570 --> 00:03:56.800
minus 3 is equal to 4.

00:03:56.800 --> 00:03:58.880
And just like that we were
able to figure out that

00:03:58.880 --> 00:04:02.490
78 minus 37 is 41.

00:04:02.490 --> 00:04:04.120
This would have been really
hard to do, it would take me

00:04:04.120 --> 00:04:07.940
forever to draw 78 apples and
to cross out 37 of them.

00:04:07.940 --> 00:04:10.150
Or to draw a number line
all the way up to 78

00:04:10.150 --> 00:04:12.450
then go back 37 spaces.

00:04:12.450 --> 00:04:14.270
That would have given you the
answer, but it would have

00:04:14.270 --> 00:04:16.390
taken you forever to
solve it that way.

00:04:16.390 --> 00:04:19.310
Just by focusing on just
each column, you're able

00:04:19.310 --> 00:04:21.080
to get the right answer.

00:04:21.080 --> 00:04:24.590
Well, you might say, hey Sal,
but what happens if I can't --

00:04:24.590 --> 00:04:26.910
well, let me give you an
example where this will start

00:04:26.910 --> 00:04:28.810
to become difficult
doing it this way.

00:04:28.810 --> 00:04:29.910
I'll do one more
example like this.

00:04:29.910 --> 00:04:37.890
So let's say I had 95 minus 31.

00:04:37.890 --> 00:04:40.590
Just like that, 5 minus 1 is 4.

00:04:40.590 --> 00:04:42.270
9 minus 3 is 6.

00:04:42.270 --> 00:04:44.700
95 minus 31 is 64.

00:04:44.700 --> 00:04:47.280
You're probably saying,
Sal, subtraction is easy.

00:04:47.280 --> 00:04:50.580
I can just look at each place,
the ones place and subtract,

00:04:50.580 --> 00:04:52.240
tens places and subtract.

00:04:52.240 --> 00:04:54.620
But I'm about to show you
that it's not always

00:04:54.620 --> 00:04:55.560
at least that easy.

00:04:55.560 --> 00:04:57.450
With a little bit of practice
hopefully you'll realize

00:04:57.450 --> 00:05:00.700
that it's also not too bad.

00:05:00.700 --> 00:05:08.510
So what if I were to ask
you what 22 minus 17 is.

00:05:11.410 --> 00:05:14.400
Now once again, I could draw 22
oranges or apples and take away

00:05:14.400 --> 00:05:16.770
17 of them and you could count
what's left and you would get

00:05:16.770 --> 00:05:18.730
the right answer, but that
would take you forever.

00:05:18.730 --> 00:05:21.140
Is there any way I could
do that maybe just on

00:05:21.140 --> 00:05:22.890
the paper right here?

00:05:22.890 --> 00:05:25.360
Now your reaction might
say let me just do what

00:05:25.360 --> 00:05:26.780
you just did before.

00:05:26.780 --> 00:05:31.280
But if you look here, if I try
to subtract 7 from 2, if I have

00:05:31.280 --> 00:05:34.130
two things, at least for the
mathematics that we know right

00:05:34.130 --> 00:05:35.960
now, I can't give away 7.

00:05:35.960 --> 00:05:37.170
I only have 2 to give away.

00:05:37.170 --> 00:05:39.900
This would give me something
smaller than 0 which

00:05:39.900 --> 00:05:40.960
we don't know about.

00:05:40.960 --> 00:05:42.640
That's a negative number.

00:05:42.640 --> 00:05:46.560
As far as we know right now,
we can't subtract 7 from 2.

00:05:46.560 --> 00:05:49.540
But we know that 17
is smaller than 22.

00:05:49.540 --> 00:05:52.870
So what can we do here
to actually do this

00:05:52.870 --> 00:05:54.670
subtraction problem?

00:05:54.670 --> 00:05:57.980
So what we do here, and you
might call it borrowing, you

00:05:57.980 --> 00:06:00.090
might call it regrouping.

00:06:00.090 --> 00:06:05.250
This 2 right here, this 22 is
the same thing as 20 plus 2.

00:06:05.250 --> 00:06:07.200
That's the 22 right there.

00:06:07.200 --> 00:06:08.980
It's 20 plus 2.

00:06:08.980 --> 00:06:12.740
The 17 is 10 plus 7.

00:06:12.740 --> 00:06:15.640
That's just another
way to write 17.

00:06:15.640 --> 00:06:16.760
Now we have a 2 here.

00:06:16.760 --> 00:06:19.990
We want something larger
than a 7 to subtract from.

00:06:19.990 --> 00:06:24.240
So what we can do is we can
borrow from this 2 or from this

00:06:24.240 --> 00:06:26.660
20, they're the same thing.

00:06:26.660 --> 00:06:29.230
Let me do that in
another color.

00:06:29.230 --> 00:06:34.020
This 2 right here is the
same thing as that 20.

00:06:34.020 --> 00:06:37.150
A 2 in the tens place
means two $10 bills.

00:06:37.150 --> 00:06:40.530
Two $10 bills is the
same thing as $20.

00:06:40.530 --> 00:06:42.280
That's what that 2 represents.

00:06:42.280 --> 00:06:45.500
So if I want to make this 2
into something larger, why

00:06:45.500 --> 00:06:48.130
don't I take a $10
bill from here.

00:06:48.130 --> 00:06:51.710
If I take a $10 bill from here
and I turn it into ones -- I

00:06:51.710 --> 00:06:54.580
go to the cashier and say
give me a bunch of ones.

00:06:54.580 --> 00:06:57.770
So if I take a $10 bill
from here, then this

00:06:57.770 --> 00:06:59.500
will become $10.

00:06:59.500 --> 00:07:02.300
And then I cash into a bunch
of ones and put it here.

00:07:02.300 --> 00:07:05.020
So then this will become $12.

00:07:05.020 --> 00:07:08.690
If we look over here, what it
looks like I did is I took a 1

00:07:08.690 --> 00:07:12.250
from this 2, so this 2 will
now become a 1, right?

00:07:12.250 --> 00:07:15.270
We went from two $10s to
one $10 and it became

00:07:15.270 --> 00:07:17.240
just one $10 bill.

00:07:17.240 --> 00:07:19.760
Then I gave that 1 to this 2.

00:07:19.760 --> 00:07:22.260
This 2 then becomes a 12.

00:07:22.260 --> 00:07:24.650
And now we can
actually subtract.

00:07:24.650 --> 00:07:28.770
12 minus 7 is 5.

00:07:28.770 --> 00:07:32.220
12 minus 7 -- I'm just doing
the same problem just written

00:07:32.220 --> 00:07:36.340
slightly different on this
right hand side -- is also 5.

00:07:36.340 --> 00:07:39.290
Then we have 1 minus 1 is 0.

00:07:39.290 --> 00:07:41.250
I could write this as
05, but that's just

00:07:41.250 --> 00:07:42.660
the same thing as 5.

00:07:42.660 --> 00:07:46.310
And here I'd have 10 minus 10
-- well, 10 minus 10 is just 0.

00:07:46.310 --> 00:07:47.480
So it's just 05.

00:07:47.480 --> 00:07:51.140
So 22 minus 17 is 5.

00:07:51.140 --> 00:07:55.020
Let's try to extend this to
an even harder problem.

00:07:55.020 --> 00:07:57.660
Hopefully you'll get the hang
of how this borrowing or

00:07:57.660 --> 00:07:59.530
regrouping, depending and how
you want to view it,

00:07:59.530 --> 00:08:00.990
actually works.

00:08:00.990 --> 00:08:07.225
So let's say that we
have 703 minus 67.

00:08:09.890 --> 00:08:12.160
So if I tried the technique
that we learned earlier in

00:08:12.160 --> 00:08:14.040
this video, I immediately
hit a roadblock.

00:08:14.040 --> 00:08:18.050
I say 3 minus 7 -- well if
I have 3 apples, I can't

00:08:18.050 --> 00:08:19.390
take away 7 from there.

00:08:19.390 --> 00:08:21.470
So I'm at an impasse.

00:08:21.470 --> 00:08:22.590
I don't know what to do next.

00:08:22.590 --> 00:08:24.430
And you say well,
maybe I can borrow.

00:08:24.430 --> 00:08:27.070
But I look to the left, well
gee, there's a 0 there,

00:08:27.070 --> 00:08:29.390
how can I borrow from a 0?

00:08:29.390 --> 00:08:31.670
Then well, there's a 7 there,
but then how do I borrow

00:08:31.670 --> 00:08:33.120
from the 7, all of that.

00:08:33.120 --> 00:08:35.370
And the best way to think about
it and the more practice you do

00:08:35.370 --> 00:08:41.560
the better, remember this 703
is seven $100 bills plus zero

00:08:41.560 --> 00:08:45.390
$10 bills plus three $1 bills.

00:08:45.390 --> 00:08:50.940
And 67 is six $10
bills or $60 plus 7.

00:08:50.940 --> 00:08:53.860
So if we can't borrow from here
because I have no $10 bills,

00:08:53.860 --> 00:08:58.270
what we want to do is break
one of the $100 bills.

00:08:58.270 --> 00:09:01.520
So what I do is I take $100
bill from here, so now

00:09:01.520 --> 00:09:03.860
I'm left with $600.

00:09:03.860 --> 00:09:06.280
So this 7 becomes a 6, right?

00:09:06.280 --> 00:09:09.510
It's a 6 in the hundredths
place and it represents six

00:09:09.510 --> 00:09:12.610
hundredths, six $100 bills.

00:09:12.610 --> 00:09:15.610
So, remember, I took
out a $100 bill.

00:09:15.610 --> 00:09:19.050
And then what I can do is I can
split that $100 bill, I can

00:09:19.050 --> 00:09:22.950
give $10 to this guy -- or
sorry, I can give $90 to this

00:09:22.950 --> 00:09:29.980
guy right here, and then I can
give $1 to this guy -- sorry, I

00:09:29.980 --> 00:09:34.340
could give $90 to this guy and
I can give $10 to that

00:09:34.340 --> 00:09:34.850
guy right there.

00:09:34.850 --> 00:09:37.280
I have $100 to
work with, right?

00:09:37.280 --> 00:09:38.350
So what happens?

00:09:38.350 --> 00:09:41.470
If I do that, if I take that
$100 bill that I took out

00:09:41.470 --> 00:09:43.520
from here, went to the
cash register, I got

00:09:43.520 --> 00:09:45.620
nine 10s or $90.

00:09:45.620 --> 00:09:48.140
So now I have nine 10s here.

00:09:48.140 --> 00:09:53.960
And then I have ten 1s here, so
I add 10 plus 3, it becomes 13.

00:09:53.960 --> 00:09:56.800
And just like that, all my
numbers in each column, if I

00:09:56.800 --> 00:09:59.640
were to draw columns like
this, divide them up.

00:09:59.640 --> 00:10:02.130
Everything on top is bigger
than everything on the bottom

00:10:02.130 --> 00:10:04.090
so now I can subtract.

00:10:04.090 --> 00:10:06.960
So 13 minus 7 is 6.

00:10:06.960 --> 00:10:11.230
9 minus 6 is 3.

00:10:11.230 --> 00:10:13.840
6 minus nothing is 6.

00:10:13.840 --> 00:10:17.620
So 703 minus 67 is 636.

00:10:17.620 --> 00:10:19.570
Now you might be saying, OK
Sal, I kind of get what you

00:10:19.570 --> 00:10:23.140
did, you took 100 from here,
you put 90 here, so that

00:10:23.140 --> 00:10:24.540
became a 9, you gave 10 here.

00:10:24.540 --> 00:10:26.630
But how did you know to
do that or what's a more

00:10:26.630 --> 00:10:28.480
systematic way of doing.

00:10:28.480 --> 00:10:30.660
This kind of is a conceptual
way, which is, in my

00:10:30.660 --> 00:10:32.350
mind, the most important
way to understand it.

00:10:32.350 --> 00:10:36.080
But let me show you kind of a
mechanical way to do that.

00:10:36.080 --> 00:10:40.060
So let's say we have 700 --
I'll do the same problem

00:10:40.060 --> 00:10:43.490
over again -- 703 minus 67.

00:10:43.490 --> 00:10:45.790
I look at all of the numbers on
the top and I say are they all

00:10:45.790 --> 00:10:47.150
larger than the numbers
on the bottom?

00:10:47.150 --> 00:10:50.190
I said well, 3 -- well, 7 is
larger than 3, that's not good.

00:10:50.190 --> 00:10:51.695
6 is larger than 0,
that's not good.

00:10:51.695 --> 00:10:53.200
So I need to do something.

00:10:53.200 --> 00:10:56.170
So what I do is I start with
this 3 right here, and I say

00:10:56.170 --> 00:10:59.540
well, can I borrow from
this number to the left?

00:10:59.540 --> 00:11:01.470
And I look to the number
to the left and I can

00:11:01.470 --> 00:11:02.640
not borrow from 0.

00:11:02.640 --> 00:11:04.720
So then I look to the two
numbers to the left and

00:11:04.720 --> 00:11:07.740
say can I borrow from 70?

00:11:07.740 --> 00:11:10.500
I say well gee, I can
definitely borrow from 70 --

00:11:10.500 --> 00:11:12.330
we know this is actually 700.

00:11:12.330 --> 00:11:14.840
So if I borrow from
70 what happens?

00:11:14.840 --> 00:11:23.200
If I borrow one 10 from
70, 70 becomes 69, right?

00:11:23.200 --> 00:11:26.910
If I borrow one from
70, it becomes 69.

00:11:26.910 --> 00:11:30.970
And I take that 1 and it's
essentially a 10, right?

00:11:30.970 --> 00:11:33.850
So that 10 plus 3 is now 13.

00:11:33.850 --> 00:11:35.710
And now these are my columns.

00:11:35.710 --> 00:11:38.120
Just just like.

00:11:38.120 --> 00:11:41.950
You have 13 minus 7 is
6, 9 minus 6 is 3.

00:11:41.950 --> 00:11:44.800
And then 6 right down here.

00:11:44.800 --> 00:11:48.180
Now, another way you can
think about it, I'll do

00:11:48.180 --> 00:11:50.050
the exact same problem.

00:11:50.050 --> 00:11:54.800
703 minus 67.

00:11:54.800 --> 00:11:56.210
You could start at the left.

00:11:56.210 --> 00:11:58.270
You could say look, 7
is, well, it's larger

00:11:58.270 --> 00:11:58.860
than what's below it.

00:11:58.860 --> 00:12:01.100
Nothing is below it,
so I'm cool there.

00:12:01.100 --> 00:12:02.770
And then you go 1 right
to the right of it.

00:12:02.770 --> 00:12:07.040
And you say well, 0 -- well,
0 is not bigger than what's

00:12:07.040 --> 00:12:10.800
below it; it's not bigger
than the 6 below it.

00:12:10.800 --> 00:12:12.830
So I'm going to need to borrow.

00:12:12.830 --> 00:12:16.030
So what I can do is I can
borrow 1 from the 7 -- I'm

00:12:16.030 --> 00:12:18.220
essentially borrowing
100, right?

00:12:18.220 --> 00:12:22.260
So if I borrow -- this is
700, let me make it 600.

00:12:22.260 --> 00:12:24.110
Now if I take 100 away
and I turn it to

00:12:24.110 --> 00:12:27.090
tens, that's 10 tens.

00:12:27.090 --> 00:12:29.450
It looks like we took a 1 away
and we just put the 1 in front

00:12:29.450 --> 00:12:32.390
of 0, but we essentially
added 10 tens to it.

00:12:32.390 --> 00:12:35.360
But if it helps your mind,
we took a 1 away from this,

00:12:35.360 --> 00:12:38.480
put it right in front of
the 0 just like that.

00:12:38.480 --> 00:12:42.130
This is the same 0 as
that 0 right there.

00:12:42.130 --> 00:12:44.220
And this 1 we took
from this guy.

00:12:44.220 --> 00:12:46.600
He became 6 and we
have a 1 there.

00:12:46.600 --> 00:12:48.720
And then we say OK, 10 is
definitely greater than

00:12:48.720 --> 00:12:50.020
6, we're cool there.

00:12:50.020 --> 00:12:53.300
But all of a sudden here on
the 3 we're still not good.

00:12:53.300 --> 00:12:54.900
3 is smaller than 7.

00:12:54.900 --> 00:12:56.030
Still not cool.

00:12:56.030 --> 00:12:58.690
I won't be able to subtract,
so let me borrow again.

00:12:58.690 --> 00:13:00.490
Now I have something
to borrow from.

00:13:00.490 --> 00:13:02.560
Remember we went from the left
to right this time instead

00:13:02.560 --> 00:13:03.660
of from the right to left.

00:13:03.660 --> 00:13:05.670
All of these are valid
ways of doing it.

00:13:05.670 --> 00:13:07.860
So we say let me
borrow 1 from the 10.

00:13:07.860 --> 00:13:13.680
So 10 minus 1 is 9, and let me
give that 1 to the 3 to go 13.

00:13:13.680 --> 00:13:15.050
Remember, it's not a 1.

00:13:15.050 --> 00:13:16.170
I added 10 to it.

00:13:16.170 --> 00:13:18.910
If I take 1 from the tens
place, that's like adding

00:13:18.910 --> 00:13:20.570
10 to the ones place.

00:13:20.570 --> 00:13:21.480
Don't want to confuse you.

00:13:21.480 --> 00:13:24.110
Hopefully you see
the system here.

00:13:24.110 --> 00:13:26.610
I want you to be able to do the
problems before you have to get

00:13:26.610 --> 00:13:28.960
the real deep understanding
of what's going on.

00:13:28.960 --> 00:13:35.620
So 13 minus 7 is 6, 9 minus
6 is 3, 6 minus 0 is 6.

00:13:35.620 --> 00:13:36.620
636.

00:13:36.620 --> 00:13:38.820
Let's do a couple more
problems, because the

00:13:38.820 --> 00:13:41.060
subtraction sometimes with the
borrowing it can come a little

00:13:41.060 --> 00:13:43.510
bit confusing on
what to do next.

00:13:43.510 --> 00:13:52.330
Let's say 953 minus 754.

00:13:52.330 --> 00:13:55.630
Maybe we'll do it in all of the
different ways that you can

00:13:55.630 --> 00:13:58.190
actually do this
type of problem.

00:13:58.190 --> 00:14:00.990
First, one of the ways I talked
about is to start at the right.

00:14:00.990 --> 00:14:02.520
Let's see, is 3 larger than 4?

00:14:02.520 --> 00:14:03.230
No, it's not.

00:14:03.230 --> 00:14:04.970
So we're going to have to
make it larger than 4.

00:14:04.970 --> 00:14:10.310
So let's borrow from
this 5 over here.

00:14:10.310 --> 00:14:16.960
So if I borrow from the 5, the
5 will become a 4, and I'd

00:14:16.960 --> 00:14:20.210
borrowed 1, the 3 becomes a 13.

00:14:20.210 --> 00:14:22.130
Remember, if I borrow 1
from the tens place,

00:14:22.130 --> 00:14:23.540
that's actually a 10.

00:14:23.540 --> 00:14:25.020
This is 5 tens.

00:14:25.020 --> 00:14:28.350
I took one of the 10s away, so
I'm left with four 10s, and I

00:14:28.350 --> 00:14:31.480
added that 10 to the
3, so I have 13.

00:14:31.480 --> 00:14:32.300
So this looks good.

00:14:32.300 --> 00:14:35.310
13 minus 4, I'll be able
to subtract there.

00:14:35.310 --> 00:14:36.880
But here I have a problem.

00:14:36.880 --> 00:14:38.560
4 is less than 5.

00:14:38.560 --> 00:14:41.090
It was cool before but now all
of a sudden it's messed up.

00:14:41.090 --> 00:14:42.920
So I'm going to have
to borrow again.

00:14:42.920 --> 00:14:45.590
I'm going to say well,
let me take a 1 from the

00:14:45.590 --> 00:14:48.180
hundredths place, so
that will become an 8.

00:14:48.180 --> 00:14:50.940
And let me give that
100 to my tens place.

00:14:50.940 --> 00:14:52.800
100 is 10 tens.

00:14:52.800 --> 00:14:57.380
So I'm going to add a 10 here,
so it's going to become 14.

00:14:57.380 --> 00:14:59.950
I took the 1 from there
and I borrowed it, or

00:14:59.950 --> 00:15:01.760
I rearranged that 100.

00:15:01.760 --> 00:15:04.850
I could re-write that 100 as
one 10, and so that's what

00:15:04.850 --> 00:15:08.470
got us to that from 9
to 8 -- or sorry, 100.

00:15:08.470 --> 00:15:11.470
I took away 100 from
the 900 to get 800.

00:15:11.470 --> 00:15:16.440
And when I re-wrote the 100 in
the tens place, it's ten 10s.

00:15:16.440 --> 00:15:19.990
So that's why I added a 10
to the 4 that I had before.

00:15:19.990 --> 00:15:22.890
I could have just scratched it
out and put the 14 like that to

00:15:22.890 --> 00:15:25.520
show that I had to
re-write the 4.

00:15:25.520 --> 00:15:26.820
But now all of a
sudden I'm cool.

00:15:26.820 --> 00:15:29.930
13 minus 4 is 9.

00:15:29.930 --> 00:15:32.490
14 minus 5 is 9.

00:15:32.490 --> 00:15:34.210
8 minus 7 is 1.

00:15:34.210 --> 00:15:40.220
953 minus 754 is 199.

00:15:40.220 --> 00:15:42.660
Now let's do it the
left to right way.

00:15:42.660 --> 00:15:50.470
953 -- let me use a different
color -- minus 754.

00:15:50.470 --> 00:15:52.990
Now this is will be a
little bit different

00:15:52.990 --> 00:15:53.470
than I did last time.

00:15:53.470 --> 00:15:56.510
I say well 9 is definitely
larger than 7.

00:15:56.510 --> 00:16:00.240
5 is definitely larger -- well,
at least it's equal to 5, so

00:16:00.240 --> 00:16:02.550
if I subtract maybe
I'll get a 0 there.

00:16:02.550 --> 00:16:03.980
And 3 is less than 4.

00:16:03.980 --> 00:16:07.100
So maybe I'll just
have to borrow here.

00:16:07.100 --> 00:16:09.795
If I borrow here than this is
going to become a 4 and I'm

00:16:09.795 --> 00:16:11.630
going to have to borrow
from there and give me 14.

00:16:11.630 --> 00:16:14.100
It'll essentially boil down
to what we did on this

00:16:14.100 --> 00:16:15.720
left hand side right here.

00:16:15.720 --> 00:16:19.710
Instead, one thing you can do
is say OK, 9 is larger than 7.

00:16:19.710 --> 00:16:20.590
That's cool.

00:16:20.590 --> 00:16:24.390
Or even better you could say
953 is larger than 754.

00:16:24.390 --> 00:16:25.030
You know that.

00:16:25.030 --> 00:16:27.160
You know that this is going
to be a positive number.

00:16:27.160 --> 00:16:28.920
That this number is
larger than that.

00:16:28.920 --> 00:16:31.340
Then you shift over
one to the left.

00:16:31.340 --> 00:16:34.090
Is 53 larger than 54?

00:16:34.090 --> 00:16:37.410
Well no, 53 is not
larger than 54.

00:16:37.410 --> 00:16:42.250
And because 53 is not larger
than 54, let's borrow.

00:16:42.250 --> 00:16:45.000
Let's borrow from the
hundredths place.

00:16:45.000 --> 00:16:49.840
So this will become an 8, and
we have 100 to work with.

00:16:49.840 --> 00:16:52.290
So maybe we'll just throw
that 100 right here.

00:16:52.290 --> 00:16:55.960
So if we throw the 100 into
the tens place, it's ten 10s.

00:16:55.960 --> 00:16:59.170
So the 5 becomes 15.

00:16:59.170 --> 00:17:01.030
We're going from left to right.

00:17:01.030 --> 00:17:04.700
So now we say 8 is
larger than 7.

00:17:04.700 --> 00:17:06.930
Well, 8 is definitely larger
than 7, 15 is definitely

00:17:06.930 --> 00:17:08.250
larger than 5.

00:17:08.250 --> 00:17:10.810
And then here, once again,
we see 3 is less than 4.

00:17:10.810 --> 00:17:13.120
But now we can
borrow from the 15.

00:17:13.120 --> 00:17:16.590
So if we borrow from the 15,
the 15 becomes a 14, and

00:17:16.590 --> 00:17:18.450
then the 3 becomes a 13.

00:17:18.450 --> 00:17:21.500
Because you take 1 away from
the tens place, one $10

00:17:21.500 --> 00:17:23.210
bill is equal to 10 ones.

00:17:23.210 --> 00:17:26.110
So that's why you added 10
to the 3 and you got 13.

00:17:26.110 --> 00:17:28.550
And notice, we ended up really
with the same thing no matter

00:17:28.550 --> 00:17:30.390
how we did this problem.

00:17:30.390 --> 00:17:33.680
So just like that you
get 13 minus 4 is 9.

00:17:33.680 --> 00:17:35.820
14 minus 5 is 9.

00:17:35.820 --> 00:17:39.060
8 minus 7 is 1.

00:17:39.060 --> 00:17:41.550
Hopefully you found that
pretty straightforward.

00:17:41.550 --> 00:17:44.290
These are, frankly, as hard as
the borrowing problems get.

00:17:44.290 --> 00:17:46.350
The ones where you don't have
something to borrow from or

00:17:46.350 --> 00:17:50.590
when you do borrow from it, all
of a sudden you get a number

00:17:50.590 --> 00:17:52.790
that -- then you need to
borrow from something else.

00:17:52.790 --> 00:17:55.460
If you ever get really
confused about it, you should

00:17:55.460 --> 00:17:56.760
always go back to this.

00:17:56.760 --> 00:18:00.620
You should always go back to
this notion of regrouping.

00:18:00.620 --> 00:18:04.170
This notion of OK, if these
things are all too small, let

00:18:04.170 --> 00:18:08.470
me take $100 bill over here, so
I have six $100 bills left.

00:18:08.470 --> 00:18:12.760
And let me regroup that $100
bills into the other spaces.

00:18:12.760 --> 00:18:17.510
In this case, we took the $100
bill and we put 90 here or nine

00:18:17.510 --> 00:18:21.620
10s, nine $10 bills, and then
$10 of it right there to make

00:18:21.620 --> 00:18:24.060
everything in the numerator
larger than everything

00:18:24.060 --> 00:18:24.740
in the denominator.