MTEL Math Practice Test: 5-8

WEBVTT
Kind: captions
Language: en

00:00:00.730 --> 00:00:01.760
Problem 5.

00:00:01.760 --> 00:00:04.180
Use the expression below
to answer the

00:00:04.180 --> 00:00:05.560
question that follows.

00:00:05.560 --> 00:00:08.150
OK, there's my expression,
and here's the

00:00:08.150 --> 00:00:09.350
question that follows.

00:00:09.350 --> 00:00:13.100
Which of the following is the
best estimate of the value of

00:00:13.100 --> 00:00:14.240
the expression above?

00:00:14.240 --> 00:00:16.770
So when they want best estimate,
it's really just

00:00:16.770 --> 00:00:18.600
saying, look, you don't have
to do all of the math.

00:00:18.600 --> 00:00:21.810
Just kind of round out
everything and try to figure

00:00:21.810 --> 00:00:22.980
out what this is saying.

00:00:22.980 --> 00:00:27.180
So if I wanted to round this
out at the 32,629, I'd say

00:00:27.180 --> 00:00:33.980
that's approximately equal to
30,000 times-- instead of 484,

00:00:33.980 --> 00:00:38.600
I'm going to say that's roughly
equal to 500, and then

00:00:38.600 --> 00:00:42.400
divide that by 306,751.

00:00:42.400 --> 00:00:48.090
I'm going to say that's roughly
equal to 300,000.

00:00:48.090 --> 00:00:50.440
So the first thing I want to do,
maybe I'll divide the top

00:00:50.440 --> 00:00:54.842
and the bottom by 3, so this
30,000 will become-- let me do

00:00:54.842 --> 00:00:58.810
it in darker color-- will
become 10,000, and this

00:00:58.810 --> 00:01:04.239
300,000 will become 100,000.

00:01:04.239 --> 00:01:06.030
And then I can start
canceling out 0's.

00:01:06.030 --> 00:01:10.080
If I divide the top and the
bottom by 10,000, I could

00:01:10.080 --> 00:01:13.070
essentially get rid of four 0's
on the top and the bottom.

00:01:13.070 --> 00:01:16.090
So then, I'd just, 10,000
divided by 10,000

00:01:16.090 --> 00:01:17.530
will just become 1.

00:01:17.530 --> 00:01:21.680
100,000 divided by 10,000
is just 10.

00:01:21.680 --> 00:01:22.720
That just becomes 10.

00:01:22.720 --> 00:01:25.690
And then we're left with
500 divided by 10.

00:01:25.690 --> 00:01:28.380
We can just cancel out
some more 0's.

00:01:28.380 --> 00:01:30.790
Divide the top and the bottom
by 10, you get a 1 in the

00:01:30.790 --> 00:01:32.800
bottom and you get
a 50 on top.

00:01:32.800 --> 00:01:36.520
So you could say this is roughly
equal to 50, and lucky

00:01:36.520 --> 00:01:40.280
for us, that's actually
one of the choices.

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Problem 6.

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Use the diagram below
to answer the

00:01:44.420 --> 00:01:46.330
question that follows.

00:01:46.330 --> 00:01:48.710
The measurements in the diagram
above are shown

00:01:48.710 --> 00:01:51.840
rounded to the nearest
whole number.

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Which of the following is a
possible value of A, the area

00:01:55.740 --> 00:01:56.570
of the rectangle?

00:01:56.570 --> 00:01:58.940
So what they're saying is that
these numbers, these aren't

00:01:58.940 --> 00:02:01.730
the actual values if we were to
be precise about it, they

00:02:01.730 --> 00:02:04.050
just rounded them to the
nearest whole number.

00:02:04.050 --> 00:02:06.190
When you just multiply these two
things to figure out the

00:02:06.190 --> 00:02:10.830
area, you get an area of 8
inches, or 8 square inches.

00:02:10.830 --> 00:02:13.720
But when you look at the
choices, I don't see an 8

00:02:13.720 --> 00:02:14.440
square inches.

00:02:14.440 --> 00:02:19.100
It seems like it's either
going to be B or C.

00:02:19.100 --> 00:02:22.370
And if you just look at these
two numbers, which one's

00:02:22.370 --> 00:02:29.640
closer-- see, 8 to 5.5, so
8 minus 5.5, that's what?

00:02:29.640 --> 00:02:32.710
8 minus 5 is 3 inches, so this
is 2 and 1/2 inches.

00:02:32.710 --> 00:02:36.990
So we're 2 and 1/2 inches from
this one, and we are 3 and 1/2

00:02:36.990 --> 00:02:37.960
inches from this one.

00:02:37.960 --> 00:02:41.110
So if I was stuck for time,
I would go with this one.

00:02:41.110 --> 00:02:44.720
But just to verify that this
definitely could be an answer,

00:02:44.720 --> 00:02:48.020
if these are rounded to the
nearest whole number, then

00:02:48.020 --> 00:02:52.760
this one could be as low
as 1.5 inches, right?

00:02:52.760 --> 00:02:56.550
If this dimension is actually
1.5 inches when they rounded

00:02:56.550 --> 00:02:57.380
it, they would have made it 2.

00:02:57.380 --> 00:02:59.270
It couldn't have been 1.49,
because then they would have

00:02:59.270 --> 00:03:00.750
rounded it down.

00:03:00.750 --> 00:03:04.600
Similarly, this could have
been as low as 3.5.

00:03:04.600 --> 00:03:06.980
When they round it, they would
have rounded it to 4.

00:03:06.980 --> 00:03:09.910
It couldn't have been 3.49,
because then they would have

00:03:09.910 --> 00:03:11.900
rounded it down to 3.

00:03:11.900 --> 00:03:15.310
So if this dimension was 3.5,
and this dimension was 1.5,

00:03:15.310 --> 00:03:17.120
what would the area have been?

00:03:17.120 --> 00:03:22.422
So 3.5 times 1.5.

00:03:22.422 --> 00:03:26.420
Let's see, 5 times 5 is 25.

00:03:26.420 --> 00:03:32.160
3 times 5 is 15, plus 2 is 17.

00:03:32.160 --> 00:03:33.350
Put a 0 down.

00:03:33.350 --> 00:03:35.490
1 times 5 is 5.

00:03:35.490 --> 00:03:38.010
1 times 3 is 3.

00:03:38.010 --> 00:03:41.610
5, 7 plus 5 is 12.

00:03:41.610 --> 00:03:44.580
And then you have 1 plus
1, plus 3 is 5.

00:03:44.580 --> 00:03:48.840
You have two numbers behind
the decimal point, 5.25.

00:03:48.840 --> 00:03:53.990
So the minimum possible area
for this rectangle is 5.25.

00:03:53.990 --> 00:03:55.170
That's the minimum.

00:03:55.170 --> 00:03:59.270
So 5.5 is definitely
a valid answer.

00:03:59.270 --> 00:04:02.240
So I'm going to stick
with my answer, B.

00:04:02.240 --> 00:04:03.490
Next problem.

00:04:06.520 --> 00:04:09.000
All right.

00:04:09.000 --> 00:04:13.340
Use the table below to answer
the questions-- the question--

00:04:13.340 --> 00:04:14.240
that follows.

00:04:14.240 --> 00:04:17.750
OK, they have a store, different
stores, discount for

00:04:17.750 --> 00:04:20.459
manufacturer's recommended
price.

00:04:20.459 --> 00:04:21.700
OK, there we go.

00:04:21.700 --> 00:04:24.120
So they're all discounting
games.

00:04:24.120 --> 00:04:28.320
Samantha wants to buy two
computer games, each of which

00:04:28.320 --> 00:04:32.260
has a manufacturer's recommended
price of $20.

00:04:32.260 --> 00:04:35.110
She checks four different stores
and finds the prices of

00:04:35.110 --> 00:04:37.940
the games discounted as shown
in the table above.

00:04:37.940 --> 00:04:40.960
At which store will Samantha be
able to buy the games for

00:04:40.960 --> 00:04:42.730
the least amount of money?

00:04:42.730 --> 00:04:43.370
That makes sense.

00:04:43.370 --> 00:04:45.210
You want to find the
cheapest place.

00:04:45.210 --> 00:04:47.280
So this is $4 off the
price of each game.

00:04:47.280 --> 00:04:48.950
Remember, she's buying two.

00:04:48.950 --> 00:04:50.800
The manufactured price is $20.

00:04:50.800 --> 00:04:54.320
So she's going to pay $4 off of
$20 for each game, so she's

00:04:54.320 --> 00:04:57.890
going to pay $16 plus $16,
which is equal to $32.

00:04:57.890 --> 00:04:59.680
That's at store number one.

00:04:59.680 --> 00:05:02.260
30% discount on each game.

00:05:02.260 --> 00:05:11.400
So 30% discount, so $20 times
30% discount is 0.3.

00:05:11.400 --> 00:05:15.770
So you can imagine 3 times 20
is 60, and then you put the

00:05:15.770 --> 00:05:16.410
decimal sign.

00:05:16.410 --> 00:05:20.990
It's going to be a $6 discount
on each game for this one.

00:05:20.990 --> 00:05:22.720
So $6 discount.

00:05:22.720 --> 00:05:28.970
Remember 30% of $20 is $6, so
$6 discount will be $14,

00:05:28.970 --> 00:05:32.270
right? $20 minus $6 per
game that she buys.

00:05:32.270 --> 00:05:35.360
So she's going to spend $28
at store number two.

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Switch colors.

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1/3 off the price of
the two games.

00:05:40.110 --> 00:05:42.090
Well, you know, you could
immediately say that 1/3 is

00:05:42.090 --> 00:05:45.380
33%, so that's a bigger discount
than this one.

00:05:45.380 --> 00:05:46.560
You could do the math.

00:05:46.560 --> 00:05:51.470
You'll figure out, you know,
instead of this being $6,

00:05:51.470 --> 00:05:55.960
it'll be $6.66, and it's going
to be $13 and something

00:05:55.960 --> 00:05:59.230
something, plus $13, and
something something.

00:05:59.230 --> 00:06:02.130
You're going to get something,
you know, $27 and some change.

00:06:02.130 --> 00:06:03.770
But you know that this is a
better deal than this one,

00:06:03.770 --> 00:06:07.880
because this is the same thing
as 33% off, which is clearly

00:06:07.880 --> 00:06:09.720
better than 30% off.

00:06:09.720 --> 00:06:13.570
And then this fourth one-- buy
one game, and get the second

00:06:13.570 --> 00:06:15.560
at 1/2 price.

00:06:15.560 --> 00:06:20.620
So here, she's going to spend
$20 on the first game, and

00:06:20.620 --> 00:06:23.400
then the second one is going
to be 1/2 price.

00:06:23.400 --> 00:06:27.790
So she's going to spend
a total of $30.

00:06:27.790 --> 00:06:30.790
So the best deal is store number
three, where it's going

00:06:30.790 --> 00:06:33.910
to be $27 something.

00:06:33.910 --> 00:06:34.230
Right?

00:06:34.230 --> 00:06:36.210
I mean, store number two is
definitely better than store

00:06:36.210 --> 00:06:38.030
number four, which is definitely
better than store

00:06:38.030 --> 00:06:38.820
number one.

00:06:38.820 --> 00:06:40.650
And then store number three is
definitely better than store

00:06:40.650 --> 00:06:40.950
number two.

00:06:40.950 --> 00:06:42.520
It's a 33% discount.

00:06:42.520 --> 00:06:47.180
So I'm going to go with
store number three.

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Next problem.

00:06:49.550 --> 00:06:52.560
Go to the next problem.

00:06:52.560 --> 00:06:53.020
8.

00:06:53.020 --> 00:06:55.450
Use the procedure below
to answer the

00:06:55.450 --> 00:06:56.760
question that follows.

00:06:56.760 --> 00:06:59.640
OK, n is equal to 0.632, OK.

00:06:59.640 --> 00:07:02.690
100n is equal to 63, just
multiply it by 100.

00:07:02.690 --> 00:07:04.280
OK, they're trying to eliminate

00:07:04.280 --> 00:07:05.430
the repeating decimals.

00:07:05.430 --> 00:07:06.520
I get it.

00:07:06.520 --> 00:07:09.410
The procedure above shows how to
convert a repeating decimal

00:07:09.410 --> 00:07:10.360
to a fraction.

00:07:10.360 --> 00:07:11.520
All right.

00:07:11.520 --> 00:07:18.270
If 0.12561256 is a decimal with
four repeating digits,

00:07:18.270 --> 00:07:19.920
which of the following
represents this

00:07:19.920 --> 00:07:21.590
decimal as a fraction?

00:07:21.590 --> 00:07:23.640
So what you do, we'll just do
what the procedure we did

00:07:23.640 --> 00:07:26.540
before, and this might bring you
back memories from algebra

00:07:26.540 --> 00:07:28.150
class, or pre-algebra
class, you get

00:07:28.150 --> 00:07:28.960
when you first started.

00:07:28.960 --> 00:07:30.670
You say n.

00:07:30.670 --> 00:07:32.920
Or we can just do exactly what
they did there, is equal to

00:07:32.920 --> 00:07:45.230
0.12561256, and then we
can multiply that.

00:07:45.230 --> 00:07:46.500
And you can even
pattern match.

00:07:46.500 --> 00:07:48.510
Here, you had two digits
repeating, they

00:07:48.510 --> 00:07:50.025
multiplied it by 100.

00:07:50.025 --> 00:07:52.430
And 100 has two 0's.

00:07:52.430 --> 00:07:54.800
Here we have four digits
repeating, so we're going to

00:07:54.800 --> 00:07:58.240
multiply it by something
with four 0's.

00:07:58.240 --> 00:08:01.430
So we'll have 1, 1, 2, 3, 4.

00:08:01.430 --> 00:08:02.420
There's our four 0's.

00:08:02.420 --> 00:08:06.970
So that's 10,000n is going
to be equal to what?

00:08:06.970 --> 00:08:08.660
What's 0.1 of 10,000?

00:08:08.660 --> 00:08:10.020
It's 1,000.

00:08:10.020 --> 00:08:11.800
What's 0.02 of 10,000?

00:08:11.800 --> 00:08:13.350
I think you get the idea.

00:08:13.350 --> 00:08:15.710
It is 2,000.

00:08:15.710 --> 00:08:16.870
Sorry, it's 200.

00:08:16.870 --> 00:08:25.340
So you get 1,256.12561256.

00:08:25.340 --> 00:08:27.860
It just keeps repeating,
on and on and on.

00:08:27.860 --> 00:08:28.560
You get the idea.

00:08:28.560 --> 00:08:31.230
We just multiplied this by
10,000 because that allowed us

00:08:31.230 --> 00:08:35.159
to bring one whole repetition
to the left of the decimal.

00:08:35.159 --> 00:08:35.990
You could verify that.

00:08:35.990 --> 00:08:38.770
Actually, let's multiply it out,
just to verify that this

00:08:38.770 --> 00:08:39.559
actually works.

00:08:39.559 --> 00:08:50.920
If I multiply 12561256 times
10,000, what you could do is,

00:08:50.920 --> 00:08:53.340
you could just multiply
it by 1.

00:08:53.340 --> 00:09:01.190
So you get 12561256, add
four 0's, 1, 2, 3, 4.

00:09:01.190 --> 00:09:04.200
And then count how many decimal
points you have, 1, 2,

00:09:04.200 --> 00:09:06.590
3, 4, 5, 6, 7, 8.

00:09:06.590 --> 00:09:10.080
1, 2, 3, 4, 5, 6, 7, 8.

00:09:10.080 --> 00:09:11.770
And we verify that it works.

00:09:11.770 --> 00:09:13.210
Now, of course, I didn't
multiply the

00:09:13.210 --> 00:09:14.420
entire repeating part.

00:09:14.420 --> 00:09:17.380
If it just kept repeating, then
we'd have a 1256 and it'd

00:09:17.380 --> 00:09:19.550
keep repeating, so
on and so forth.

00:09:19.550 --> 00:09:21.900
But you saw it worked in the
pattern, and it works here.

00:09:21.900 --> 00:09:24.240
So once we get that, we just
essentially want to subtract

00:09:24.240 --> 00:09:25.820
this guy from this guy.

00:09:25.820 --> 00:09:29.390
So we say minus n, or you could
say this is equal to

00:09:29.390 --> 00:09:38.200
minus 0.12561256, and we are
left with-- on this side,

00:09:38.200 --> 00:09:41.330
what's 10,000 minus 1?

00:09:41.330 --> 00:09:49.610
Well, that's 9,999 is equal
to-- well, when you do the

00:09:49.610 --> 00:09:52.230
subtraction, this and this part
are going to cancel out.

00:09:52.230 --> 00:09:53.610
The decimal parts cancel
out, and you're

00:09:53.610 --> 00:09:57.160
just left with 1,256.

00:09:57.160 --> 00:10:00.960
So 9,999n-- remember, there's
a coefficient there, I don't

00:10:00.960 --> 00:10:03.920
want to lose that--
is equal to 1,256.

00:10:03.920 --> 00:10:09.430
Or if we divide both sides by
9,999, you get-- so n is equal

00:10:09.430 --> 00:10:15.620
to 1,256 divided by 9,999.

00:10:15.620 --> 00:10:18.230
And that is one of
our choices.

00:10:18.230 --> 00:10:22.280
1,256 divided by 9,999.


MTEL Math Practice Test: 1-4

WEBVTT
Kind: captions
Language: en

00:00:00.600 --> 00:00:02.280
Problem number one.

00:00:02.280 --> 00:00:07.050
In the number 2,010, or 2,010,
the value represented by the

00:00:07.050 --> 00:00:11.100
digit 1 is what fraction of
the value represented

00:00:11.100 --> 00:00:13.060
by the digit 2?

00:00:13.060 --> 00:00:18.830
We have the number 2,010, or we
could rewrite this as 2,000

00:00:18.830 --> 00:00:23.750
plus 0 hundreds plus
10 plus 0.

00:00:23.750 --> 00:00:26.700
And they're saying the value
represented by the digit 1--

00:00:26.700 --> 00:00:30.690
well, the value represented by
the digit 1 is 10-- is what

00:00:30.690 --> 00:00:33.130
fraction of the value
represented by the digit 2?

00:00:33.130 --> 00:00:36.440
Well, the digit 2 represents
2,000.

00:00:36.440 --> 00:00:41.190
So the fraction is going to be
the 10 divided by what the 2

00:00:41.190 --> 00:00:43.790
represents, 2,000.

00:00:43.790 --> 00:00:47.550
The 1 represents 10, the
2 represents 2,000.

00:00:47.550 --> 00:00:52.210
You can cancel out a 0 right
there, we get 1 over 200,

00:00:52.210 --> 00:00:54.920
which is choice B.

00:00:54.920 --> 00:00:56.770
Problem two.

00:00:56.770 --> 00:01:01.000
If P is a positive integer,
which of the following must

00:01:01.000 --> 00:01:04.050
also be a positive integer?

00:01:04.050 --> 00:01:05.349
Let's see, choice A.

00:01:05.349 --> 00:01:06.760
1 minus P.

00:01:06.760 --> 00:01:10.860
Well, if P was 2, 2 is a
positive integer, then 1 minus

00:01:10.860 --> 00:01:12.850
2 would be equal to minus 1.

00:01:12.850 --> 00:01:15.180
This is not a positive
integer.

00:01:15.180 --> 00:01:16.315
This is a negative integer.

00:01:16.315 --> 00:01:18.200
So it can't be A.

00:01:18.200 --> 00:01:19.250
1 over P.

00:01:19.250 --> 00:01:21.712
Well, once again, I'm just
picking 2 at random, a

00:01:21.712 --> 00:01:23.060
positive integer.

00:01:23.060 --> 00:01:28.730
If P is 2, then 1 over 2 is not
a positive integer, so it

00:01:28.730 --> 00:01:30.250
can't be B.

00:01:30.250 --> 00:01:32.550
Let me cross that out.

00:01:32.550 --> 00:01:34.980
Cross that out right there.

00:01:34.980 --> 00:01:36.830
Well, I'm going to keep running
with my number 2.

00:01:36.830 --> 00:01:38.300
If it doesn't work for number
2, it's definitely not going

00:01:38.300 --> 00:01:40.380
to work for any positive
integer.

00:01:40.380 --> 00:01:45.010
So if P is 2, right here, then
the square root of 2, once

00:01:45.010 --> 00:01:48.420
again, not a positive integer.

00:01:48.420 --> 00:01:50.100
And then finally P squared.

00:01:50.100 --> 00:01:54.250
Well, for 2, if I say P is equal
to 2, then P squared is

00:01:54.250 --> 00:01:55.300
equal to 4.

00:01:55.300 --> 00:01:58.660
And in general, if I take any
positive integer and I square

00:01:58.660 --> 00:02:01.630
it, if I multiply it by itself,
I'm just going to get

00:02:01.630 --> 00:02:03.200
another-- it's definitely going
to be positive, it's

00:02:03.200 --> 00:02:04.180
definitely going to
be an integer.

00:02:04.180 --> 00:02:07.910
So my choice is D.

00:02:07.910 --> 00:02:10.389
Next problem.

00:02:10.389 --> 00:02:12.095
Problem three.

00:02:12.095 --> 00:02:15.610
Let me switch colors,
just for fun.

00:02:15.610 --> 00:02:18.860
According to an article in a
financial journal, a certain

00:02:18.860 --> 00:02:23.600
company earned 3.85-- now
why isn't it writing?

00:02:23.600 --> 00:02:25.340
[UNINTELLIGIBLE]--

00:02:25.340 --> 00:02:29.450
earned $3.85 million
last year.

00:02:29.450 --> 00:02:33.120
Based on this report of the
company's yearly earnings, a

00:02:33.120 --> 00:02:36.390
person reading the article
estimates that the company

00:02:36.390 --> 00:02:41.240
earned an average of
approximately $30,000 a month,

00:02:41.240 --> 00:02:42.520
and they're saying estimates.

00:02:42.520 --> 00:02:44.740
So we don't have to
do the exact math.

00:02:44.740 --> 00:02:46.970
Which of the following
statements best describes the

00:02:46.970 --> 00:02:49.900
reasonableness of this estimate
for the company's

00:02:49.900 --> 00:02:52.770
average monthly earnings?

00:02:52.770 --> 00:02:57.380
So $3.85 million last year, and
then we want to be able to

00:02:57.380 --> 00:02:59.675
estimate how many monthly
earnings.

00:02:59.675 --> 00:03:07.830
So we want to divide 3.85
million by 12 months.

00:03:07.830 --> 00:03:10.490
That's 3.85 million a
year, and we want to

00:03:10.490 --> 00:03:11.820
divide it by 12.

00:03:11.820 --> 00:03:13.725
We could do the exact number,
but we could say,

00:03:13.725 --> 00:03:14.260
hey, you know what?

00:03:14.260 --> 00:03:18.030
This is pretty close
to 3.6 million.

00:03:18.030 --> 00:03:20.380
The reason why I'm picking
3.6 million is because

00:03:20.380 --> 00:03:22.960
36 is 3 times 12.

00:03:22.960 --> 00:03:28.040
So if we do 3.6 million, we
could say that this is

00:03:28.040 --> 00:03:31.340
approximately 3.6 million
divided by 12,

00:03:31.340 --> 00:03:32.620
which is equal to what?

00:03:32.620 --> 00:03:35.300
If this was 36 million
divided by 12, we

00:03:35.300 --> 00:03:37.360
would have 3 million.

00:03:37.360 --> 00:03:39.990
But it's not 36 million
divided by 12,

00:03:39.990 --> 00:03:41.430
it's 1/10 of that.

00:03:41.430 --> 00:03:43.620
It's 3.6 million
divided by 12.

00:03:43.620 --> 00:03:50.000
So it would be 0.3-- and you
could put a 0 out front-- 0.3

00:03:50.000 --> 00:03:55.510
million per month.

00:03:55.510 --> 00:04:03.060
Or another way to write 0.3
million is 300,000 per month.

00:04:03.060 --> 00:04:07.530
Now, someone estimated that they
made $30,000 per month.

00:04:07.530 --> 00:04:11.290
So they were off, they were
too low by a factor of 10.

00:04:11.290 --> 00:04:14.310
You would have to divide by
this, the actual estimate, the

00:04:14.310 --> 00:04:17.519
correct estimate, by 10
to get their estimate.

00:04:17.519 --> 00:04:20.640
So their estimate is too
low by a factor of 10.

00:04:20.640 --> 00:04:22.220
That is choice B.

00:04:22.220 --> 00:04:24.180
Another way you could have
thought about this is instead

00:04:24.180 --> 00:04:28.060
of writing 3.85 million, you
could have written that as

00:04:28.060 --> 00:04:33.470
3,850K divided by 12.

00:04:33.470 --> 00:04:38.770
Or, you could have said, well
that's approximately 3,600K

00:04:38.770 --> 00:04:40.550
divided by 12, and then
you would have

00:04:40.550 --> 00:04:41.870
said, OK, that's 300,000.

00:04:41.870 --> 00:04:45.295
You would have gotten the same
answer, which is 10 times more

00:04:45.295 --> 00:04:46.220
than their estimate.

00:04:46.220 --> 00:04:49.750
Or their estimate was too
low by a factor of 10.

00:04:49.750 --> 00:04:51.900
Problem four.

00:04:51.900 --> 00:04:55.160
The mean distance from the
earth to the sun is

00:04:55.160 --> 00:04:58.990
approximately 93 million
miles, or one

00:04:58.990 --> 00:05:00.970
astronomical unit.

00:05:00.970 --> 00:05:04.820
The mean distance from Neptune
to the sun is approximately

00:05:04.820 --> 00:05:09.790
2.794 times 10 to
the ninth miles.

00:05:09.790 --> 00:05:13.210
What is the approximate mean
distance from Neptune to the

00:05:13.210 --> 00:05:16.080
sun in astronomical units?

00:05:16.080 --> 00:05:19.410
So essentially we want to divide
the average distance of

00:05:19.410 --> 00:05:26.450
Neptune-- 2.794 times 10 to the
ninth miles-- divided by 1

00:05:26.450 --> 00:05:30.750
astronomical unit, which
is 93 million.

00:05:30.750 --> 00:05:33.620
When you write it like this,
it's kind of hard to digest,

00:05:33.620 --> 00:05:34.740
or see what's going on.

00:05:34.740 --> 00:05:38.300
But what we can do is write
this guy, right here, in

00:05:38.300 --> 00:05:39.960
scientific notation as well.

00:05:39.960 --> 00:05:46.890
So 93 million looks like that.

00:05:46.890 --> 00:05:54.330
We could say that this is 9.3
times 10 to the one, two,

00:05:54.330 --> 00:05:58.660
three, four, five, six,
seventh power.

00:05:58.660 --> 00:06:05.430
So now this thing, up here,
simplifies to 2.794 times 10

00:06:05.430 --> 00:06:15.180
to the ninth over 9.3 times
10 to the seventh.

00:06:15.180 --> 00:06:17.980
Now we could just divide this,
but the way my brain works, I

00:06:17.980 --> 00:06:20.240
would like, instead of this
to be 2.7, I would

00:06:20.240 --> 00:06:21.810
like this to be 27.

00:06:21.810 --> 00:06:24.350
And the reason why I would like
this to be 27 is because

00:06:24.350 --> 00:06:25.760
we have a 9 down here.

00:06:25.760 --> 00:06:27.950
Then we could say, hey,
27 divided by 9 is

00:06:27.950 --> 00:06:29.160
roughly equal to 3.

00:06:29.160 --> 00:06:32.000
So we can rewrite the
top part of this.

00:06:32.000 --> 00:06:33.060
We could rewrite this.

00:06:33.060 --> 00:06:37.500
If we multiply this part by 10,
we would have to divide

00:06:37.500 --> 00:06:39.680
this part by 10 in order to
not change the number.

00:06:39.680 --> 00:06:41.720
We don't want to actually
change the value of the

00:06:41.720 --> 00:06:49.650
number, so we get 27.94 times
10 to the eighth.

00:06:49.650 --> 00:06:52.610
All I did is I multiplied this
part by 10, and to offset

00:06:52.610 --> 00:06:54.360
that, I divided this
part by 10.

00:06:54.360 --> 00:06:58.390
10 to the ninth divided by 10 is
10 to the eighth divided by

00:06:58.390 --> 00:07:02.230
9.3 times 10 to the seventh.

00:07:02.230 --> 00:07:06.820
And now you could say, look,
27.94 divided by 9.3, that's

00:07:06.820 --> 00:07:08.870
going to be approximately 3.

00:07:08.870 --> 00:07:11.890
Remember, we're trying to find
the approximate mean distance.

00:07:11.890 --> 00:07:13.300
We can estimate a little bit.

00:07:13.300 --> 00:07:15.710
And then 10 to the eighth
divided by ten to the

00:07:15.710 --> 00:07:20.110
seventh-- you could just
subtract 7 from 8 of the

00:07:20.110 --> 00:07:23.670
exponents, and so that's
times 10 to the one.

00:07:23.670 --> 00:07:25.950
10 to eighth divided by 10 to
the seventh is exactly 10

00:07:25.950 --> 00:07:27.620
times 10 to the seventh.

00:07:27.620 --> 00:07:30.350
So our approximate answer
is going to be 3

00:07:30.350 --> 00:07:31.600
times 10 to the one.

00:07:31.600 --> 00:07:33.120
Or 3 times 10.

00:07:33.120 --> 00:07:38.330
Or approximately equal to
30 astronomical units.

00:07:38.330 --> 00:07:40.960
And that is choice A.


Why lattice multiplication works

WEBVTT
Kind: captions
Language: en

00:00:00.000 --> 00:00:02.390
In the last video we did a
couple of lattice

00:00:02.390 --> 00:00:04.850
multiplication problems and
we saw it was pretty

00:00:04.850 --> 00:00:05.460
straightforward.

00:00:05.460 --> 00:00:07.810
You got to do all your
multiplication first and then

00:00:07.810 --> 00:00:09.090
do all of your addition.

00:00:09.090 --> 00:00:12.460
Well, let's try to understand
why exactly it worked.

00:00:12.460 --> 00:00:14.160
It almost seemed like magic.

00:00:14.160 --> 00:00:16.540
And to see why it worked I'm
going to redo this problem up

00:00:16.540 --> 00:00:18.950
here then I'll also try to
explain what we did in

00:00:18.950 --> 00:00:19.800
the longer problems.

00:00:19.800 --> 00:00:24.490
So when we multiplied 27-- so
you write your 2 and your 7

00:00:24.490 --> 00:00:27.210
just like that-- times 48.

00:00:27.210 --> 00:00:29.680
I'm just doing exactly what we
did in the previous video.

00:00:29.680 --> 00:00:34.560
We drew a lattice, gave the 2
a column and the 7 a column.

00:00:34.560 --> 00:00:36.480
Just like that.

00:00:36.480 --> 00:00:40.820
We gave the 4 a row and
we gave the 8 a row.

00:00:40.820 --> 00:00:42.970
And then we drew our diagonal.

00:00:42.970 --> 00:00:45.640
And the key here is the
diagonal as you can imagine,

00:00:45.640 --> 00:00:47.790
otherwise we wouldn't
be drawing them.

00:00:47.790 --> 00:00:49.130
So you have your diagonals.

00:00:49.130 --> 00:00:51.820
Now the way to think about it
is each of these diagonals

00:00:51.820 --> 00:00:53.280
are a number place.

00:00:53.280 --> 00:00:55.980
So for example, this
diagonal right here,

00:00:55.980 --> 00:00:59.980
that is the 1's place.

00:00:59.980 --> 00:01:04.220
The next diagonal, I'll do it
in this light green color.

00:01:04.220 --> 00:01:07.360
The next diagonal right here
in the light green color,

00:01:07.360 --> 00:01:09.340
that is the 10's place.

00:01:09.340 --> 00:01:12.870
Now the next diagonal to the
left or above that, depending

00:01:12.870 --> 00:01:14.700
on how you want to view it,
I'll do in this little

00:01:14.700 --> 00:01:16.950
pink color right here.

00:01:16.950 --> 00:01:21.750
You could guess, that's going
to be the 100's place.

00:01:21.750 --> 00:01:25.000
And then finally, we have this
little diagonal there and I'll

00:01:25.000 --> 00:01:27.180
do it in this light
blue collar.

00:01:27.180 --> 00:01:29.485
That is the 1,000's place.

00:01:32.090 --> 00:01:35.630
So whenever we multiply one
digit times another digit, we

00:01:35.630 --> 00:01:38.810
just make sure we put it in
the right bucket or

00:01:38.810 --> 00:01:39.660
in the right place.

00:01:39.660 --> 00:01:41.790
And you'll see what
I mean in a second.

00:01:41.790 --> 00:01:43.790
So we did 7 times 4.

00:01:43.790 --> 00:01:46.160
Well, we know that
7 times 4 is 28.

00:01:46.160 --> 00:01:50.470
We just simply wrote a 2
and an 8 just like that.

00:01:50.470 --> 00:01:51.640
But what did we really do?

00:01:51.640 --> 00:01:53.470
And I guess the best way to
think about it, this 7--

00:01:53.470 --> 00:01:55.340
this is the 7 in 27.

00:01:55.340 --> 00:01:58.320
So it's just a regular 7.

00:01:58.320 --> 00:02:02.140
But this 4, it's the 4 in 48.

00:02:02.140 --> 00:02:04.920
So it's not just a regular
4, it's really a 40.

00:02:04.920 --> 00:02:09.050
48 can be rewritten
as 40 plus 8.

00:02:09.050 --> 00:02:13.530
This 4 right here actually
represents a 40.

00:02:13.530 --> 00:02:16.730
So right here we're not really
multiplying 7 times 4, we're

00:02:16.730 --> 00:02:19.820
actually multiplying
7 times 40.

00:02:19.820 --> 00:02:27.370
And 7 times 40 isn't
just 28, it's 280.

00:02:27.370 --> 00:02:29.450
And 280, how can we
think about that?

00:02:29.450 --> 00:02:37.330
We could say that's two
100's plus eight 10's.

00:02:37.330 --> 00:02:39.630
And that's exactly what
we wrote right here.

00:02:39.630 --> 00:02:44.830
Notice: this column or I'm
sorry, this diagonal right

00:02:44.830 --> 00:02:48.110
here, I already told you,
it was the 10's diagonal.

00:02:48.110 --> 00:02:50.820
And we multiplied 7 times 40.

00:02:50.820 --> 00:02:54.540
We put the 8 right here
in the 10's diagonal.

00:02:54.540 --> 00:02:56.590
So that means eight 10's.

00:02:56.590 --> 00:02:59.250
7 times 40 is two 100's.

00:02:59.250 --> 00:03:01.590
We wrote a 2 in the
100's diagonal.

00:03:01.590 --> 00:03:03.320
And eight 10's.

00:03:03.320 --> 00:03:04.610
That's what this 2 8 here is.

00:03:04.610 --> 00:03:06.820
We actually wrote 280.

00:03:06.820 --> 00:03:07.930
Let's keep going.

00:03:07.930 --> 00:03:10.510
When I multiply 2 times 4.

00:03:10.510 --> 00:03:11.700
You might say, oh, 2 times 4.

00:03:11.700 --> 00:03:12.290
That's 8.

00:03:12.290 --> 00:03:13.150
What am I really doing?

00:03:13.150 --> 00:03:15.310
This is the 2 in 27.

00:03:15.310 --> 00:03:18.520
This is really a 20 and
this is really a 40.

00:03:18.520 --> 00:03:26.130
So 20 times 40 is equal
to just 8 with two 0's.

00:03:26.130 --> 00:03:27.315
Is equal to 800.

00:03:27.315 --> 00:03:28.300
And what did we do?

00:03:28.300 --> 00:03:31.640
We multiplied 2 times 4 and
we said, oh, 2 times 4 is 8.

00:03:31.640 --> 00:03:35.090
We wrote a 0 and en
8 just like that.

00:03:35.090 --> 00:03:37.000
But notice where
we wrote the 8.

00:03:37.000 --> 00:03:41.110
We wrote the 8 in
the 100's diagonal.

00:03:41.110 --> 00:03:42.720
Let me use a different color.

00:03:42.720 --> 00:03:44.760
We wrote it in the
100's diagonal.

00:03:44.760 --> 00:03:46.740
So we literally wrote-- even
though it looked like we

00:03:46.740 --> 00:03:49.580
multiplied 2 times 4 and saying
it's 8, the way we accounted

00:03:49.580 --> 00:03:54.630
for it, we really did 20 times
40 is equal to eight 100's.

00:03:54.630 --> 00:03:56.780
Remember, this is the 100's
diagonal, this whole

00:03:56.780 --> 00:03:57.900
thing right there.

00:03:57.900 --> 00:04:00.180
And we can keep going.

00:04:00.180 --> 00:04:02.270
When you multiply 7 times 8.

00:04:02.270 --> 00:04:06.100
Remember, this is really 7--
well, this is the 7 in 27,

00:04:06.100 --> 00:04:07.100
so it's just a regular 7.

00:04:07.100 --> 00:04:09.890
This is the 8 in 48, so
it's just a regular 8.

00:04:09.890 --> 00:04:11.860
7 times 8 is 56.

00:04:11.860 --> 00:04:14.180
You write a 6 in the 1's place.

00:04:14.180 --> 00:04:17.810
56 is just five 10's and one 6.

00:04:17.810 --> 00:04:23.920
So it's five 10's in the 10's
diagonal and one 6, 56.

00:04:23.920 --> 00:04:27.020
Then when you multiply 2
times 8 notice, that's not

00:04:27.020 --> 00:04:28.220
really just 2 times 8.

00:04:28.220 --> 00:04:30.850
I mean we did write it's just
16 when we did the problem

00:04:30.850 --> 00:04:33.640
over here, but we're
actually multiplying 20.

00:04:33.640 --> 00:04:35.520
This is a 20 times 8.

00:04:35.520 --> 00:04:39.820
20 times 8 is equal to 160.

00:04:39.820 --> 00:04:43.460
Or you could say it's 100,
notice the 1 in the 100's

00:04:43.460 --> 00:04:45.840
diagonal-- and six 10's.

00:04:45.840 --> 00:04:48.000
That's what 160 is.

00:04:48.000 --> 00:04:52.000
So what we did by doing this
lattice multiplication, is we

00:04:52.000 --> 00:04:54.120
accounted all of the digits,
the right digits in

00:04:54.120 --> 00:04:54.970
the right places.

00:04:54.970 --> 00:04:56.840
We put the 6 in the 1's.

00:04:56.840 --> 00:04:59.600
We put the 6, the 5, and
the 8 in the 10's place.

00:04:59.600 --> 00:05:02.090
We put the 1, the 8, and
the 2 in the 100's place.

00:05:02.090 --> 00:05:04.940
And we put nothing right
now in the 1000's place.

00:05:04.940 --> 00:05:07.410
Then, now that we're done with
all the multiplication we can

00:05:07.410 --> 00:05:09.730
actually do our adding up.

00:05:09.730 --> 00:05:12.350
And then you just keep adding,
and if there's something that

00:05:12.350 --> 00:05:14.840
goes over to the next place
you just carry that number.

00:05:14.840 --> 00:05:18.240
So 6 in the 1's place,
well, that's just a 6.

00:05:18.240 --> 00:05:19.610
Then you go the 10's place.

00:05:19.610 --> 00:05:22.650
8 plus 5 plus 6 is what?

00:05:22.650 --> 00:05:24.160
8 plus 5 is 13.

00:05:24.160 --> 00:05:26.580
Plus 6 is 19.

00:05:26.580 --> 00:05:28.060
But notice, we're
in the 10's place.

00:05:28.060 --> 00:05:34.620
It's nineteen 10's or we could
say it's nine 10's and 100.

00:05:34.620 --> 00:05:36.650
We carry the 1 up here,
if you can see it, it's

00:05:36.650 --> 00:05:38.860
in the 100's place.

00:05:38.860 --> 00:05:40.510
Now we add up all the 100's.

00:05:40.510 --> 00:05:43.860
100 plus 200 plus 800 plus 100.

00:05:43.860 --> 00:05:45.120
Or, what is this?

00:05:45.120 --> 00:05:46.750
1,200.

00:05:46.750 --> 00:05:49.180
Well you write 2 in
the 100's place.

00:05:49.180 --> 00:05:53.180
1,200 is the same thing
as two 100's plus 1,000.

00:05:53.180 --> 00:05:57.120
And now you only have 1,000
in your 1,000's diagonal.

00:05:57.120 --> 00:05:59.010
And so you write
that 1 right there.

00:05:59.010 --> 00:06:01.140
That's exactly how we did it.

00:06:01.140 --> 00:06:05.770
The same reasoning applied to
the more complex problem.

00:06:05.770 --> 00:06:07.030
We can label our places.

00:06:07.030 --> 00:06:10.700
This was the 1's
place right there.

00:06:10.700 --> 00:06:11.500
And it made sense.

00:06:11.500 --> 00:06:15.080
When we multiplied the 9 times
the 7 those are just literally

00:06:15.080 --> 00:06:17.530
9's and 7's and 63.

00:06:17.530 --> 00:06:19.780
Six 10's and three 1's.

00:06:19.780 --> 00:06:22.620
This right here is
the 10's diagonal.

00:06:22.620 --> 00:06:25.130
Then we got six 10's
and three 1's.

00:06:25.130 --> 00:06:30.510
When we multiplied 9 times 80--
remember, 787, that's the same

00:06:30.510 --> 00:06:35.060
thing as seven 100's plus eight
10's plus seven, just

00:06:35.060 --> 00:06:36.370
regular seven 1's.

00:06:36.370 --> 00:06:39.060
So this 9 times 8
really 9 times 80.

00:06:39.060 --> 00:06:42.870
9 times 80 is 720.

00:06:42.870 --> 00:06:46.360
Seven 100's-- this
is the 100's place.

00:06:46.360 --> 00:06:52.820
Seven 100's and 20-- two
10's just right there.

00:06:52.820 --> 00:06:53.860
And you can keep going.

00:06:53.860 --> 00:06:56.400
This up here, this is
the 1000's place.

00:06:56.400 --> 00:06:58.690
This is the 10,000's.

00:06:58.690 --> 00:07:00.020
I'll write it like that.

00:07:00.020 --> 00:07:04.050
This is the 100,000's place.

00:07:04.050 --> 00:07:06.060
And then this was the
1,000,000's place.

00:07:08.800 --> 00:07:10.850
So we did all of our
multiplication at once,

00:07:10.850 --> 00:07:13.320
accounted for things in their
proper place based on what

00:07:13.320 --> 00:07:15.640
those numbers really are.

00:07:15.640 --> 00:07:19.580
This entry right here, it looks
like we just multiplied 4 times

00:07:19.580 --> 00:07:24.360
8 and got 32, but we actually
were multiplying 400--

00:07:24.360 --> 00:07:27.180
this is a 400-- times 80.

00:07:27.180 --> 00:07:35.610
And 400 times 80 is equal
to 3 2 and three 0's.

00:07:35.610 --> 00:07:37.280
Is equal to 32,000.

00:07:37.280 --> 00:07:41.880
And the way we counted for it--
notice, we put a 2 right there

00:07:41.880 --> 00:07:43.160
and what diagonal is that?

00:07:43.160 --> 00:07:45.830
That is the 1,000's diagonal.

00:07:45.830 --> 00:07:49.520
So we say it's 2,000
and three 10,000's.

00:07:49.520 --> 00:07:51.510
So three 10,000
and two 1,000's.

00:07:51.510 --> 00:07:53.005
That's 32,000.

00:07:53.005 --> 00:07:54.990
So hopefully that gives
you an understanding.

00:07:54.990 --> 00:07:58.510
I mean it's fun to maybe do
some lattice multiplication and

00:07:58.510 --> 00:08:01.000
get practice, but sometimes it
looks like this bizarre

00:08:01.000 --> 00:08:02.000
magical thing.

00:08:02.000 --> 00:08:03.920
But hopefully from this video
you understand that all it is

00:08:03.920 --> 00:08:06.850
is just a different way of
keeping track of where the 1's,

00:08:06.850 --> 00:08:08.260
10's, and 100's place are.

00:08:08.260 --> 00:08:09.980
With the advantage that
it's kind of nice and

00:08:09.980 --> 00:08:12.320
compartmentalized, it doesn't
take up a lot of space.

00:08:12.320 --> 00:08:15.800
And, it allows you to do all
your multiplication at once and

00:08:15.800 --> 00:08:20.760
then, switch your brain into
addition and carrying mode.


Lattice multiplication

WEBVTT
Kind: captions
Language: en

00:00:00.350 --> 00:00:02.340
I'm going to do a couple
of lattice multiplication

00:00:02.340 --> 00:00:03.490
examples in this video.

00:00:03.490 --> 00:00:06.640
And in the next one we'll try
to understand why it worked.

00:00:06.640 --> 00:00:14.235
Let's say we're trying to
multiply 27 times 48.

00:00:14.235 --> 00:00:18.780
What you do is you
write down your 27.

00:00:18.780 --> 00:00:21.650
The 2 and the 7 are going to
get separate columns and you

00:00:21.650 --> 00:00:24.470
write your 48 down the
right-hand side, and then

00:00:24.470 --> 00:00:25.345
you draw a lattice.

00:00:25.345 --> 00:00:28.340
This is why it's called
lattice multiplication.

00:00:28.340 --> 00:00:30.580
So the 2 is going to
get its own column.

00:00:30.580 --> 00:00:33.020
The 7 is going to
get its own column.

00:00:33.020 --> 00:00:36.330
The 4 is going to get its
own row and the 8 is

00:00:36.330 --> 00:00:37.900
going to get its own row.

00:00:37.900 --> 00:00:40.460
Now the fun thing about lattice
multiplication is you get to do

00:00:40.460 --> 00:00:43.220
all of your multiplication at
one time and then you can

00:00:43.220 --> 00:00:44.930
finish up the problem
with all your addition.

00:00:44.930 --> 00:00:46.890
You don't have to keep
switching gears by

00:00:46.890 --> 00:00:47.930
carrying and all of that.

00:00:47.930 --> 00:00:49.590
Although there is carrying,
but it's all while you're

00:00:49.590 --> 00:00:51.260
doing the addition step.

00:00:51.260 --> 00:00:52.510
So we're almost done
with our lattice.

00:00:52.510 --> 00:00:53.800
We actually have to draw
these diagonals here.

00:00:53.800 --> 00:00:55.430
We'll understand in the
next video why these

00:00:55.430 --> 00:00:57.330
diagonals even work.

00:00:57.330 --> 00:00:58.550
Just like that.

00:00:58.550 --> 00:01:00.310
And now we're ready
to multiply.

00:01:00.310 --> 00:01:02.440
7 times 4 is 28.

00:01:02.440 --> 00:01:05.230
7 times 4 is equal to 28.

00:01:05.230 --> 00:01:08.310
So you write down a 2 and
an 8 just like that.

00:01:08.310 --> 00:01:12.580
2 times 4 is equal to 8.

00:01:12.580 --> 00:01:17.380
So you write down a
0, 8 just like that.

00:01:17.380 --> 00:01:19.690
Then you have 7 times 8.

00:01:19.690 --> 00:01:23.785
7 times 8 is equal to 56.

00:01:23.785 --> 00:01:27.240
So we write down a 5 and a 6.

00:01:27.240 --> 00:01:32.490
And then finally, 2
times 8 is equal to 16.

00:01:32.490 --> 00:01:35.800
You write down a 1 and
a 6 just like that.

00:01:35.800 --> 00:01:37.750
And we're done all
of our multiplying.

00:01:37.750 --> 00:01:39.070
Now we're ready to add.

00:01:39.070 --> 00:01:42.740
So what you do is you go
down these diagonals

00:01:42.740 --> 00:01:43.450
that I drew here.

00:01:43.450 --> 00:01:46.930
So this first diagonal, which
is really the 1's diagonal, you

00:01:46.930 --> 00:01:48.110
just have a 6 sitting here.

00:01:48.110 --> 00:01:50.500
So you write a 6
just like that.

00:01:50.500 --> 00:01:52.140
Then we move over to
the next diagonal.

00:01:52.140 --> 00:01:54.600
This diagonal with the
6, 5, and 8 in it.

00:01:54.600 --> 00:01:56.360
That's our 10's diagonal.

00:01:56.360 --> 00:01:59.960
So 8 plus 5 is 13.

00:01:59.960 --> 00:02:03.600
13 plus 6 is 19.

00:02:03.600 --> 00:02:07.310
So you write your 9 right here
in the 10's place and now you

00:02:07.310 --> 00:02:11.700
carry the 1 in 19 up there into
the 100's place because this

00:02:11.700 --> 00:02:13.900
isn't just 19, it's
actually 190.

00:02:13.900 --> 00:02:15.850
It's nineteen 10's.

00:02:15.850 --> 00:02:17.580
Anyway, you carry your 1.

00:02:17.580 --> 00:02:19.510
You have 1 plus 2 is 3.

00:02:19.510 --> 00:02:21.780
3 plus 8 is 11.

00:02:21.780 --> 00:02:25.620
11 plus 1 is 12.

00:02:25.620 --> 00:02:30.130
You write the 2 in your 100's
place and you carry the 1

00:02:30.130 --> 00:02:32.020
into your 1,000's place.

00:02:32.020 --> 00:02:35.760
1 plus 0 is 1, so you just
have a 1 in your 1,000's

00:02:35.760 --> 00:02:37.210
place just like that.

00:02:37.210 --> 00:02:38.440
And you get our answer.

00:02:38.440 --> 00:02:49.730
27 times 48 is equal to 1,296/
Let's do a harder problem.

00:02:49.730 --> 00:02:53.310
One that requires more digits,
just to show that this'll

00:02:53.310 --> 00:02:56.160
work for any problem.

00:02:56.160 --> 00:03:04.160
Let's say we had 5,479 times--
let's do a three-digit number.

00:03:04.160 --> 00:03:09.650
Times 787.

00:03:09.650 --> 00:03:12.610
So just like we did in the last
time, we make four columns.

00:03:12.610 --> 00:03:15.080
One for the 5, the 4,
the 7, and the 9.

00:03:15.080 --> 00:03:23.740
We'lll have 5,479
and then times 787.

00:03:23.740 --> 00:03:26.555
So they each get their own row.

00:03:26.555 --> 00:03:30.780
787.

00:03:30.780 --> 00:03:31.560
Looks like that.

00:03:31.560 --> 00:03:34.060
Then we have to
draw our lattice.

00:03:34.060 --> 00:03:36.790
Draw the lattice.

00:03:36.790 --> 00:03:40.050
Each of these guys get
their own column.

00:03:40.050 --> 00:03:44.830
Draw the columns
just like that.

00:03:44.830 --> 00:03:47.780
And then each one of these
characters got their own row.

00:03:47.780 --> 00:03:54.000
One row for the 7, one
row for the 8, and one

00:03:54.000 --> 00:03:56.280
row for this other 7.

00:03:56.280 --> 00:03:58.520
Then we have to draw
the diagonals.

00:03:58.520 --> 00:03:59.470
Draw it like that.

00:03:59.470 --> 00:04:06.490
One diagonal, two diagonals,
so three diagonals,

00:04:06.490 --> 00:04:07.800
four diagonals.

00:04:07.800 --> 00:04:09.870
I think you get the idea
and than we have just

00:04:09.870 --> 00:04:12.740
one, two more diagonals.

00:04:12.740 --> 00:04:15.110
We're ready to multiply now.

00:04:15.110 --> 00:04:16.790
So it's 9 times 7.

00:04:16.790 --> 00:04:17.970
I won't do it on the side here.

00:04:17.970 --> 00:04:19.240
We know our times tables.

00:04:19.240 --> 00:04:21.860
9 times 7 is 63.

00:04:21.860 --> 00:04:25.640
7 times 7 is 49.

00:04:25.640 --> 00:04:29.560
4 times 7 is 28.

00:04:29.560 --> 00:04:33.470
5 times 7 is 35.

00:04:33.470 --> 00:04:35.600
Let me switch callers
arbitrarily.

00:04:35.600 --> 00:04:39.350
9 times 8 is 72.

00:04:39.350 --> 00:04:43.210
7 times 8 is 56.

00:04:43.210 --> 00:04:46.970
4 times 8 is 32.

00:04:46.970 --> 00:04:49.850
5 times 8 is 40.

00:04:49.850 --> 00:04:51.850
I'll switch colors again.

00:04:51.850 --> 00:04:54.750
9 times 7-- we saw that before.

00:04:54.750 --> 00:04:57.050
It's 63.

00:04:57.050 --> 00:05:00.950
7 times 7 is 49.

00:05:00.950 --> 00:05:04.290
4 times 7 is 28.

00:05:04.290 --> 00:05:07.320
And then 5 times 7 is 35.

00:05:07.320 --> 00:05:08.940
We're done all of
our multiplying.

00:05:08.940 --> 00:05:12.210
Now we can switch our
brains into addition mode.

00:05:12.210 --> 00:05:16.860
Let me find a nice suitable
color for addition.

00:05:16.860 --> 00:05:19.270
Maybe a pink will
do for addition.

00:05:19.270 --> 00:05:20.520
So we start at our 1's place.

00:05:20.520 --> 00:05:23.005
Just have a 3 there, so you
write the 3 in your 1's place.

00:05:23.005 --> 00:05:24.730
You go to the 10's place.

00:05:24.730 --> 00:05:26.830
2 plus 6 is 8.

00:05:26.830 --> 00:05:29.620
8 plus 9 is 17.

00:05:29.620 --> 00:05:31.860
Write the 7 in the 10's
place, carry the 1

00:05:31.860 --> 00:05:34.000
into the 100's place.

00:05:34.000 --> 00:05:35.420
I wrote a 1 really small here.

00:05:35.420 --> 00:05:38.240
1 plus 3 is 4.

00:05:38.240 --> 00:05:40.930
4 plus 7 is 11.

00:05:40.930 --> 00:05:44.060
11 plus 6 is 17.

00:05:44.060 --> 00:05:46.590
17 plus 4 is 21.

00:05:46.590 --> 00:05:50.480
21 plus 8 is 29.

00:05:50.480 --> 00:05:54.780
Write the 9 in the 100's
place and carry the 2.

00:05:54.780 --> 00:05:56.690
2 plus 6 is 8.

00:05:56.690 --> 00:05:58.396
8 plus 9 is 17.

00:05:58.396 --> 00:06:02.290
17 plus 5 is 22.

00:06:02.290 --> 00:06:05.700
22 plus 2 is 24.

00:06:05.700 --> 00:06:08.060
24 plus 2 is 26.

00:06:08.060 --> 00:06:10.470
26 plus 5 is 31.

00:06:13.080 --> 00:06:14.920
Carry the 3.

00:06:14.920 --> 00:06:16.460
3 plus 4 is 7.

00:06:16.460 --> 00:06:19.160
7 plus 8 is 15.

00:06:19.160 --> 00:06:21.930
15 plus 3 is 18.

00:06:21.930 --> 00:06:23.730
18 plus 0 is 18.

00:06:23.730 --> 00:06:25.950
18 plus 3 is 21.

00:06:25.950 --> 00:06:28.110
Write the 1, carry the 2.

00:06:28.110 --> 00:06:29.520
2 plus 2 is 4.

00:06:29.520 --> 00:06:31.110
4 plus 5 is 9.

00:06:31.110 --> 00:06:33.270
9 plus 4 is 13.

00:06:33.270 --> 00:06:35.610
Write the 3, carry the 1.

00:06:35.610 --> 00:06:38.450
1 plus 3 is 4.

00:06:38.450 --> 00:06:39.430
And we're done.

00:06:39.430 --> 00:06:40.570
That easy.

00:06:40.570 --> 00:06:42.370
Well, there's two
advantages here.

00:06:42.370 --> 00:06:45.350
One is we got to do all of
our multiplication at once.

00:06:45.350 --> 00:06:47.090
And then we got to do all
of our addition at once.

00:06:47.090 --> 00:06:49.370
The other advantage is it's
kind of neat and clean.

00:06:49.370 --> 00:06:52.160
When you just do it the
traditional way with carrying

00:06:52.160 --> 00:06:54.610
and number places, it
takes up a lot of space.

00:06:54.610 --> 00:06:56.850
But notice, we did our whole
problem in a nice, neat

00:06:56.850 --> 00:06:59.130
and clean area like that
and we got our answer.

00:06:59.130 --> 00:07:09.900
Our answer is 4,311,973.

00:07:09.900 --> 00:07:10.870
There you go.

00:07:10.870 --> 00:07:12.630
Now in the next video we're
going to try to understand

00:07:12.630 --> 00:07:14.550
why this worked.


Oxidative Phosphorylation and Chemiosmosis

WEBVTT
Kind: captions
Language: en

00:00:00.550 --> 00:00:02.910
I made a slight error
in the electron

00:00:02.910 --> 00:00:04.150
transport chain video.

00:00:04.150 --> 00:00:06.040
And I just wanted to correct
it in this one.

00:00:06.040 --> 00:00:08.540
And it's also an opportunity for
me to include a little bit

00:00:08.540 --> 00:00:11.560
of terminology that I forgot
to include in that video.

00:00:11.560 --> 00:00:14.310
So when I described the electron
transport chain, you

00:00:14.310 --> 00:00:16.810
remember, it's just you have
some high-energy electrons in

00:00:16.810 --> 00:00:20.520
NADH and they get transferred
from one molecule to another.

00:00:20.520 --> 00:00:22.810
And as they get transferred
they go into lower energy

00:00:22.810 --> 00:00:24.870
states and they release
energy.

00:00:24.870 --> 00:00:28.540
And then the final electron
acceptor was oxygen.

00:00:28.540 --> 00:00:30.200
Oxygen got reduced right here.

00:00:30.200 --> 00:00:33.190
But if you look at both sides of
this equation, the mistake

00:00:33.190 --> 00:00:34.510
was, I need two hydrogens.

00:00:34.510 --> 00:00:36.400
If I have two hydrogens on the
right-hand side of the water,

00:00:36.400 --> 00:00:38.710
I need two hydrogens on
the left-hand side.

00:00:38.710 --> 00:00:42.330
So there should be
a 2 right there.

00:00:42.330 --> 00:00:46.280
So that was what I would
consider to be a minor mistake

00:00:46.280 --> 00:00:47.200
in the last video.

00:00:47.200 --> 00:00:49.510
But this also gives me a chance
to introduce you to

00:00:49.510 --> 00:00:51.110
some more terminology.

00:00:51.110 --> 00:00:54.850
So this whole process, we know
that this is called oxidation.

00:00:54.850 --> 00:00:57.690
When NADH loses a hydrogen.

00:00:57.690 --> 00:01:00.820
Remember oxidation is losing,
formally electrons.

00:01:00.820 --> 00:01:02.770
But when it loses the hydrogen,
it loses the

00:01:02.770 --> 00:01:05.640
opportunity to hog that
hydrogen's electrons.

00:01:05.640 --> 00:01:08.210
So this whole process of the
electron transport chain is

00:01:08.210 --> 00:01:11.450
one molecule after another
getting oxidized until you

00:01:11.450 --> 00:01:14.410
have a final electron
acceptor in water.

00:01:14.410 --> 00:01:17.280
So this is-- obviously you could
call this oxidation.

00:01:17.280 --> 00:01:18.950
You know, just very generally.

00:01:18.950 --> 00:01:22.410
And then the second part of the
electron transport chain--

00:01:22.410 --> 00:01:24.810
or maybe we shouldn't even call
this part of the electron

00:01:24.810 --> 00:01:26.720
transport chain-- the
process where the

00:01:26.720 --> 00:01:28.620
ATP is actually formed.

00:01:28.620 --> 00:01:32.365
The adding of a phosphate group
to another molecule is

00:01:32.365 --> 00:01:33.615
called phosphorylation.

00:01:40.800 --> 00:01:45.000
So the whole process of creating
ATP through the

00:01:45.000 --> 00:01:46.590
electron transport chain.

00:01:46.590 --> 00:01:48.390
Remember the electron transport
chain releases

00:01:48.390 --> 00:01:51.010
energy that creates this
hydrogen gradient.

00:01:51.010 --> 00:01:54.540
It pumps the hydrogens to
the outer compartment.

00:01:54.540 --> 00:01:58.640
And then that gradient, those
hydrogens that want to get

00:01:58.640 --> 00:02:02.130
back into the matrix,
essentially going back through

00:02:02.130 --> 00:02:03.740
this ATP synthase.

00:02:03.740 --> 00:02:06.880
This process of generating ATP
this way is called oxidative

00:02:06.880 --> 00:02:08.130
phosphorylation.

00:02:17.240 --> 00:02:18.120
It's a good word to know.

00:02:18.120 --> 00:02:21.440
You might see it on some
standardized tests or on your

00:02:21.440 --> 00:02:23.560
exams. And it's called
this because you have

00:02:23.560 --> 00:02:25.770
an oxidative part.

00:02:25.770 --> 00:02:30.200
Each of these molecules gets
oxidized in the electron

00:02:30.200 --> 00:02:33.220
transport chain as they lose
their hydrogens or as they

00:02:33.220 --> 00:02:34.500
lose their electrons.

00:02:34.500 --> 00:02:36.890
That creates a hydrogen
gradient.

00:02:36.890 --> 00:02:40.280
And then that, through
chemiosmosis, allows for

00:02:40.280 --> 00:02:41.430
phosphorylation.

00:02:41.430 --> 00:02:43.670
So that's another good
word to know.

00:02:43.670 --> 00:02:47.060
The transfer of these hydrogens,
these kind of going

00:02:47.060 --> 00:02:48.740
through this membrane
selectively.

00:02:48.740 --> 00:02:51.900
This membrane, this ATP
synthase, wouldn't allow just

00:02:51.900 --> 00:02:53.500
any molecule to go through it.

00:02:53.500 --> 00:02:56.360
It's allowing these hydrogen
protons to go through it.

00:02:56.360 --> 00:02:58.750
This process right here of this
hydrogen going through is

00:02:58.750 --> 00:03:00.000
called chemiosmosis.

00:03:04.030 --> 00:03:05.900
Another good word to know.

00:03:05.900 --> 00:03:07.880
So the entire process
is called oxidative

00:03:07.880 --> 00:03:09.060
phosphorylation.

00:03:09.060 --> 00:03:10.530
They don't happen at
the same time.

00:03:10.530 --> 00:03:14.470
Oxidative generates the energy
because the energy to push the

00:03:14.470 --> 00:03:15.140
hydrogens out.

00:03:15.140 --> 00:03:17.430
And then the phosphorylation
happens as the hydrogens

00:03:17.430 --> 00:03:21.050
experience chemiosmosis and go
back in and turn this little

00:03:21.050 --> 00:03:27.160
axle and then push the ADP and
the phosphate groups together.

00:03:27.160 --> 00:03:30.080
And then you can contrast
that with substrate.

00:03:30.080 --> 00:03:34.000
Substrate phosphorylations.

00:03:34.000 --> 00:03:36.590
Since I'm in the mood to
introduce you to terminology.

00:03:36.590 --> 00:03:37.950
Substrate phosphorylation.

00:03:37.950 --> 00:03:41.120
This is actually what happens
when the ATP is produced

00:03:41.120 --> 00:03:44.270
directly in glycolysis
in the Krebs cycle.

00:03:49.420 --> 00:03:54.360
And this is where you have an
enzyme directly helping to

00:03:54.360 --> 00:03:55.990
peruse the ATP without
any type of

00:03:55.990 --> 00:03:58.620
chemiosmosis or proton gradient.

00:03:58.620 --> 00:04:02.480
So if you imagine an
enzyme, some blurb,

00:04:02.480 --> 00:04:04.420
some big protein blurb.

00:04:04.420 --> 00:04:09.110
And let's say it has the
ADP there with its

00:04:09.110 --> 00:04:10.510
two phosphate groups.

00:04:10.510 --> 00:04:12.890
And then maybe it has another
phosphate group that attaches

00:04:12.890 --> 00:04:15.230
at some other part of the
enzyme, this enzyme

00:04:15.230 --> 00:04:19.180
facilitates without any kind of
chemiosmosis or oxidation.

00:04:19.180 --> 00:04:23.960
It facilitates, probably in
conjunction with other energy

00:04:23.960 --> 00:04:27.870
releasing reactions that may be
occurring on other parts of

00:04:27.870 --> 00:04:28.500
the enzyme.

00:04:28.500 --> 00:04:31.830
So maybe you can imagine a
little spark right there and

00:04:31.830 --> 00:04:34.815
then that twists this
entire enzyme.

00:04:34.815 --> 00:04:36.560
This isn't exactly how
it might work,

00:04:36.560 --> 00:04:37.640
but it's a good idea.

00:04:37.640 --> 00:04:40.090
And then these two things maybe
get pushed together.

00:04:40.090 --> 00:04:41.780
When it's just an enzyme
without any of this

00:04:41.780 --> 00:04:44.830
chemiosmosis that's driven by
oxidation, like we learned in

00:04:44.830 --> 00:04:47.870
the electron transport chain,
we call this substrate

00:04:47.870 --> 00:04:48.780
phosphorylation.

00:04:48.780 --> 00:04:52.350
And the substrates are just the
things that attach to the

00:04:52.350 --> 00:04:54.750
enzyme and have something
performed on them.

00:04:54.750 --> 00:04:56.260
So anyway, hopefully you
found this little

00:04:56.260 --> 00:04:58.710
video mildly useful.


Electron Transport Chain

WEBVTT
Kind: captions
Language: en

00:00:00.440 --> 00:00:02.660
After being done with glycolysis
and the Krebs

00:00:02.660 --> 00:00:10.315
Cycle, we're left with 10
NADHs and 2 FADH2s.

00:00:12.970 --> 00:00:15.240
And I told you that these are
going to be used in the

00:00:15.240 --> 00:00:16.650
electron transport chain.

00:00:16.650 --> 00:00:19.140
And they're all sitting in the
matrix of our mitochondria.

00:00:19.140 --> 00:00:20.996
And I said they're going to be
used in the electron transport

00:00:20.996 --> 00:00:26.190
chain in order to actually
generate ATP.

00:00:26.190 --> 00:00:28.750
So that's what I'm going to
focus on in this video.

00:00:28.750 --> 00:00:30.000
The electron transport chain.

00:00:37.900 --> 00:00:41.290
And just so you know, a lot
of this stuff is known.

00:00:41.290 --> 00:00:42.990
But some of the details
are actually

00:00:42.990 --> 00:00:44.360
current areas of research.

00:00:44.360 --> 00:00:45.790
People have models and
they're trying to

00:00:45.790 --> 00:00:46.960
substantiate the models.

00:00:46.960 --> 00:00:50.090
But things are happening at such
a small scale here that

00:00:50.090 --> 00:00:52.620
people can just look at the
evidence, some of which is

00:00:52.620 --> 00:00:54.940
indirect, and say, this is
probably what's happening.

00:00:54.940 --> 00:00:57.650
Most of this is very well
established, but some of the

00:00:57.650 --> 00:01:02.110
exact mechanisms-- for example,
how exactly some of

00:01:02.110 --> 00:01:05.630
the proteins work-- aren't
completely understood.

00:01:05.630 --> 00:01:08.080
So I think it's very important
for you to understand that

00:01:08.080 --> 00:01:11.280
this is at the cutting edge,
that you're already there.

00:01:11.280 --> 00:01:15.060
So the basic idea here is that
the NADHs-- and that's where

00:01:15.060 --> 00:01:15.670
I'll focus.

00:01:15.670 --> 00:01:17.780
FADH2 is kind of
the same idea.

00:01:17.780 --> 00:01:19.960
Although its electrons
are just at slightly

00:01:19.960 --> 00:01:21.210
lower energy state.

00:01:21.210 --> 00:01:23.780
So they won't produce
quite as many ATPs.

00:01:23.780 --> 00:01:32.570
Each NADH is going to be-- as
you'll see-- indirectly

00:01:32.570 --> 00:01:36.500
responsible for the production
of three ATPs.

00:01:36.500 --> 00:01:42.100
And each FADH2, in a very
efficient cell, in both of

00:01:42.100 --> 00:01:44.980
these cases, will be indirectly
responsible for the

00:01:44.980 --> 00:01:48.520
production of two ATPs.

00:01:48.520 --> 00:01:52.020
And the reason why this guy
produces fewer ATPs is because

00:01:52.020 --> 00:01:55.420
the electrons that he has
going into the electron

00:01:55.420 --> 00:01:58.400
transport chain are at a
slightly lower energy level

00:01:58.400 --> 00:02:00.580
than the ones from NADH.

00:02:00.580 --> 00:02:02.110
So in general, I just
said indirectly.

00:02:02.110 --> 00:02:04.620
How does this whole
business work?

00:02:04.620 --> 00:02:11.680
Well in general, NADH, when it
gets oxidized-- remember,

00:02:11.680 --> 00:02:14.750
oxidation is the losing of
electrons or the losing of

00:02:14.750 --> 00:02:17.010
hydrogens that happen
to have electrons.

00:02:17.010 --> 00:02:19.620
We can write its half
reaction like this.

00:02:19.620 --> 00:02:21.810
Its oxidation reaction
like this.

00:02:21.810 --> 00:02:25.790
You'll have some NAD plus, which
you can then go and use

00:02:25.790 --> 00:02:29.130
back in the Krebs Cycle
and in glycolysis.

00:02:29.130 --> 00:02:33.630
You have some NAD plus, you'll
have a proton, a positive

00:02:33.630 --> 00:02:35.940
hydrogen ion is just a proton.

00:02:35.940 --> 00:02:38.450
And then you'll have
two electrons.

00:02:38.450 --> 00:02:39.700
This is the oxidation of NADH.

00:02:44.480 --> 00:02:46.310
It's losing these
two electrons.

00:02:46.310 --> 00:02:48.520
Oxidation is losing electrons.

00:02:48.520 --> 00:02:49.620
OIL RIG.

00:02:49.620 --> 00:02:51.310
Oxidation is losing electrons.

00:02:51.310 --> 00:02:54.110
Or you can imagine it's losing
hydrogens, from which it can

00:02:54.110 --> 00:02:55.600
hog electrons.

00:02:55.600 --> 00:02:57.250
Either one of those
is the case.

00:02:57.250 --> 00:02:59.650
Now this is really the
first step of the

00:02:59.650 --> 00:03:00.990
electron transport chain.

00:03:00.990 --> 00:03:05.030
These electrons are transported
out of the NADH.

00:03:05.030 --> 00:03:08.120
Now, the last step of the
electron transport chain is

00:03:08.120 --> 00:03:12.130
you have two electrons-- and you
could view it as the same

00:03:12.130 --> 00:03:16.320
two electrons if you like--
two electrons plus two

00:03:16.320 --> 00:03:17.610
hydrogen protons.

00:03:17.610 --> 00:03:20.110
And obviously if you just add
these two together, you're

00:03:20.110 --> 00:03:22.610
just going to have two hydrogen
atoms, which is just

00:03:22.610 --> 00:03:24.280
a proton and an electron.

00:03:24.280 --> 00:03:28.210
Plus one oxygen atom, so
I could say one half of

00:03:28.210 --> 00:03:29.450
molecular oxygen.

00:03:29.450 --> 00:03:32.190
That's the same thing as
saying one oxygen atom.

00:03:32.190 --> 00:03:35.030
And you're going to produce--
if I have one oxygen and two

00:03:35.030 --> 00:03:37.105
complete hydrogens, I'm
left with water.

00:03:39.690 --> 00:03:42.850
And you could view this, we're
adding electron or we're

00:03:42.850 --> 00:03:44.480
gaining electrons to oxygen.

00:03:44.480 --> 00:03:45.890
OIL RIG.

00:03:45.890 --> 00:03:48.740
Reduction is gaining
electrons.

00:03:48.740 --> 00:03:54.140
So this is the reduction
of oxygen to water.

00:03:54.140 --> 00:03:59.060
This is the oxidation
of NADH to NAD plus.

00:03:59.060 --> 00:04:02.480
Now, these electrons that are
popping out of-- these

00:04:02.480 --> 00:04:06.720
electrons right here-- that are
popping out of this NADH.

00:04:06.720 --> 00:04:08.270
And when they're in
NADH they're at a

00:04:08.270 --> 00:04:11.150
very high energy state.

00:04:11.150 --> 00:04:13.310
And what happens over the
course of the electron

00:04:13.310 --> 00:04:17.260
transport chain is that these
electrons get transported to a

00:04:17.260 --> 00:04:18.920
series of, I guess
you could call

00:04:18.920 --> 00:04:20.589
them transition molecules.

00:04:20.589 --> 00:04:22.790
But these transition molecules,
as the electrons go

00:04:22.790 --> 00:04:24.770
from one to the other,
they go into slightly

00:04:24.770 --> 00:04:26.010
lower energy states.

00:04:26.010 --> 00:04:28.900
And I won't even go into the
details of these molecules.

00:04:28.900 --> 00:04:33.170
One is coenzyme Q,
and cytochrome C.

00:04:36.390 --> 00:04:38.820
And then they eventually end
up right here and they are

00:04:38.820 --> 00:04:43.980
used to reduce your
oxygen into water.

00:04:43.980 --> 00:04:46.830
Now every time an electron
goes from a higher energy

00:04:46.830 --> 00:04:48.960
state to a lower energy state--
and that's what it's

00:04:48.960 --> 00:04:52.220
doing over the course of this
electron transport chain--

00:04:52.220 --> 00:04:53.515
it's releasing energy.

00:05:00.770 --> 00:05:02.990
So energy is released when you
go from a higher state to a

00:05:02.990 --> 00:05:03.380
lower state.

00:05:03.380 --> 00:05:06.060
When these electrons were in
NADH, they were at a higher

00:05:06.060 --> 00:05:09.650
state than they are when they
bond to coenzyme Q.

00:05:09.650 --> 00:05:11.140
So they release energy.

00:05:11.140 --> 00:05:13.270
Then they go to cytochrome
C and release energy.

00:05:13.270 --> 00:05:17.300
Now that energy is used to
pump protons across the

00:05:17.300 --> 00:05:20.410
cristae across the inner
membrane of the mitochondria.

00:05:20.410 --> 00:05:22.580
And I know this is all very
complicated sounding.

00:05:22.580 --> 00:05:25.800
And this is the cutting edge.

00:05:25.800 --> 00:05:27.760
So it maybe should sound
a little complicated.

00:05:27.760 --> 00:05:30.770
Let me draw a mitochondria.

00:05:30.770 --> 00:05:33.630
So let me draw a small
mitochondria just so you know

00:05:33.630 --> 00:05:34.490
where we're operating.

00:05:34.490 --> 00:05:36.000
That's its outer membrane.

00:05:36.000 --> 00:05:38.980
And then its inner membrane,
or its cristae,

00:05:38.980 --> 00:05:40.340
would look like that.

00:05:45.010 --> 00:05:47.680
And let me zoom in
on the membrane.

00:05:47.680 --> 00:05:52.210
So let's say if I were to
zoom in right there.

00:05:52.210 --> 00:05:54.690
So if I were to zoom that out,
that box would look like this.

00:05:54.690 --> 00:05:57.490
You have your crista here.

00:05:57.490 --> 00:06:00.010
And I'm going to
draw it thick.

00:06:00.010 --> 00:06:01.020
So I'm zooming in.

00:06:01.020 --> 00:06:02.330
This green line right
here, I'm going to

00:06:02.330 --> 00:06:03.300
draw it really thick.

00:06:03.300 --> 00:06:06.510
I'm going to color it in with
the green, just like that.

00:06:06.510 --> 00:06:09.050
And then you have your
outer membrane.

00:06:09.050 --> 00:06:12.090
This outer membrane, I
can do it up here.

00:06:12.090 --> 00:06:13.070
And I'll just color it in.

00:06:13.070 --> 00:06:16.400
You don't even have to see the
outside of the outer membrane.

00:06:16.400 --> 00:06:18.950
Right here, this space right
here, this is the outer

00:06:18.950 --> 00:06:20.970
compartment.

00:06:20.970 --> 00:06:23.720
And then we learned in the last
video, this space right

00:06:23.720 --> 00:06:24.970
here is the matrix.

00:06:27.150 --> 00:06:29.690
This is where our Krebs
cycle occurred.

00:06:29.690 --> 00:06:31.850
And where a lot of our NADH,
or really all of

00:06:31.850 --> 00:06:33.420
our NADH, is sitting.

00:06:33.420 --> 00:06:37.900
So what happens is, every time
NADH gets oxidized to NAD

00:06:37.900 --> 00:06:41.120
plus, and the electrons keep
transferring from one molecule

00:06:41.120 --> 00:06:44.600
to another, it's occurring in
these big protein complexes.

00:06:44.600 --> 00:06:46.600
And I'm not going to go into
the details on this.

00:06:46.600 --> 00:06:51.860
So each of these protein
complexes span-- so let's say

00:06:51.860 --> 00:06:55.810
that's a protein complex where
this first oxidation reaction

00:06:55.810 --> 00:06:58.350
is occurring and releasing
energy.

00:06:58.350 --> 00:07:00.970
And then let's say there's
another protein complex here,

00:07:00.970 --> 00:07:03.610
where the second oxidation
reaction is occurring and

00:07:03.610 --> 00:07:04.860
releasing energy.

00:07:04.860 --> 00:07:09.320
And these proteins are able to
use that energy to essentially

00:07:09.320 --> 00:07:12.910
pump-- this might all seem
very complicated-- to

00:07:12.910 --> 00:07:16.810
essentially pump hydrogens
into the outer membrane.

00:07:16.810 --> 00:07:19.220
It actually pumps hydrogen
protons.

00:07:19.220 --> 00:07:19.940
And let me be very clear.

00:07:19.940 --> 00:07:24.610
Hydrogen protons into
the outer membrane.

00:07:24.610 --> 00:07:27.150
And every one of these reactions
pump out a certain

00:07:27.150 --> 00:07:29.250
number of hydrogen protons.

00:07:29.250 --> 00:07:32.980
So by the end of the electron
transport chain, or if we just

00:07:32.980 --> 00:07:35.750
followed one set of electrons,
by the time that they've gone

00:07:35.750 --> 00:07:40.560
from their high energy state in
NADH to their lower energy

00:07:40.560 --> 00:07:44.450
state in water, by the time
they've done that, they've

00:07:44.450 --> 00:07:48.540
supplied the energy to these
protein complexes that span

00:07:48.540 --> 00:07:53.330
our cristae to pump hydrogen
from the matrix

00:07:53.330 --> 00:07:55.720
into the outer membrane.

00:07:55.720 --> 00:08:00.650
So really the only byproduct of
the oxidation of NADH into,

00:08:00.650 --> 00:08:04.670
eventually, water, or the
oxidation of NADH and the

00:08:04.670 --> 00:08:08.630
reduction of oxygen into
water, isn't ATPs yet.

00:08:08.630 --> 00:08:11.950
It's just this gradient where we
have a lot higher hydrogen

00:08:11.950 --> 00:08:16.660
proton concentration in the
outer compartment than we do

00:08:16.660 --> 00:08:17.630
in the matrix.

00:08:17.630 --> 00:08:19.480
Or you could say that the outer
compartment becomes a

00:08:19.480 --> 00:08:20.290
lot more acidic.

00:08:20.290 --> 00:08:23.650
Remember acidity is just
hydrogen proton concentration,

00:08:23.650 --> 00:08:26.020
the concentration of
hydrogen protons.

00:08:26.020 --> 00:08:29.640
So the byproduct of all of this
energy is used to really

00:08:29.640 --> 00:08:32.780
just pump these protons into
the outer membrane.

00:08:32.780 --> 00:08:33.570
So you have two things.

00:08:33.570 --> 00:08:37.039
The outer membrane becomes
more acidic

00:08:37.039 --> 00:08:38.539
than the matrix inside.

00:08:38.539 --> 00:08:40.110
Maybe we could call
that basic.

00:08:40.110 --> 00:08:42.640
And obviously these are all
positively charged particles.

00:08:42.640 --> 00:08:48.790
So there's actually an electric
gradient, an electric

00:08:48.790 --> 00:08:50.440
potential between the
outer membrane

00:08:50.440 --> 00:08:51.250
and the inner membrane.

00:08:51.250 --> 00:08:53.190
This becomes slightly negative,
that becomes

00:08:53.190 --> 00:08:54.300
slightly positive.

00:08:54.300 --> 00:08:56.990
These guys wouldn't naturally
do this on their own.

00:08:56.990 --> 00:09:00.170
If this is already acidic and
it's already positive, left to

00:09:00.170 --> 00:09:02.715
its own devices, these more
protons wouldn't be entering.

00:09:02.715 --> 00:09:06.950
And the energy to do that is
supplied by electrons going

00:09:06.950 --> 00:09:11.270
from high energy state in NADH
to going to a lower energy

00:09:11.270 --> 00:09:14.730
state, eventually, on the
oxygen in the water.

00:09:14.730 --> 00:09:15.650
That's what's happening.

00:09:15.650 --> 00:09:18.660
But essentially all that's
happening is protons being

00:09:18.660 --> 00:09:22.160
pumped from the matrix into
the outer compartment.

00:09:22.160 --> 00:09:24.420
Now once that gradient
forms, these guys

00:09:24.420 --> 00:09:26.250
want to get back in.

00:09:26.250 --> 00:09:29.760
These guys want to get
back into the matrix.

00:09:29.760 --> 00:09:32.940
And that is where the
ATPs are formed.

00:09:32.940 --> 00:09:36.300
So there's a protein that
also spans this.

00:09:36.300 --> 00:09:37.730
Let me draw.

00:09:37.730 --> 00:09:40.020
Remember this is all this inner
membrane right here.

00:09:40.020 --> 00:09:42.980
Let me just draw it a little
bit bigger right here.

00:09:42.980 --> 00:09:47.090
So that's our inner membrane,
our cristae right there.

00:09:47.090 --> 00:09:51.950
There's a special protein
called-- and I'll show you

00:09:51.950 --> 00:09:54.960
actually a better diagram of
what looks like in a second--

00:09:54.960 --> 00:09:56.295
called ATP synthase.

00:10:04.740 --> 00:10:07.000
And what happens is, remember
because of the electron

00:10:07.000 --> 00:10:09.462
transport chain, we have all
of these hydrogen ions up

00:10:09.462 --> 00:10:12.540
here, all of these
protons really.

00:10:12.540 --> 00:10:13.370
All they are is a proton.

00:10:13.370 --> 00:10:18.210
That really want to get back
into the matrix down here.

00:10:21.090 --> 00:10:21.990
But they can't.

00:10:21.990 --> 00:10:24.520
This crista is impermeable to
them so they have to find a

00:10:24.520 --> 00:10:25.960
special way to get through.

00:10:25.960 --> 00:10:28.420
They were able to go the reverse
direction through the

00:10:28.420 --> 00:10:30.600
special protein complexes.

00:10:30.600 --> 00:10:32.390
Now they're going to
go back into the

00:10:32.390 --> 00:10:35.250
matrix through ATP synthase.

00:10:35.250 --> 00:10:36.830
So they're going
to go back, but

00:10:36.830 --> 00:10:38.080
something interesting happens.

00:10:38.080 --> 00:10:40.970
And this is really an area of
current research where people

00:10:40.970 --> 00:10:42.510
think they know how it works
but they're not sure.

00:10:42.510 --> 00:10:46.290
Because you can't just take
these proteins apart and watch

00:10:46.290 --> 00:10:48.946
them operate like you can a
regular mechanical engine.

00:10:48.946 --> 00:10:51.360
These are ultra-small and they
have to be in a living system.

00:10:51.360 --> 00:10:52.550
And they have to have the
right conditions.

00:10:52.550 --> 00:10:55.590
And you can't even-- it's hard
to see hydrogen protons.

00:10:55.590 --> 00:10:58.465
These are ultra-small things
that are, pretty much, you

00:10:58.465 --> 00:10:59.580
can't see them.

00:10:59.580 --> 00:11:04.490
But what happens, the current
model is, as these enter, as

00:11:04.490 --> 00:11:08.040
these go through
my ATP synthase

00:11:08.040 --> 00:11:09.800
there's actually an axle.

00:11:09.800 --> 00:11:11.370
So you can kind of view
this as a housing.

00:11:11.370 --> 00:11:12.530
And then there's an axle.

00:11:12.530 --> 00:11:14.910
And this is all just
a big protein.

00:11:14.910 --> 00:11:17.280
And there's an axle and then
there's another part of the

00:11:17.280 --> 00:11:20.050
synthase down here.

00:11:20.050 --> 00:11:22.190
So you can imagine, this is
kind of mind-blowing.

00:11:22.190 --> 00:11:26.460
That something this fancy is
occurring on the membranes of

00:11:26.460 --> 00:11:29.210
pretty much all living
systems' cells.

00:11:29.210 --> 00:11:30.230
It's not just eukaryotes.

00:11:30.230 --> 00:11:31.420
Even prokaryotes do this.

00:11:31.420 --> 00:11:32.900
They don't do it in their
mitochondria; they do it in

00:11:32.900 --> 00:11:34.300
their cellular membrane.

00:11:34.300 --> 00:11:36.530
But it's a pretty neat thing.

00:11:36.530 --> 00:11:39.030
And what happens is, as these
go through, you can kind of

00:11:39.030 --> 00:11:41.860
imagine as water flowing
through a turbine.

00:11:41.860 --> 00:11:46.540
It mechanically causes
this structure in

00:11:46.540 --> 00:11:48.080
the middle to spin.

00:11:48.080 --> 00:11:49.280
To actually spin.

00:11:49.280 --> 00:11:50.700
This is the current thinking.

00:11:50.700 --> 00:11:51.970
And this thing is all uneven.

00:11:51.970 --> 00:11:54.000
It's not, like, this
nice tube.

00:11:54.000 --> 00:11:55.870
It'll look all crazy
like that.

00:11:55.870 --> 00:11:59.830
And what happens is that an ADP
molecule-- let's say that

00:11:59.830 --> 00:12:03.730
this is the A part of the ADP.

00:12:03.730 --> 00:12:05.270
And then you have two
phosphate groups.

00:12:07.860 --> 00:12:09.770
It'll attach to one part
of this protein.

00:12:09.770 --> 00:12:11.910
And maybe a phosphate will
just randomly attach to

00:12:11.910 --> 00:12:13.570
another part of this protein.

00:12:13.570 --> 00:12:14.280
Just like that.

00:12:14.280 --> 00:12:16.580
So right now it's just
ADP and a phosphate.

00:12:16.580 --> 00:12:24.290
But as this inner axle turns--
because it's not a symmetrical

00:12:24.290 --> 00:12:26.440
tube, it has different things
sticking out that have

00:12:26.440 --> 00:12:30.680
different amounts of atomic
charge and it's going to play

00:12:30.680 --> 00:12:33.340
with this outer housing
right here.

00:12:33.340 --> 00:12:36.880
And so as this turns, the outer
housing, because of just

00:12:36.880 --> 00:12:39.450
the proteins bumping against
each other and electrical

00:12:39.450 --> 00:12:43.590
charge and whatever else, it's
going to squeeze the ADP and

00:12:43.590 --> 00:12:48.460
the phosphate together to form,
actually form, ATP.

00:12:48.460 --> 00:12:50.120
And actually the current
thinking is that it does it on

00:12:50.120 --> 00:12:52.240
three different sites
simultaneously.

00:12:52.240 --> 00:12:57.900
So as this spins around, ADP and
phosphate groups kind of

00:12:57.900 --> 00:13:01.300
show up on the inside
of this housing.

00:13:01.300 --> 00:13:03.080
You could imagine
it like that.

00:13:03.080 --> 00:13:04.430
And I don't even know if
it's on the inside.

00:13:04.430 --> 00:13:05.830
But they show up
on the housing.

00:13:05.830 --> 00:13:08.750
And as this thing spins around,
it stretches and pulls

00:13:08.750 --> 00:13:11.810
on this outer part and pushes
these two things together.

00:13:11.810 --> 00:13:15.070
So it's using the energy from
this proton gradient

00:13:15.070 --> 00:13:16.580
to drive this axle.

00:13:16.580 --> 00:13:19.230
And because it's all strange, it
does all these distortions

00:13:19.230 --> 00:13:21.280
on this outer part and
actually pushes

00:13:21.280 --> 00:13:23.180
the two ATPs together.

00:13:23.180 --> 00:13:28.540
So when you start off with your
10 NADHs, it'll provided

00:13:28.540 --> 00:13:32.250
just enough energy and just
enough protons to put into the

00:13:32.250 --> 00:13:35.190
outer membrane that when they
go back through our ATP

00:13:35.190 --> 00:13:38.350
synthase-- you could almost
view it as an ATP synthase

00:13:38.350 --> 00:13:41.800
motor-- just based on people's
observations they see that

00:13:41.800 --> 00:13:44.730
this will produce, on
a per-NADH level,

00:13:44.730 --> 00:13:46.390
roughly three ATPs.

00:13:46.390 --> 00:13:49.690
On a per-FADH2 level,
roughly two ATPs.

00:13:49.690 --> 00:13:51.355
And I've said multiple times
in the videos, this

00:13:51.355 --> 00:13:52.480
is kind of an ideal.

00:13:52.480 --> 00:13:54.590
That a lot of times, maybe
you'll have some protons leak,

00:13:54.590 --> 00:13:56.740
so their energy can't be
captured properly.

00:13:56.740 --> 00:13:59.600
Or maybe some of these electrons
might somehow jump

00:13:59.600 --> 00:14:02.360
the gun or jump some steps, so
some of the energy gets lost.

00:14:02.360 --> 00:14:06.030
So you don't always have a
completely efficient system.

00:14:06.030 --> 00:14:08.580
And just so you believe that
this is actually occurring on

00:14:08.580 --> 00:14:10.740
our membrane, there's
actual visual

00:14:10.740 --> 00:14:12.050
depictions of these proteins.

00:14:12.050 --> 00:14:16.680
This is the actual protein
structure of ATP synthase

00:14:16.680 --> 00:14:17.360
right here.

00:14:17.360 --> 00:14:18.610
That is actually ATP synthase.

00:14:21.840 --> 00:14:24.450
And as you can see, there's
this piece right here that

00:14:24.450 --> 00:14:30.490
holds this part and that part.

00:14:30.490 --> 00:14:32.590
You can kind of imagine it
relatively stationary.

00:14:32.590 --> 00:14:34.490
The hydrogen comes
through here.

00:14:34.490 --> 00:14:36.200
The axle gets spun.

00:14:36.200 --> 00:14:39.940
And as the axle gets spun, ADP
and phosphate groups that are

00:14:39.940 --> 00:14:42.450
lodged inside this
F1 part of the

00:14:42.450 --> 00:14:45.600
protein, get pushed together.

00:14:45.600 --> 00:14:47.950
You have to put energy into the
reaction in order to make

00:14:47.950 --> 00:14:48.780
them stick together.

00:14:48.780 --> 00:14:52.060
But they get pushed together by
the protein itself as this

00:14:52.060 --> 00:14:53.280
axle turns around.

00:14:53.280 --> 00:14:56.100
And this axle turns around
from the energy of the

00:14:56.100 --> 00:14:57.000
hydrogen going.

00:14:57.000 --> 00:14:59.270
I don't even know what the
mechanics would look like.

00:14:59.270 --> 00:15:02.940
But you could imagine-- in my
head I imagine, the simplest

00:15:02.940 --> 00:15:03.880
thing is a windmill.

00:15:03.880 --> 00:15:10.300
Or not a windmill, as maybe some
type of water turbine or

00:15:10.300 --> 00:15:12.320
maybe the simplest thing
is, if you have

00:15:12.320 --> 00:15:13.010
something like that.

00:15:13.010 --> 00:15:14.090
I don't know if that's
what the protein

00:15:14.090 --> 00:15:14.850
actually looks like.

00:15:14.850 --> 00:15:17.440
If you have any kind of
thing passing by, it's

00:15:17.440 --> 00:15:18.770
going to spin it.

00:15:18.770 --> 00:15:19.990
It's going to spin
it like that.

00:15:19.990 --> 00:15:22.070
And you could be more creative
if you want to change the

00:15:22.070 --> 00:15:23.270
angle of the spin and whatnot.

00:15:23.270 --> 00:15:25.620
And that's all, people are
really still trying to

00:15:25.620 --> 00:15:28.340
understand this at a deeper
and deeper level.

00:15:28.340 --> 00:15:32.640
But for your purposes,
especially in an introductory

00:15:32.640 --> 00:15:35.570
biology level, you just have to
realize that two things are

00:15:35.570 --> 00:15:37.870
happening in the electron
transport chain.

00:15:37.870 --> 00:15:41.890
Electrons are moving from the
NADHs and the FADH2s to

00:15:41.890 --> 00:15:45.520
eventually show up and
reduce the oxygen.

00:15:45.520 --> 00:15:48.700
And as they do that, they're
releasing energy as they go

00:15:48.700 --> 00:15:50.400
from one molecule to another.

00:15:50.400 --> 00:15:52.570
They're going to lower
energy states.

00:15:52.570 --> 00:15:57.210
That energy is used to pump
hydrogen protons into the

00:15:57.210 --> 00:15:59.420
outer compartment of
the mitochondria.

00:15:59.420 --> 00:16:02.450
And then that gradient, those
hydrogen protons want to get

00:16:02.450 --> 00:16:05.520
back into the matrix of
the mitochondria.

00:16:05.520 --> 00:16:09.770
So as they go back in, that
drives this ATP synthase

00:16:09.770 --> 00:16:13.970
engine, which actually
produces the ATP.

00:16:13.970 --> 00:16:16.680
So just like we said in the
past, when you have 10 of

00:16:16.680 --> 00:16:20.520
these, on average-- let me say
this way-- on average each

00:16:20.520 --> 00:16:22.720
NADH is going to
produce 3 ATPs.

00:16:22.720 --> 00:16:23.450
Not directly.

00:16:23.450 --> 00:16:26.380
It produces enough of a gradient
of hydrogen protons

00:16:26.380 --> 00:16:29.680
to produce 3 ATPs in
the ATP synthase.

00:16:29.680 --> 00:16:33.440
And each FADH2, on average,
produces enough of a hydrogen

00:16:33.440 --> 00:16:35.870
gradient to produce 2 ATPs.

00:16:35.870 --> 00:16:39.150
So if we come in with 10 NADH,
they're going to produce-- in

00:16:39.150 --> 00:16:42.250
this ideal world-- 30 ATP.

00:16:42.250 --> 00:16:47.660
And then our 2 FADH2s are
going to produce 4 ATP.

00:16:47.660 --> 00:16:52.170
And then if you remember from
glycolysis, we had 2 net ATPs

00:16:52.170 --> 00:16:53.300
directly produced.

00:16:53.300 --> 00:16:56.530
And from the Krebs cycle we had
2 ATPs directly produced.

00:16:56.530 --> 00:17:04.170
So then you have 4 from
glycolysis and Krebs, and that

00:17:04.170 --> 00:17:08.230
gets us, once again, to our
magic 38 ATPs from one

00:17:08.230 --> 00:17:09.900
molecule of glucose.

00:17:09.900 --> 00:17:13.880
And now, I think you have a
pretty good grasp of cellular

00:17:13.880 --> 00:17:15.130
respiration.