Molecular and Empirical Forumlas from Percent Composition

WEBVTT
Kind: captions
Language: en

00:00:00.520 --> 00:00:04.000
Using all of the major
components in oil of cloves.

00:00:04.000 --> 00:00:10.700
It has a molar mass of 164.2
grams per mole, and is 73.14%

00:00:10.700 --> 00:00:14.710
carbon, and 7.37% hydrogen.

00:00:14.710 --> 00:00:16.140
The remainder is oxygen.

00:00:16.140 --> 00:00:17.940
What are the empirical
and molecular

00:00:17.940 --> 00:00:19.660
formulas for eugenol?

00:00:19.660 --> 00:00:22.370
And just as a refresher,
empirical formula is the

00:00:22.370 --> 00:00:25.300
simplest ratio of the atoms
in the molecule.

00:00:25.300 --> 00:00:26.450
And we'll see that
in a second.

00:00:26.450 --> 00:00:30.300
And the molecular formula is the
actual number of atoms in

00:00:30.300 --> 00:00:30.715
the molecule.

00:00:30.715 --> 00:00:32.640
So let's see if we can
figure this out.

00:00:32.640 --> 00:00:35.840
So the first piece of
information they gave us is

00:00:35.840 --> 00:00:39.430
that, the molar mass
of eugenol is

00:00:39.430 --> 00:00:42.220
164.2 grams per mole.

00:00:42.220 --> 00:00:47.480
So just to simplify things in
our head, let's just assume

00:00:47.480 --> 00:00:56.100
that we have 1 mole
of eugenol.

00:00:56.100 --> 00:00:59.190
And just as a bit of a
refresher, a mole is just a

00:00:59.190 --> 00:01:00.570
huge number.

00:01:00.570 --> 00:01:03.760
It's like saying we have a
million molecules of eugenol,

00:01:03.760 --> 00:01:06.750
but a mole is just an
even bigger number.

00:01:06.750 --> 00:01:09.310
And we know that the molar mass
of eugenol-- if we have

00:01:09.310 --> 00:01:13.090
that many molecules of eugenol,
then since we have 1

00:01:13.090 --> 00:01:17.180
mole, we know that, that is
going to have a mass of 164.2

00:01:17.180 --> 00:01:19.450
grams. So another way to
say it is, we have

00:01:19.450 --> 00:01:26.500
164.2 grams of eugenol.

00:01:26.500 --> 00:01:28.020
Now they gave us the
composition.

00:01:28.020 --> 00:01:29.970
They tell us what percentage
is carbon, what's hydrogen,

00:01:29.970 --> 00:01:31.750
and the remainder is oxygen.

00:01:31.750 --> 00:01:35.480
So if we assume we have a mole
of eugenol and we know that

00:01:35.480 --> 00:01:40.460
mole will have a mass of 164.2
grams, we can just use the

00:01:40.460 --> 00:01:43.580
percentages to figure out what
is our mass of carbon,

00:01:43.580 --> 00:01:44.880
hydrogen, and oxygen.

00:01:44.880 --> 00:01:46.380
So let's figure this out.

00:01:46.380 --> 00:01:48.840
So let's start off with this.

00:01:48.840 --> 00:01:57.750
So 164.2 grams of eugenol
times-- let me do it in

00:01:57.750 --> 00:02:03.630
another color-- times 73.14%.

00:02:03.630 --> 00:02:06.950
This will tell us what is our
mass of carbon that we're

00:02:06.950 --> 00:02:08.080
dealing with.

00:02:08.080 --> 00:02:10.139
So let's figure this out.

00:02:10.139 --> 00:02:13.990
So our mass of carbon-- get
the calculator up here.

00:02:13.990 --> 00:02:23.210
All right, so we have 164.2
times-- so 73.14% is the same

00:02:23.210 --> 00:02:27.780
thing as 0.7314.

00:02:27.780 --> 00:02:32.920
So we have 120.1.

00:02:32.920 --> 00:02:34.080
Let's go with that.

00:02:34.080 --> 00:02:35.690
We have four significant
digits in each of these

00:02:35.690 --> 00:02:40.180
numbers, so let's just go with
120.1 grams of carbon.

00:02:40.180 --> 00:02:47.280
So this is 120.1 grams
of carbon.

00:02:47.280 --> 00:02:48.560
Now let's do the same
thing for the

00:02:48.560 --> 00:02:49.750
hydrogen and the oxygen.

00:02:49.750 --> 00:02:58.070
So we have 164.2 grams of
eugenol times-- what's our

00:02:58.070 --> 00:02:59.450
percent composition
of hydrogen?

00:02:59.450 --> 00:03:06.340
It's right here, 7.37%--
so times 7.37%.

00:03:06.340 --> 00:03:08.620
What is this going
to be equal to?

00:03:08.620 --> 00:03:09.910
Get the calculator out.

00:03:09.910 --> 00:03:19.240
So we have 164.2 times--
7.37% is 0.0737.

00:03:19.240 --> 00:03:23.200
And we will get 12.1.

00:03:23.200 --> 00:03:25.660
So we have 12.1 grams
of carbon.

00:03:30.300 --> 00:03:33.050
And they don't give us,
explicitly, the percent

00:03:33.050 --> 00:03:34.220
composition of oxygen.

00:03:34.220 --> 00:03:36.610
But we could figure it out
fairly easily, because we know

00:03:36.610 --> 00:03:38.780
everything left over
is oxygen.

00:03:38.780 --> 00:03:42.100
So we could take the mass of
carbon, the mass of hydrogen--

00:03:42.100 --> 00:03:44.590
oh sorry, this isn't
grams of carbon.

00:03:44.590 --> 00:03:46.220
That's grams of hydrogen.

00:03:46.220 --> 00:03:49.400
We could take the mass of
hydrogen, the mass of carbon,

00:03:49.400 --> 00:03:53.660
subtract them both from 164.2,
and whatever is left

00:03:53.660 --> 00:03:55.060
over will be oxygen.

00:03:55.060 --> 00:03:56.570
So let's do it that way.

00:03:56.570 --> 00:03:58.590
Or we could figure out the
percentage that's oxygen,

00:03:58.590 --> 00:04:01.250
because these all have to add up
to 100%, and then multiply.

00:04:01.250 --> 00:04:03.180
Either way would work.

00:04:03.180 --> 00:04:04.290
So let's do that.

00:04:04.290 --> 00:04:10.540
So if we have 1 mole of eugenol,
it's 164.2 grams. We

00:04:10.540 --> 00:04:17.769
just figured out that 120.1 of
those grams are carbon, and

00:04:17.769 --> 00:04:24.330
that 12.1 of those grams
are hydrogen.

00:04:24.330 --> 00:04:25.100
So what's left over?

00:04:25.100 --> 00:04:30.170
We have exactly 32
grams of oxygen.

00:04:30.170 --> 00:04:32.840
So what's left over when you
subtract these two guys out?

00:04:32.840 --> 00:04:36.600
I'll do that in green.

00:04:36.600 --> 00:04:40.980
We are left with 32
grams of oxygen.

00:04:40.980 --> 00:04:43.860
So if you have a mole of
eugenol, it has a mass of

00:04:43.860 --> 00:04:47.650
164.2 grams. And if you break
it down by the masses of the

00:04:47.650 --> 00:04:52.060
constituent molecules, 120 grams
of carbon, 12 grams of

00:04:52.060 --> 00:04:55.050
hydrogen, 32 grams of oxygen.

00:04:55.050 --> 00:04:57.820
Now what we need to do is figure
out how many moles of

00:04:57.820 --> 00:05:01.310
carbon this is, how many moles
of hydrogen this is, and how

00:05:01.310 --> 00:05:03.440
many moles of oxygen.

00:05:03.440 --> 00:05:06.780
And this is maybe something that
you should have memorized

00:05:06.780 --> 00:05:09.210
at some point, because these
are the three most common

00:05:09.210 --> 00:05:11.030
elements you'll ever
deal with.

00:05:11.030 --> 00:05:13.980
But just as a refresher, you
could look up on any periodic

00:05:13.980 --> 00:05:18.710
table for carbon, you would see
in the periodic table the

00:05:18.710 --> 00:05:21.920
atomis-- well, most periodic
tables will give you the

00:05:21.920 --> 00:05:25.260
atomic weight, which is the
weighted average of the

00:05:25.260 --> 00:05:27.130
different isotopes
of carbon around.

00:05:27.130 --> 00:05:30.360
But in general, the atomic
weight, or the weighted

00:05:30.360 --> 00:05:33.400
average of the atomic masses
of the different isotopes.

00:05:33.400 --> 00:05:36.360
But carbon, you just remember
that the atomic weight is

00:05:36.360 --> 00:05:42.300
pretty close to 12 atomic
mass units.

00:05:42.300 --> 00:05:47.870
Which means, that carbon
has a molar mass of

00:05:47.870 --> 00:05:50.760
12 grams per mole.

00:05:50.760 --> 00:05:54.710
Or if you have a mole of carbon
molecules, it will have

00:05:54.710 --> 00:05:58.370
a mass of 12 grams. We do the
same thing for the hydrogen

00:05:58.370 --> 00:05:59.740
and the oxygen.

00:05:59.740 --> 00:06:04.770
Hydrogen has, whether you take
a single isotope or you take

00:06:04.770 --> 00:06:07.650
the weighted average, its
atomic weight or mass,

00:06:07.650 --> 00:06:12.540
depending which 1 you use, is
pretty darn close to 1.

00:06:12.540 --> 00:06:17.980
And so hydrogen's molar mass
is 1 gram per mole.

00:06:17.980 --> 00:06:19.950
There's some decimals here if
you look it up on a periodic

00:06:19.950 --> 00:06:23.050
table, but I just remember
carbon as 12, hydrogen is 1,

00:06:23.050 --> 00:06:26.410
and then finally,
oxygen is 16.

00:06:26.410 --> 00:06:32.910
So oxygen's is approximately
16 atomic mass units.

00:06:32.910 --> 00:06:35.460
I guess, if you take a specific
isotope, atomic mass.

00:06:35.460 --> 00:06:37.760
If you take its weighted
average, atomic weight.

00:06:37.760 --> 00:06:45.670
And that means that its molar
mass is 16 grams per mole.

00:06:45.670 --> 00:06:48.070
Now we have the number
of grams of oxygen,

00:06:48.070 --> 00:06:49.940
hydrogen, and oxygen.

00:06:49.940 --> 00:06:51.950
So now we should be able to use
this information down here

00:06:51.950 --> 00:06:55.460
to figure out how many
moles this is.

00:06:55.460 --> 00:06:56.620
So let's do this.

00:06:56.620 --> 00:07:02.060
So it's 12 grams per mole, but
we want to divide by grams

00:07:02.060 --> 00:07:04.660
because we want this gram to
disappear in the numerator.

00:07:04.660 --> 00:07:07.630
So what we could do is, if it's
12 grams per mole, that's

00:07:07.630 --> 00:07:16.090
the same thing as 1 mole for
every 12 grams. All I did is,

00:07:16.090 --> 00:07:17.860
I took the reciprocal
of this right here.

00:07:17.860 --> 00:07:20.080
If we have 12 grams for every
mole, that's also true that we

00:07:20.080 --> 00:07:22.800
have 1 mole for every
12 grams. And the

00:07:22.800 --> 00:07:24.320
grams cancel out.

00:07:24.320 --> 00:07:29.070
And we are left with 120.1
divided by 12, which is pretty

00:07:29.070 --> 00:07:31.730
close to 10.

00:07:31.730 --> 00:07:38.230
So this is equal to 10
moles of carbon.

00:07:38.230 --> 00:07:39.960
So we know how many moles
of carbon we have

00:07:39.960 --> 00:07:41.920
in 1 mole of eugenol.

00:07:41.920 --> 00:07:43.560
Now let's do the hydrogen.

00:07:43.560 --> 00:07:45.160
So we do the multiplication
here.

00:07:45.160 --> 00:07:49.510
And so here we have 1 mole of
hydrogen-- if we take the

00:07:49.510 --> 00:07:53.570
inverse of this, or the
reciprocal of this-- has a

00:07:53.570 --> 00:07:55.370
mass of 1 gram.

00:07:55.370 --> 00:07:57.390
So really, this is just
going to multiply out.

00:07:57.390 --> 00:08:01.170
So we literally have, we could
say 12.1 moles of hydrogen.

00:08:01.170 --> 00:08:04.810
But because we're looking for
formulas, that's pretty darn

00:08:04.810 --> 00:08:06.390
close to 12.

00:08:06.390 --> 00:08:10.860
So we should just say 12
moles of hydrogen.

00:08:10.860 --> 00:08:14.950
And then finally, we
have our oxygen.

00:08:14.950 --> 00:08:22.800
And we have 1 mole of oxygen for
every 16 grams of oxygen.

00:08:22.800 --> 00:08:26.420
32 divided by-- the grams cancel
out, of course-- 32

00:08:26.420 --> 00:08:28.350
divided by 16 is 2.

00:08:28.350 --> 00:08:34.450
So this is equal to
2 moles of oxygen.

00:08:34.450 --> 00:08:37.190
So if we have 1 mole of eugenol,
we have 10 moles of

00:08:37.190 --> 00:08:40.990
carbon, 12 moles of hydrogen,
and 2 moles of oxygen.

00:08:40.990 --> 00:08:43.000
So we now have the ratio.

00:08:43.000 --> 00:08:46.020
Or you could even think of, if
you had 1 molecule of eugenol,

00:08:46.020 --> 00:08:55.700
we would have 10 carbons,
we have 12 hydrogens,

00:08:55.700 --> 00:08:56.950
and we have 2 oxygens.

00:08:59.770 --> 00:09:00.330
And we're done.

00:09:00.330 --> 00:09:05.010
This is the molecular formula
we have for every mole.

00:09:05.010 --> 00:09:06.860
We could think of it in moles
which is a huge number.

00:09:06.860 --> 00:09:09.270
Or you could think of, for every
molecule of eugenol, we

00:09:09.270 --> 00:09:12.480
have 10 molecules of carbon,
12 molecules of hydrogen, 6

00:09:12.480 --> 00:09:14.710
molecules of oxygen.

00:09:14.710 --> 00:09:16.395
This right here is molecular
formula.

00:09:23.290 --> 00:09:26.040
And the empirical formula is
essentially taking this ratio

00:09:26.040 --> 00:09:28.600
to the simplest terms. And
all of these have a

00:09:28.600 --> 00:09:30.230
common factor of 2.

00:09:30.230 --> 00:09:38.240
So the empirical formula, we
essentially just put this

00:09:38.240 --> 00:09:40.910
ratio in simplest terms. So we
can divide all of them by 2.

00:09:40.910 --> 00:09:42.780
So let's divide all
of them by 2.

00:09:42.780 --> 00:09:49.480
And you have 5 carbons for
every 6 hydrogens.

00:09:49.480 --> 00:09:50.290
This isn't O,6.

00:09:50.290 --> 00:09:51.550
This is 2 oxygens.

00:09:51.550 --> 00:09:52.800
So let me make that clear.

00:09:55.440 --> 00:09:57.770
I'll have to erase a lot
of stuff to get there.

00:09:57.770 --> 00:09:58.240
There you go.

00:09:58.240 --> 00:09:59.260
That was 2 oxygens.

00:09:59.260 --> 00:10:00.320
Don't want to make
that blunder.

00:10:00.320 --> 00:10:04.360
We saw we have 2 moles of
oxygen, so this is the

00:10:04.360 --> 00:10:05.610
molecular formula.

00:10:10.540 --> 00:10:15.930
And the empirical formula,
at least the 2 is still

00:10:15.930 --> 00:10:16.740
divisible by 2.

00:10:16.740 --> 00:10:18.820
So you divide all
of these by 2.

00:10:18.820 --> 00:10:20.570
You get the simplest ratio.

00:10:20.570 --> 00:10:27.590
For every 5 carbons, you
have 6 hydrogens,

00:10:27.590 --> 00:10:29.260
and you have 1 oxygen.

00:10:29.260 --> 00:10:31.640
Or you can put a 1 right
there if you like.

00:10:31.640 --> 00:10:33.240
And we're done.


Polymerization of alkenes with acid

WEBVTT
Kind: captions
Language: en

00:00:00.690 --> 00:00:02.870
Let's say we have some
chloroethene here, and you

00:00:02.870 --> 00:00:05.770
wouldn't have to call this
1-chloro-eth-1-ene, because if

00:00:05.770 --> 00:00:07.370
you just go with chloroethene,
there's only

00:00:07.370 --> 00:00:09.490
one way to draw this.

00:00:09.490 --> 00:00:10.710
And the common name for

00:00:10.710 --> 00:00:13.880
chloroethene is vinyl chloride.

00:00:13.880 --> 00:00:18.370
So let's say we have a bunch
of chloroethene molecules

00:00:18.370 --> 00:00:22.130
along with or mixed with
some hydrogen chloride.

00:00:22.130 --> 00:00:24.710
And I've drawn all of the
valence electrons for the

00:00:24.710 --> 00:00:27.910
chlorine atom and I've drawn a
little magenta electron, the

00:00:27.910 --> 00:00:30.960
one that the hydrogen atom
brought to the table.

00:00:30.960 --> 00:00:33.120
So we've seen something
like this before.

00:00:33.120 --> 00:00:34.960
What is likely to happen?

00:00:34.960 --> 00:00:37.910
Well, maybe one of these carbons
is willing to give up

00:00:37.910 --> 00:00:38.630
an electron.

00:00:38.630 --> 00:00:42.310
That electron goes to the
hydrogen because this electron

00:00:42.310 --> 00:00:45.450
is already being hogged by the
chlorine, so this hydrogen has

00:00:45.450 --> 00:00:49.140
a partially positive charge.

00:00:49.140 --> 00:00:52.280
Chlorine has a partially
negative charge, so that

00:00:52.280 --> 00:00:54.810
electron would be attracted
to the hydrogen.

00:00:54.810 --> 00:00:57.330
Then this electron
can be completely

00:00:57.330 --> 00:00:59.390
hogged by the chlorine.

00:00:59.390 --> 00:01:02.710
And if we had to decide which
of these carbons is more

00:01:02.710 --> 00:01:05.750
likely to give up the electron,
you just have to say

00:01:05.750 --> 00:01:08.910
which one is bonded to things
that it can share electrons a

00:01:08.910 --> 00:01:09.580
little bit with.

00:01:09.580 --> 00:01:13.890
This carbon is only bonded to
hydrogens, so it's already

00:01:13.890 --> 00:01:16.590
hogging their one electron each,
and there are no more

00:01:16.590 --> 00:01:18.150
electrons to share with it.

00:01:18.150 --> 00:01:21.260
This guy is bonded to a
chlorine, so the chlorine has

00:01:21.260 --> 00:01:22.410
a bunch of valence electrons.

00:01:22.410 --> 00:01:26.220
It might be able share a little
bit with this carbon if

00:01:26.220 --> 00:01:28.600
this guy became a carbocation.

00:01:28.600 --> 00:01:30.680
So this guy will lose
an electron.

00:01:30.680 --> 00:01:33.170
This carbon will form the
bond with that hydrogen.

00:01:33.170 --> 00:01:35.420
So let's draw it out.

00:01:35.420 --> 00:01:38.980
So let's say this carbon's
electron is that blue thing

00:01:38.980 --> 00:01:40.580
right there.

00:01:40.580 --> 00:01:41.880
Well, we could draw
it like this.

00:01:41.880 --> 00:01:45.790
It goes to the hydrogen, and
then the hydrogen's magenta

00:01:45.790 --> 00:01:48.560
electron goes to the chlorine.

00:01:48.560 --> 00:01:51.620
This is just a plausible
mechanism.

00:01:51.620 --> 00:01:55.730
Now, once that happens, what
will our setup look like?

00:01:55.730 --> 00:01:59.070
What will it look like?

00:01:59.070 --> 00:02:03.630
It will have this carbon over
here bonded to two hydrogens.

00:02:03.630 --> 00:02:06.700
It has its single bond to that
other carbon that just lost

00:02:06.700 --> 00:02:12.300
its electron, which is bonded to
a hydrogen and a chlorine.

00:02:12.300 --> 00:02:14.980
And now this carbon on
the left, it is now

00:02:14.980 --> 00:02:16.190
bonded to the hydrogen.

00:02:16.190 --> 00:02:18.750
That electron went to the
hydrogen and it formed a bond

00:02:18.750 --> 00:02:21.810
with it, so then it
forms a bond.

00:02:21.810 --> 00:02:25.490
So that little blue electron is
at this end of the-- I want

00:02:25.490 --> 00:02:26.710
to make it blue.

00:02:26.710 --> 00:02:31.080
That little blue electron is at
this end of the bond, and

00:02:31.080 --> 00:02:34.050
it is now the hydrogen's
electron.

00:02:34.050 --> 00:02:38.500
And that magenta electron went
to the chlorine, so now it is

00:02:38.500 --> 00:02:40.380
a negative ion.

00:02:40.380 --> 00:02:41.910
It is a chloride ion.

00:02:41.910 --> 00:02:44.350
So we have a chloride ion.

00:02:44.350 --> 00:02:48.100
It has its standard seven
valence electrons that it

00:02:48.100 --> 00:02:51.150
started off with, but now it
took that magenta electron

00:02:51.150 --> 00:02:53.610
from the hydrogen,
and so now it has

00:02:53.610 --> 00:02:55.110
eight valence electrons.

00:02:55.110 --> 00:02:56.170
It gained an electron.

00:02:56.170 --> 00:02:58.620
It now has a negative charge.

00:02:58.620 --> 00:03:01.420
This guy over here
lost an electron.

00:03:01.420 --> 00:03:04.300
He now has a positive charge.

00:03:04.300 --> 00:03:07.000
Now, the next thing that you
might expect to happen, if we

00:03:07.000 --> 00:03:10.220
just followed the pattern of
the last several videos, is

00:03:10.220 --> 00:03:13.980
you would say, hey, this guy
will now take an electron from

00:03:13.980 --> 00:03:17.940
the chlorine, which is-- or the
chloride anion, I should

00:03:17.940 --> 00:03:21.860
say, which is completely
plausible, but there's also a

00:03:21.860 --> 00:03:23.010
bunch of the chloroethane.

00:03:23.010 --> 00:03:25.650
This isn't the only molecule
of chloroethene.

00:03:25.650 --> 00:03:28.190
I should say chloroethene,
not chloroethane.

00:03:28.190 --> 00:03:29.680
Chloroethene sitting around.

00:03:29.680 --> 00:03:34.930
So let's let us throw another
one of those in there.

00:03:34.930 --> 00:03:37.110
So we have more molecules
of this.

00:03:37.110 --> 00:03:43.390
So he could take an electron
from this chloride ion, or he

00:03:43.390 --> 00:03:45.920
could take an electron from
this guy over here.

00:03:45.920 --> 00:03:53.360
Remember, this guy, just like
this guy, who was this guy,

00:03:53.360 --> 00:03:55.260
this guy is OK.

00:03:55.260 --> 00:03:58.900
It doesn't require a super
amount of energy to make this

00:03:58.900 --> 00:04:00.980
guy lose his electron.

00:04:00.980 --> 00:04:03.130
He's bonded to other things that
are willing to share with

00:04:03.130 --> 00:04:04.030
him a little bit.

00:04:04.030 --> 00:04:07.770
Maybe he's willing to lose his
electron as opposed to the

00:04:07.770 --> 00:04:10.540
chloride ion.

00:04:10.540 --> 00:04:13.720
So this guy has-- let me draw
it in-- so this end of this

00:04:13.720 --> 00:04:15.150
bond is green.

00:04:15.150 --> 00:04:19.140
And then this goes and bonds
with this carbon.

00:04:19.140 --> 00:04:21.640
So this will be a long
bond right here.

00:04:21.640 --> 00:04:24.830
So this goes and bonds with
that carbon, essentially

00:04:24.830 --> 00:04:26.650
giving that electron
to that carbon.

00:04:26.650 --> 00:04:29.340
And then what will our
setup look like?

00:04:29.340 --> 00:04:32.542
So after that happens,
we'll look like this.

00:04:32.542 --> 00:04:34.940
I probably should have copied
and pasted this

00:04:34.940 --> 00:04:35.900
from the get go.

00:04:35.900 --> 00:04:38.950
Actually, let me do that before
I-- let me copy and

00:04:38.950 --> 00:04:41.260
paste this.

00:04:41.260 --> 00:04:44.820
So now let me just draw, copy
and paste this whole thing.

00:04:47.330 --> 00:04:49.550
Nope, that's not what
I wanted to do.

00:04:49.550 --> 00:04:52.360
Let me select it again.

00:04:52.360 --> 00:04:53.560
All right.

00:04:53.560 --> 00:04:55.890
Copy and then paste.

00:04:55.890 --> 00:04:56.960
There you go.

00:04:56.960 --> 00:04:59.520
So then we have that thing.

00:04:59.520 --> 00:05:02.250
And let me redraw what I
had erased, so that I

00:05:02.250 --> 00:05:03.910
could copy and paste.

00:05:03.910 --> 00:05:10.420
And then we have this guy went
over to this carbocation, so

00:05:10.420 --> 00:05:15.730
he's no longer a carbocation, so
let me erase this, because

00:05:15.730 --> 00:05:17.360
now he's gained an electron.

00:05:17.360 --> 00:05:20.320
He gained that green electron
right there.

00:05:20.320 --> 00:05:22.260
He gained that green electron.

00:05:22.260 --> 00:05:23.580
I'll just draw it right there.

00:05:23.580 --> 00:05:26.240
And now he's formed a bond
with this carbon.

00:05:26.240 --> 00:05:29.760
And I'll make it blue, just so
we know which carbon we're

00:05:29.760 --> 00:05:30.590
talking about.

00:05:30.590 --> 00:05:32.270
He's formed a bond.

00:05:32.270 --> 00:05:34.800
This bond now moved over to
that carbon because the

00:05:34.800 --> 00:05:35.760
electron went with it.

00:05:35.760 --> 00:05:40.780
So now that bond is to this
carbon right here.

00:05:40.780 --> 00:05:44.270
That carbon right over there,
which is bonded to two

00:05:44.270 --> 00:05:50.065
hydrogens, and now has a single
bond to the electron

00:05:50.065 --> 00:05:53.940
that gave up the carbon, has a
single bond to that character

00:05:53.940 --> 00:05:57.590
right over here, who is bonded
to a hydrogen and a chlorine.

00:06:01.360 --> 00:06:04.960
And since he now lost an
electron, he now has a

00:06:04.960 --> 00:06:06.290
positive charge.

00:06:06.290 --> 00:06:08.850
So if you look at this setup
right here, it looks very

00:06:08.850 --> 00:06:11.380
similar to this setup, although
we've added one more

00:06:11.380 --> 00:06:12.830
vinyl chloride to the mix.

00:06:12.830 --> 00:06:16.250
And the one that we added lost
its electron, or this carbon

00:06:16.250 --> 00:06:19.260
lost it electron, and now
it's a carbocation.

00:06:19.260 --> 00:06:21.320
So what could happen next?

00:06:21.320 --> 00:06:25.030
Well, we have more of this vinyl
chloride sitting around.

00:06:27.820 --> 00:06:29.850
Let me draw another
vinyl chloride.

00:06:29.850 --> 00:06:35.530
So I have a carbon, a hydrogen,
a hydrogen, and then

00:06:35.530 --> 00:06:38.130
it is double bonded
to a carbon, a

00:06:38.130 --> 00:06:40.636
hydrogen, and a chlorine.

00:06:40.636 --> 00:06:42.790
And let me copy and
paste this.

00:06:42.790 --> 00:06:46.200
I think you see where this might
be going, how this could

00:06:46.200 --> 00:06:48.200
keep on going and
going and going.

00:06:48.200 --> 00:06:49.450
So copy.

00:06:51.440 --> 00:06:53.250
Well, I just copy
that for now.

00:06:53.250 --> 00:06:54.880
So what's going to happen now?

00:06:54.880 --> 00:06:58.430
This guy could go and give an
electron to this guy and form

00:06:58.430 --> 00:07:02.200
a bond, or we could have the
same process happen over and

00:07:02.200 --> 00:07:05.130
over and over again.

00:07:05.130 --> 00:07:07.760
Let me get my pen tool going.

00:07:07.760 --> 00:07:12.040
So this electron could be given
to this carbocation

00:07:12.040 --> 00:07:13.290
right there.

00:07:17.010 --> 00:07:18.840
And then what happens?

00:07:18.840 --> 00:07:21.560
Well, if that happens, then
we're going to get-- I'll move

00:07:21.560 --> 00:07:24.030
to the left now.

00:07:24.030 --> 00:07:25.470
We have our original molecule.

00:07:25.470 --> 00:07:26.970
I'm going to run out
of space soon.

00:07:26.970 --> 00:07:29.710
We have this original molecule,
and now this guy has

00:07:29.710 --> 00:07:30.490
bonded to that.

00:07:30.490 --> 00:07:37.970
So this carbon right here is
going to be this carbon, and

00:07:37.970 --> 00:07:40.610
now it is bonded to this guy.

00:07:40.610 --> 00:07:43.180
That orange electron
is now given to

00:07:43.180 --> 00:07:45.240
this guy who was positive.

00:07:45.240 --> 00:07:48.220
So he now has-- let me make
it a little bit neater.

00:07:48.220 --> 00:07:49.790
I can do a better
job than that.

00:07:49.790 --> 00:07:51.700
So the carbon's here.

00:07:51.700 --> 00:07:54.750
The bond goes to this guy.

00:07:54.750 --> 00:07:58.980
He now has the orange
electron.

00:07:58.980 --> 00:08:01.170
He no longer has a
positive charge.

00:08:03.970 --> 00:08:06.570
He's got all of his valence
electrons now.

00:08:06.570 --> 00:08:08.330
And now this guy is bonded
to two hydrogens.

00:08:11.430 --> 00:08:13.450
That guy is bonded
to two hydrogens.

00:08:13.450 --> 00:08:16.260
And he has a single bond, this
single bond right here to the

00:08:16.260 --> 00:08:18.890
carbon that just lost his
electron, who's bonded to a

00:08:18.890 --> 00:08:20.690
hydrogen and a chlorine.

00:08:20.690 --> 00:08:24.760
And because he lost his
electron, he now is the

00:08:24.760 --> 00:08:26.780
carbocation.

00:08:26.780 --> 00:08:29.050
He is now a carbocation.

00:08:29.050 --> 00:08:30.800
So I think you see where
we're going.

00:08:30.800 --> 00:08:34.780
We can just keep adding and
adding and adding to this

00:08:34.780 --> 00:08:36.745
chain of vinyl chloride.

00:08:36.745 --> 00:08:40.200
So if this process just went
on and on and on, we could

00:08:40.200 --> 00:08:41.190
make it like this.

00:08:41.190 --> 00:08:43.010
It would look something
like this.

00:08:43.010 --> 00:08:45.800
Let me see how well
I can draw it.

00:08:45.800 --> 00:08:48.160
So it would look like this.

00:08:48.160 --> 00:08:49.670
So this is a CH3.

00:08:49.670 --> 00:08:57.330
So I'll just draw it as H3C, and
then this is bonded to a

00:08:57.330 --> 00:09:02.090
carbon, that is bonded to a--
well, maybe I'll call it a CH,

00:09:02.090 --> 00:09:03.720
which is bonded to a chlorine.

00:09:03.720 --> 00:09:05.840
So we're that far
in the molecule.

00:09:05.840 --> 00:09:08.980
And then we have-- let's see
the part that repeats.

00:09:08.980 --> 00:09:15.270
This part right here is going
to keep repeating.

00:09:15.270 --> 00:09:18.850
That part right there is going
to keep repeating, and I'm

00:09:18.850 --> 00:09:20.280
going to do it like this.

00:09:20.280 --> 00:09:23.910
So I'm just going to draw one
of them, so you have a CH2.

00:09:23.910 --> 00:09:29.100
That's that right there,
connected to a CH, which is

00:09:29.100 --> 00:09:32.190
that right there, which is
connected to a chlorine.

00:09:32.190 --> 00:09:35.360
And so that part right there
will keep repeating.

00:09:35.360 --> 00:09:38.590
And then maybe the very last
one, so you have this guy

00:09:38.590 --> 00:09:41.640
right here, but maybe the very
last one that joins on-- I

00:09:41.640 --> 00:09:43.430
mean, this can happen
millions of times.

00:09:43.430 --> 00:09:45.340
I just it made it happen
two or three times.

00:09:45.340 --> 00:09:48.170
It could happen millions of
times and form a super long

00:09:48.170 --> 00:09:50.400
chain or a polymer.

00:09:50.400 --> 00:09:53.000
And what we are describing in
this video is actually a

00:09:53.000 --> 00:09:55.730
polymer that you have probably
dealt with at some

00:09:55.730 --> 00:09:56.650
point in your life.

00:09:56.650 --> 00:09:58.380
In fact, I guarantee there's
some of it in

00:09:58.380 --> 00:09:59.730
your house right now.

00:09:59.730 --> 00:10:01.530
So then we'd have that
part right there.

00:10:01.530 --> 00:10:07.720
And we could just make
that as CH2, CH, Cl.

00:10:10.290 --> 00:10:12.960
And now, the way we've drawn
it, it's a carbocation, but

00:10:12.960 --> 00:10:17.530
maybe we've run out of all of
the vinyl chloride molecules,

00:10:17.530 --> 00:10:20.060
or we could also call them
chloroethene molecules.

00:10:20.060 --> 00:10:23.510
And now finally, when everything
is said and done,

00:10:23.510 --> 00:10:27.080
this last guy, since he's run
out of vinyl chloride

00:10:27.080 --> 00:10:30.790
molecules to take their
electrons from, he now finally

00:10:30.790 --> 00:10:33.160
takes it from the chlorine.

00:10:33.160 --> 00:10:36.820
So you can imagine this happens
many, many times.

00:10:36.820 --> 00:10:39.310
So this repeats many times.

00:10:39.310 --> 00:10:44.190
After this repeats many times,
then finally, one of these

00:10:44.190 --> 00:10:50.180
electrons from the chlorine go
to that final carbocation,

00:10:50.180 --> 00:10:54.220
because they've run out of other
vinyl chlorides, and

00:10:54.220 --> 00:10:58.720
then he attaches right over
here to the chlorine.

00:10:58.720 --> 00:11:02.250
Now, this is called-- so when we
say that this might happen

00:11:02.250 --> 00:11:04.630
many times, you might write an
N here, just to show that it

00:11:04.630 --> 00:11:06.000
repeats many, many times.

00:11:06.000 --> 00:11:08.530
If you know how many times it
repeats, if you know that

00:11:08.530 --> 00:11:11.960
there were a thousand molecules
here, you would

00:11:11.960 --> 00:11:15.140
write a thousand repetitions,
but this is called a polymer.

00:11:17.880 --> 00:11:22.170
And the name for this molecule
right here is-- each of these

00:11:22.170 --> 00:11:23.640
units is vinyl chloride,
right?

00:11:28.530 --> 00:11:29.800
Vinyl chloride.

00:11:29.800 --> 00:11:33.170
I guess the official name is
chloroethene, but the typical

00:11:33.170 --> 00:11:36.070
name, the one people actually
to use, is vinyl chloride.

00:11:36.070 --> 00:11:37.590
That's for each of
these units.

00:11:37.590 --> 00:11:38.450
It's a polymer.

00:11:38.450 --> 00:11:41.940
We have many of them, so we'll
put a poly- in front of it.

00:11:44.450 --> 00:11:49.630
So this molecule right here is
polyvinyl chloride, or, and

00:11:49.630 --> 00:11:54.140
now I think it'll ring a
bell, or PVC for short.

00:11:54.140 --> 00:11:56.600
And you've probably heard
of PVC piping.

00:11:56.600 --> 00:11:58.610
It's what most people have
for their plumbing.

00:11:58.610 --> 00:11:59.780
It's those plastic pipes.

00:11:59.780 --> 00:12:00.820
And that's what it is.

00:12:00.820 --> 00:12:02.230
It's polyvinyl chloride.


Entgegen-Zusammen naming scheme for alkenes examples

WEBVTT
Kind: captions
Language: en

00:00:00.000 --> 00:00:02.880
Based on what we learned in the
last video, let's see if

00:00:02.880 --> 00:00:04.800
we can name these two
molecules here.

00:00:04.800 --> 00:00:06.630
Let's start with
this blue one.

00:00:06.630 --> 00:00:09.410
So the first thing we notice,
it is an alkene.

00:00:09.410 --> 00:00:11.140
It has a double bond
right there.

00:00:11.140 --> 00:00:13.750
So we can, right from the get
go, write that it's going to

00:00:13.750 --> 00:00:15.780
end with an ene.

00:00:15.780 --> 00:00:17.470
And then we need to figure
out what the longest

00:00:17.470 --> 00:00:18.790
carbon chain is.

00:00:18.790 --> 00:00:20.120
And it looks like it's
this one here.

00:00:20.120 --> 00:00:24.680
One, two, three, four, five,
six, seven carbons.

00:00:24.680 --> 00:00:31.310
So it's going to be hept as
our prefix on the alkene.

00:00:31.310 --> 00:00:36.080
Let me write it out a little
bit further to the left.

00:00:36.080 --> 00:00:38.060
And then we have to figure out
where the double bond is.

00:00:38.060 --> 00:00:40.410
And we always want to start
numbering our carbons from the

00:00:40.410 --> 00:00:43.630
direction that bumps into the
double bond first. And so the

00:00:43.630 --> 00:00:45.300
double bond is closer
to this end of the

00:00:45.300 --> 00:00:46.220
chain than that end.

00:00:46.220 --> 00:00:47.540
So we're going to start
numbering here.

00:00:47.540 --> 00:00:54.720
So one, two, three, four,
five, six, seven.

00:00:54.720 --> 00:00:57.320
And so the double bond starts
on the three carbon.

00:00:57.320 --> 00:01:00.550
So it is hept-3-ene.

00:01:00.550 --> 00:01:03.270
And we also have a
functional group.

00:01:03.270 --> 00:01:06.550
We have a methyl group sitting
on the number four carbon.

00:01:06.550 --> 00:01:16.280
So it is 4-methylhept-3-ene,
which is correct.

00:01:16.280 --> 00:01:19.280
But we still haven't considered
what's going on, on

00:01:19.280 --> 00:01:21.010
either side of the
double bond.

00:01:21.010 --> 00:01:24.970
Whether the higher priority
functional group is closer to

00:01:24.970 --> 00:01:26.960
each other on both sides of
the double bond or whether

00:01:26.960 --> 00:01:28.690
they're farther away
from each other.

00:01:28.690 --> 00:01:30.970
And to do that we first have
to identify the higher

00:01:30.970 --> 00:01:34.490
priority group on each side
of the double bond.

00:01:34.490 --> 00:01:37.000
So on the right side of the
double bond-- let me circle it

00:01:37.000 --> 00:01:39.780
in magenta on each side-- so
on the right side of the

00:01:39.780 --> 00:01:41.250
double bond, we only
have one functional

00:01:41.250 --> 00:01:42.580
group, right over here.

00:01:42.580 --> 00:01:45.160
You could view this
as an ethyl group.

00:01:45.160 --> 00:01:46.040
That's pretty obvious.

00:01:46.040 --> 00:01:48.360
There is no other functional
group bonded to the carbon.

00:01:48.360 --> 00:01:50.250
There's only a hydrogen
over here.

00:01:50.250 --> 00:01:52.540
Now on the left side it's a
little bit less obvious.

00:01:52.540 --> 00:01:54.580
We have two functional groups
from the point of

00:01:54.580 --> 00:01:55.780
view of this carbon.

00:01:55.780 --> 00:01:58.130
You have the methyl that we
already pointed out, and you

00:01:58.130 --> 00:02:01.160
also have these three carbons
right over here.

00:02:01.160 --> 00:02:02.980
You could view that
as a propyl group.

00:02:02.980 --> 00:02:05.470
And what we need to do to
identify the highest priority

00:02:05.470 --> 00:02:10.220
group is to use the
Cahn-Ingold-Prelog namings or

00:02:10.220 --> 00:02:13.950
priority scheme that we learned
several videos ago.

00:02:13.950 --> 00:02:17.540
And there you literally go from
this carbon, you look at

00:02:17.540 --> 00:02:21.390
what it's bonded to, and you
compare the atomic numbers.

00:02:21.390 --> 00:02:23.570
But in both cases it's
a carbon to a carbon.

00:02:23.570 --> 00:02:25.330
This is a carbon to a carbon.

00:02:25.330 --> 00:02:27.440
So their atomic numbers
are the same.

00:02:27.440 --> 00:02:30.450
So then you go one bond further
away and you see which

00:02:30.450 --> 00:02:34.140
one is bonded to a higher
atomic number atom.

00:02:34.140 --> 00:02:36.830
This carbon bonds to a
carbon, which is a

00:02:36.830 --> 00:02:37.940
higher atomic number.

00:02:37.940 --> 00:02:39.850
This carbon only bonds
to three hydrogens.

00:02:39.850 --> 00:02:41.940
This one does two hydrogens
and one carbon.

00:02:41.940 --> 00:02:45.000
Because it's bonded to another
carbon, it takes priority.

00:02:45.000 --> 00:02:49.620
This propyl group is a higher
priority functional group.

00:02:49.620 --> 00:02:53.120
So now when we're trying to
decide whether it is entgegen

00:02:53.120 --> 00:02:56.770
or zusammen, we look
at these 2 groups.

00:02:56.770 --> 00:02:59.360
And we see that they are sitting
on the same side of

00:02:59.360 --> 00:03:00.090
the double bond.

00:03:00.090 --> 00:03:01.720
They are both above
the carbons.

00:03:01.720 --> 00:03:03.680
They are closer to each other.

00:03:03.680 --> 00:03:07.030
So this molecule is zusammen.

00:03:07.030 --> 00:03:10.350
Which on some levels, you can
think of as the same thing as

00:03:10.350 --> 00:03:13.350
cis, but cis and trans stops
applying when you start having

00:03:13.350 --> 00:03:14.770
more than two functional
groups.

00:03:14.770 --> 00:03:16.010
In this case, we have three.

00:03:16.010 --> 00:03:24.570
So we would call this
Z-4-methylhept-3-ene.

00:03:24.570 --> 00:03:27.780
And that's because the higher
priority functional groups are

00:03:27.780 --> 00:03:30.880
on the same side of
the double bond.

00:03:30.880 --> 00:03:32.390
Now let's do this
one over here.

00:03:32.390 --> 00:03:34.930
And someone pointed out,
rightly, that I had misspelled

00:03:34.930 --> 00:03:37.150
zusammen in the last video.

00:03:37.150 --> 00:03:40.880
It's actually spelled
like this, zusammen.

00:03:40.880 --> 00:03:43.260
I had spelled it with
two s's and one m.

00:03:43.260 --> 00:03:44.350
I guess you can forgive me.

00:03:44.350 --> 00:03:45.580
I don't speak German.

00:03:45.580 --> 00:03:46.770
But anyway, I thought I
would point that out.

00:03:46.770 --> 00:03:49.820
Now let's try to label this
thing right over here.

00:03:49.820 --> 00:03:52.530
So the first thing, this once
again is an alkene.

00:03:52.530 --> 00:03:55.510
Let's identify the longest
carbon chain here.

00:03:55.510 --> 00:03:59.160
So it looks like one, two,
three, four, five, six, seven,

00:03:59.160 --> 00:04:00.670
eight carbons.

00:04:00.670 --> 00:04:02.740
Double bonds are closer
to the left hand side.

00:04:02.740 --> 00:04:04.390
So we will start
numbering here.

00:04:04.390 --> 00:04:10.140
One, two, three, four, five,
six, seven, eight.

00:04:10.140 --> 00:04:13.770
So just the main chain is oct--
let me make sure I have

00:04:13.770 --> 00:04:21.310
some space here--
it is oct-3-ene.

00:04:21.310 --> 00:04:24.630
And then we have, well we have
one functional group sitting

00:04:24.630 --> 00:04:25.920
off of the main chain.

00:04:25.920 --> 00:04:31.460
We have this bromine sitting
right over there

00:04:31.460 --> 00:04:32.950
on the third carbon.

00:04:32.950 --> 00:04:36.345
So we would call this
3-bromooct-3-ene.

00:04:40.630 --> 00:04:44.400
And now we have to figure out
is it entgegen or zusammen.

00:04:44.400 --> 00:04:46.430
So if we look on the carbon on
the right hand side, it's

00:04:46.430 --> 00:04:48.410
pretty obvious that this is
the only functional group.

00:04:48.410 --> 00:04:49.720
We just have a hydrogen there.

00:04:49.720 --> 00:04:51.130
So let me circle it
in the magenta.

00:04:54.350 --> 00:04:56.550
And then on the left hand side
we have two functional groups.

00:04:56.550 --> 00:04:58.080
We have this [UNINTELLIGIBLE]

00:04:58.080 --> 00:05:00.900
bromo or we have a bromine
sitting right there.

00:05:00.900 --> 00:05:02.550
And then we have this
propyl group.

00:05:02.550 --> 00:05:06.260
And because this propyl group
is bigger, you might be

00:05:06.260 --> 00:05:08.310
tempted to say it takes
higher priority.

00:05:08.310 --> 00:05:12.580
But remember, in the
Cahn-Ingold-Prelog system, you

00:05:12.580 --> 00:05:15.860
give higher priority to
the atom that has a

00:05:15.860 --> 00:05:17.330
higher atomic number.

00:05:17.330 --> 00:05:20.100
Bromine has an atomic
number of 35.

00:05:20.100 --> 00:05:22.780
Carbon has an atomic
number of only 6.

00:05:22.780 --> 00:05:25.810
So Bromine is actually
higher priority.

00:05:25.810 --> 00:05:28.460
So this is the higher
priority functional

00:05:28.460 --> 00:05:31.240
group right over here.

00:05:31.240 --> 00:05:35.120
So now for deciding whether it's
entgegen or zusammen, we

00:05:35.120 --> 00:05:37.840
see that our higher priority
groups are apart.

00:05:37.840 --> 00:05:40.060
They're on opposite sides
of the double bond.

00:05:40.060 --> 00:05:41.620
This one is on top.

00:05:41.620 --> 00:05:43.190
This one is below.

00:05:43.190 --> 00:05:44.370
We are apart.

00:05:44.370 --> 00:05:47.120
So this is entgegen.

00:05:47.120 --> 00:05:50.095
Or we would write this is
E-3-bromooct-3-ene.

00:05:53.130 --> 00:05:56.850
And E is for-- just as a bit
of a refresher-- it's for

00:05:56.850 --> 00:06:01.660
entgegen, a word that I enjoy
saying, entgegen.

00:06:01.660 --> 00:06:02.910
There you go.


cis-trans and E-Z naming scheme for alkenes

WEBVTT
Kind: captions
Language: en

00:00:00.530 --> 00:00:03.420
If I were to come over to your
place and say, name this

00:00:03.420 --> 00:00:06.260
molecule, the first thing you
would do is you'd say, well,

00:00:06.260 --> 00:00:08.410
look, we have a double
bond, So we're

00:00:08.410 --> 00:00:10.550
dealing with an alkene.

00:00:10.550 --> 00:00:13.140
We have four carbons in
the longest chain.

00:00:13.140 --> 00:00:14.590
There's actually
one chain here.

00:00:14.590 --> 00:00:17.220
So it's one, two, three,
four carbons.

00:00:17.220 --> 00:00:20.770
So the prefix will be but-, and
regardless of which end

00:00:20.770 --> 00:00:24.830
you count from, the double bond
starts at the number two

00:00:24.830 --> 00:00:26.700
carbon, so this is but-2-ene.

00:00:31.600 --> 00:00:33.880
I'd say, well, that's very
good, and that is correct

00:00:33.880 --> 00:00:35.870
based on everything
we've learned.

00:00:35.870 --> 00:00:39.190
But what about what about
this molecule?

00:00:39.190 --> 00:00:41.840
What about the molecule
that looks like this?

00:00:47.550 --> 00:00:49.160
And you'd go through
the same process.

00:00:49.160 --> 00:00:50.740
You'd say it has
a double bond.

00:00:50.740 --> 00:00:51.850
It's an alkene.

00:00:51.850 --> 00:00:53.960
Our longest chain has
four carbons:

00:00:53.960 --> 00:00:56.110
one, two, three, four.

00:00:56.110 --> 00:00:59.590
Regardless of which end you
start counting from, the

00:00:59.590 --> 00:01:04.150
double bond starts at the number
two carbon: one, two,

00:01:04.150 --> 00:01:05.370
three, four.

00:01:05.370 --> 00:01:07.880
So once again, you say, hey,
Sal, that's also but-2-ene.

00:01:11.590 --> 00:01:14.710
And I'd point out that these
are each fundamentally

00:01:14.710 --> 00:01:15.790
different molecules.

00:01:15.790 --> 00:01:17.880
And the reason why they're
fundamentally different

00:01:17.880 --> 00:01:21.180
molecules is because this double
bond can't rotate.

00:01:21.180 --> 00:01:23.690
It's got that pi bond there
for that second bond that

00:01:23.690 --> 00:01:26.460
keeps this carbon-carbon
bond rigid.

00:01:26.460 --> 00:01:29.450
So it's not like the molecule
can switch configurations

00:01:29.450 --> 00:01:33.390
between this-- it's not like
it can switch conformations

00:01:33.390 --> 00:01:34.940
between this and that.

00:01:34.940 --> 00:01:38.540
It cannot rotate around this
double bond, so these are

00:01:38.540 --> 00:01:40.290
different molecules.

00:01:40.290 --> 00:01:47.530
These are different molecules
that will behave different

00:01:47.530 --> 00:01:48.840
chemically.

00:01:48.840 --> 00:01:51.070
And because they behave
different, we have to have

00:01:51.070 --> 00:01:52.630
different names for them.

00:01:52.630 --> 00:01:54.390
Now, there's two different
naming conventions.

00:01:54.390 --> 00:01:59.570
One is the simpler naming
convention, and it works when

00:01:59.570 --> 00:02:02.750
we have one functional group on
each of the carbons in the

00:02:02.750 --> 00:02:03.470
double bond.

00:02:03.470 --> 00:02:05.630
And then in the next two videos,
we'll talk about the

00:02:05.630 --> 00:02:08.250
slightly more advanced naming
scheme that will work when we

00:02:08.250 --> 00:02:10.280
have more than one
functional group.

00:02:10.280 --> 00:02:13.160
So the first way to name
it is if you have

00:02:13.160 --> 00:02:14.080
your functional groups.

00:02:14.080 --> 00:02:15.860
So let me circle the
functional groups.

00:02:15.860 --> 00:02:19.640
So in this top one, our
functional groups are on

00:02:19.640 --> 00:02:21.370
opposite sides.

00:02:21.370 --> 00:02:22.080
They're apart.

00:02:22.080 --> 00:02:24.770
They're on opposite sides of the
carbon-carbon double bond.

00:02:24.770 --> 00:02:27.130
This is on the top, This
is on the bottom.

00:02:27.130 --> 00:02:30.480
In this molecule right here, our
functional groups are on

00:02:30.480 --> 00:02:32.210
the same side.

00:02:32.210 --> 00:02:34.720
So when our functional groups
are on different sides, we

00:02:34.720 --> 00:02:37.400
could call it trans.

00:02:37.400 --> 00:02:40.670
We could call it trans,
literally, I believe, Latin

00:02:40.670 --> 00:02:43.760
for, apart, or Latin
for opposite.

00:02:43.760 --> 00:02:46.160
I'm not a Latin scholar,
so forgive me.

00:02:46.160 --> 00:02:49.010
But the functional groups
are apart, so we call it

00:02:49.010 --> 00:02:50.260
trans-but-2-ene.

00:02:52.060 --> 00:02:56.100
The other convention to use
comes from the German forepart

00:02:56.100 --> 00:02:57.760
and there we call it entgegen.

00:02:57.760 --> 00:03:01.360
And instead of writing out
entgegen, we write E in

00:03:01.360 --> 00:03:02.200
parentheses.

00:03:02.200 --> 00:03:03.990
So we would call them-- let me
just use different colors

00:03:03.990 --> 00:03:06.120
since this molecule
down here is blue.

00:03:06.120 --> 00:03:08.095
So we would call this
(E)-but-2-ene.

00:03:11.920 --> 00:03:14.560
These mean the same thing.

00:03:14.560 --> 00:03:16.190
(E)-but-2-ene.

00:03:16.190 --> 00:03:19.130
But this is now kind of the
standard convention.

00:03:19.130 --> 00:03:23.140
We'll see this notation where
you use entgegen, or (E), is

00:03:23.140 --> 00:03:24.300
actually more powerful.

00:03:24.300 --> 00:03:26.600
It can extend to when we have
more than one functional group

00:03:26.600 --> 00:03:27.510
on each carbon.

00:03:27.510 --> 00:03:33.020
Let me just make it clear that
the (E) stands for entgegen,

00:03:33.020 --> 00:03:39.250
which is German for apart, or
at least I believe it is.

00:03:39.250 --> 00:03:41.260
I can't speak German so I'll
just have to take people's

00:03:41.260 --> 00:03:42.280
words for it.

00:03:42.280 --> 00:03:44.870
Now, in this situation where our
functional groups are on

00:03:44.870 --> 00:03:50.970
the same side, you could call
this cis-but-2-ene.

00:03:50.970 --> 00:03:55.940
Cis, I believe, comes from the
Latin for together, or you

00:03:55.940 --> 00:03:57.190
could call it (Z)-but-2-ene.

00:04:03.760 --> 00:04:07.310
And you could imagine
this (Z) comes from

00:04:07.310 --> 00:04:09.820
the German for together.

00:04:09.820 --> 00:04:20.910
And it stands for zusammen,
which is German for together.

00:04:20.910 --> 00:04:22.190
And that's all you have to do.

00:04:22.190 --> 00:04:24.060
And in the next few videos,
we'll do a bunch of examples

00:04:24.060 --> 00:04:27.010
here so we can really figure out
whether to label something

00:04:27.010 --> 00:04:29.060
with either an (E) or a (Z).

00:04:29.060 --> 00:04:31.960
But I wanted expose you to the
cis- and trans- naming scheme,

00:04:31.960 --> 00:04:34.490
because that's sometimes used
for simpler molecules where

00:04:34.490 --> 00:04:36.550
you only have one functional
group on each side.

00:04:36.550 --> 00:04:38.880
But I want you to realize that
they're really trying to make

00:04:38.880 --> 00:04:39.760
the same differentiation.

00:04:39.760 --> 00:04:43.190
They're really just trying to
decide whether the functional

00:04:43.190 --> 00:04:46.340
groups on one side of a double
bond and on the other side of

00:04:46.340 --> 00:04:49.460
a double bond, whether they're
on the same side, cis-, or

00:04:49.460 --> 00:04:52.860
(Z), or zusammen, or on
different sides, trans- or

00:04:52.860 --> 00:04:54.110
(E), or entgegen.


Simplifying rates and ratios

WEBVTT
Kind: captions
Language: en

00:00:00.550 --> 00:00:04.390
Simplify the rate of cans of
soda compared to people.

00:00:04.390 --> 00:00:09.400
So this ratio here says that
we have 92 cans of soda for

00:00:09.400 --> 00:00:10.920
every 28 people.

00:00:10.920 --> 00:00:13.400
What we want to do is simplify
this, and really just putting

00:00:13.400 --> 00:00:16.930
this ratio, or this fraction,
in simplest form.

00:00:16.930 --> 00:00:19.670
So the best way to do that is
just to figure out what is the

00:00:19.670 --> 00:00:24.440
largest number, or the largest
common factor, of both 92 and

00:00:24.440 --> 00:00:28.480
28, and divide both of these
numbers by that common factor.

00:00:28.480 --> 00:00:29.800
So let's figure out
what it is.

00:00:29.800 --> 00:00:33.320
And to do that, let's just take
the prime factorization

00:00:33.320 --> 00:00:37.300
of 92, and then we'll do the
prime factorization of 28.

00:00:37.300 --> 00:00:46.820
So 92 is 2 times 46, which
is 2 times 23.

00:00:46.820 --> 00:00:49.360
And 23 is a prime number,
so we're done.

00:00:49.360 --> 00:00:51.940
92 is 2 times 2 times 23.

00:00:51.940 --> 00:00:57.400
And if we did the prime
factorization of 28, 28 is 2

00:00:57.400 --> 00:01:06.100
times 14, which is 2 times 7.

00:01:06.100 --> 00:01:14.150
So we can rewrite the 92 cans of
soda as 2 times 2 times 23

00:01:14.150 --> 00:01:31.530
cans of soda for every 2
times 2 times 7 people.

00:01:31.530 --> 00:01:34.920
Now, both of these numbers have
a 2 times 2 in it, or

00:01:34.920 --> 00:01:37.060
they're both divisible by 4.

00:01:37.060 --> 00:01:39.770
That is their greatest
common factor.

00:01:39.770 --> 00:01:42.210
So let's divide both the
top number and the

00:01:42.210 --> 00:01:44.060
bottom number by 4.

00:01:44.060 --> 00:01:47.625
So if you divide the top number
by 4, or if you divide

00:01:47.625 --> 00:01:51.960
it by 2 times 2, it will cancel
out right over there.

00:01:51.960 --> 00:01:55.410
And then if you do the bottom
number divided by 4, or 2

00:01:55.410 --> 00:01:58.330
times 2, it will cancel out
with that 2 times 2.

00:01:58.330 --> 00:02:04.080
And we are left with 23 cans of
soda for every 7 people, or

00:02:04.080 --> 00:02:07.740
7 people for every
23 cans of soda.

00:02:07.740 --> 00:02:08.320
And we're done!

00:02:08.320 --> 00:02:12.540
We've simplified the rate of
cans, or the ratio of cans, of

00:02:12.540 --> 00:02:14.260
soda compared to people.

00:02:14.260 --> 00:02:16.770
I guess they're considering this
a rate, so maybe they're

00:02:16.770 --> 00:02:24.490
saying how quickly do 7 people
consume cans over some period,

00:02:24.490 --> 00:02:26.700
or you can view it as a ratio.


Ratios as fractions in simplest form

WEBVTT
Kind: captions
Language: en

00:00:00.930 --> 00:00:05.400
Write 15:25 as a fraction
in simplest form.

00:00:05.400 --> 00:00:10.350
So 15 to 25 is just a ratio,
and we can write it.

00:00:10.350 --> 00:00:14.280
So they've given us 15 to 25.

00:00:14.280 --> 00:00:20.600
And you can write this ratio as
a fraction, as 15 over 25.

00:00:20.600 --> 00:00:23.270
And if we want to put this in
simplest form, we just have to

00:00:23.270 --> 00:00:26.390
think about what is the largest
number that divides

00:00:26.390 --> 00:00:28.830
into both 15 and 25?

00:00:28.830 --> 00:00:30.810
Or what is their greatest
common factor?

00:00:30.810 --> 00:00:33.470
When you just eyeball it, you
say, well, 5 goes into both of

00:00:33.470 --> 00:00:36.120
them, and I'm pretty sure that's
the largest number that

00:00:36.120 --> 00:00:38.940
divides into both, so let's
divide both by 5.

00:00:38.940 --> 00:00:41.430
If there is a larger number,
then we might be able to see

00:00:41.430 --> 00:00:43.240
it once we've simplified
it a little bit more.

00:00:43.240 --> 00:00:46.820
So let's divide the numerator
and the denominator by 5 and

00:00:46.820 --> 00:00:48.260
see what we get.

00:00:48.260 --> 00:00:52.560
So now we get 15 divided
by 5 is equal to 3.

00:00:52.560 --> 00:01:00.470
And 25 divided by 5 is equal
to 5, and now we have 3/5.

00:01:00.470 --> 00:01:04.910
3 and 5 don't share any common
factors greater than 1, so it

00:01:04.910 --> 00:01:06.750
is in simplest form.

00:01:06.750 --> 00:01:08.580
So we've done what they asked.

00:01:08.580 --> 00:01:10.830
We've written it as a fraction
in simplest form.

00:01:10.830 --> 00:01:13.090
We could also write this, if
we want to write it in this

00:01:13.090 --> 00:01:15.625
type of notation, as 3:5.


Solving unit rates problem

WEBVTT
Kind: captions
Language: en

00:00:00.620 --> 00:00:05.510
Jayda takes 3 hours to deliver
189 newspapers

00:00:05.510 --> 00:00:06.840
on her paper route.

00:00:06.840 --> 00:00:11.080
What is the rate per
hour at which she

00:00:11.080 --> 00:00:13.040
delivers the newspaper?

00:00:13.040 --> 00:00:16.610
So this first sentence tells us
that she delivers, or she

00:00:16.610 --> 00:00:26.180
takes, 3 hours to deliver
189 newspapers.

00:00:26.180 --> 00:00:32.840
So you have 3 hours for
every 189 newspapers.

00:00:32.840 --> 00:00:34.970
That's what the first
sentence told us.

00:00:34.970 --> 00:00:37.660
But we want to figure out the
rate per hour, or the

00:00:37.660 --> 00:00:41.380
newspapers per hour, so we can
really just flip this rate

00:00:41.380 --> 00:00:41.960
right here.

00:00:41.960 --> 00:00:51.460
So if we were to just flip it,
we would have 189 newspapers

00:00:51.460 --> 00:00:59.950
for every 3 hours, which is
really the same information.

00:00:59.950 --> 00:01:02.610
We're just flipping what's in
the numerator and what's in

00:01:02.610 --> 00:01:03.860
the denominator.

00:01:03.860 --> 00:01:07.340
Now we want to write it in as
simple as possible form, and

00:01:07.340 --> 00:01:09.940
let's see if this top number
is divisible by 3.

00:01:09.940 --> 00:01:14.240
1 plus 8 is 9, plus 9 is 18.

00:01:14.240 --> 00:01:15.810
So that is divisible by 3.

00:01:15.810 --> 00:01:19.120
So let's divide this numerator
and this denominator by 3 to

00:01:19.120 --> 00:01:20.500
simplify things.

00:01:20.500 --> 00:01:22.930
So if you divide 189 by 3.

00:01:22.930 --> 00:01:25.300
Let's do it over on the
side right here.

00:01:25.300 --> 00:01:28.450
3 goes into 189.

00:01:28.450 --> 00:01:30.500
3 goes and 18 six times.

00:01:30.500 --> 00:01:32.600
6 times 3 is 18.

00:01:32.600 --> 00:01:33.720
Subtract.

00:01:33.720 --> 00:01:35.190
Bring down the 9.

00:01:35.190 --> 00:01:37.220
18 minus 18 was nothing.

00:01:37.220 --> 00:01:40.380
3 goes into 9 exactly
three times.

00:01:40.380 --> 00:01:43.150
3 times 3 is 9, no remainder.

00:01:43.150 --> 00:01:50.880
So if you divide 189 by 3, you
get 63, and if you divide 3 by

00:01:50.880 --> 00:01:52.390
3, you're going to get 1.

00:01:52.390 --> 00:01:54.710
You have to divide both the
numerator and the denominator

00:01:54.710 --> 00:01:56.440
by the same number.

00:01:56.440 --> 00:02:00.490
So now we have 63 newspapers
for every 1 hour.

00:02:00.490 --> 00:02:06.070
Or we could write this as 63
over 1 newspapers per hour.

00:02:16.150 --> 00:02:20.280
Or we could write this as 63,
because 63 over 1 is the same

00:02:20.280 --> 00:02:30.230
thing as 63 newspapers
per hour.


Find an Unknown in a Proportion

WEBVTT
Kind: captions
Language: en

00:00:00.540 --> 00:00:02.310
We're asked to solve
the proportion

00:00:02.310 --> 00:00:07.670
8/36 is equal to 10/n.

00:00:07.670 --> 00:00:10.740
So we need to figure
out what n is.

00:00:10.740 --> 00:00:14.580
And the easiest way to do this
is to multiply both sides of

00:00:14.580 --> 00:00:17.630
this equation by both
denominators.

00:00:17.630 --> 00:00:20.520
So if we multiply both sides
of this equation by

00:00:20.520 --> 00:00:23.990
n, what do we get?

00:00:28.900 --> 00:00:32.020
The whole purpose of doing that
is so that this n in the

00:00:32.020 --> 00:00:34.270
denominator will cancel out
with this n, which is

00:00:34.270 --> 00:00:35.310
essentially in the numerator.

00:00:35.310 --> 00:00:37.810
You can view this as n/1.

00:00:37.810 --> 00:00:40.620
So if you do that, the left-hand
side of our equation

00:00:40.620 --> 00:00:48.660
becomes 8/36 times n, or you
can even view it as 8n/36

00:00:48.660 --> 00:00:52.430
because you can really
do this as n/1.

00:00:52.430 --> 00:00:57.200
So the left-hand side
becomes 8n/36.

00:00:57.200 --> 00:01:01.610
And then that will be equal
to 10/n times n/1.

00:01:01.610 --> 00:01:03.590
This n and that n cancel out,
and you're left with

00:01:03.590 --> 00:01:06.690
10/1, or just 10.

00:01:06.690 --> 00:01:09.880
Now we can multiply both
sides of this equation.

00:01:09.880 --> 00:01:12.130
To really get rid of that 36
in the denominator, we can

00:01:12.130 --> 00:01:17.090
multiply both sides by 36, or
you can imagine, by 36/1.

00:01:17.090 --> 00:01:18.120
Either way.

00:01:18.120 --> 00:01:21.470
36/1 is the same thing as 36.

00:01:21.470 --> 00:01:24.140
This 36 cancels out
with that 36.

00:01:24.140 --> 00:01:28.580
And on the left-hand side, we
have 8n, and on the right-hand

00:01:28.580 --> 00:01:33.080
side is equal to 10
times 36 is 360.

00:01:33.080 --> 00:01:37.260
Now to solve for n, we can just
divide both sides of this

00:01:37.260 --> 00:01:39.040
equation by 8.

00:01:39.040 --> 00:01:42.970
So if you divide that side by
8, and that side by 8, the

00:01:42.970 --> 00:01:46.080
left-hand side, the 8's will
cancel out, and you are left

00:01:46.080 --> 00:01:51.590
with n is equal to 360 divided
by 8, and then we can figure

00:01:51.590 --> 00:01:52.880
out what that actually is.

00:01:52.880 --> 00:01:54.990
8 goes into 360.

00:01:54.990 --> 00:01:58.835
So 8 is divisible not into
3, it's divisible

00:01:58.835 --> 00:02:01.110
into 36 four times.

00:02:01.110 --> 00:02:03.520
4 times 8 is 32.

00:02:03.520 --> 00:02:04.680
Subtract.

00:02:04.680 --> 00:02:06.540
6 minus 2 is 4.

00:02:06.540 --> 00:02:08.169
3 minus 3 is nothing.

00:02:08.169 --> 00:02:10.000
Bring down the 0.

00:02:10.000 --> 00:02:13.000
8 goes into 40 exactly
five times.

00:02:13.000 --> 00:02:16.860
5 times 8 is 40, and then
you have no remainder.

00:02:16.860 --> 00:02:24.930
So n is equal to 360/8, which is
the exact same thing as 45.

00:02:24.930 --> 00:02:28.270
So going back to our original
proportion, we now solved for

00:02:28.270 --> 00:02:39.270
n, and we know that 8/36 is the
same exact thing as 10/45.


Proportion validity example

WEBVTT
Kind: captions
Language: en

00:00:00.550 --> 00:00:05.510
Is the proportion true or false
that 3/12 or 3:12 is

00:00:05.510 --> 00:00:10.300
equal to 5/35 or 5:35?

00:00:10.300 --> 00:00:12.010
Now to figure this out, we
just have to figure out

00:00:12.010 --> 00:00:14.370
whether these are equivalent
fractions, and the easiest way

00:00:14.370 --> 00:00:17.670
to do that, is to put both of
them in simplified form, and

00:00:17.670 --> 00:00:19.380
see if we get the same answer.

00:00:19.380 --> 00:00:25.660
So let's try with 3/12 first.
So if we have 3/12, both the

00:00:25.660 --> 00:00:28.400
numerator and the denominator
are divisible by 3.

00:00:28.400 --> 00:00:30.090
So let's divide by 3.

00:00:30.090 --> 00:00:32.920
So divide the numerator by
3, and let's divide the

00:00:32.920 --> 00:00:34.490
denominator by 3.

00:00:34.490 --> 00:00:36.930
We get 3 divided by 3 is 1.

00:00:36.930 --> 00:00:39.120
12 divided by 3 is 4.

00:00:39.120 --> 00:00:42.460
So 3/12 is the same
thing is 1/4.

00:00:42.460 --> 00:00:47.290
Now let's try do the same
thing for 5/35.

00:00:47.290 --> 00:00:51.640
5 over 35-- I'm leaving some
space so we can divide-- well,

00:00:51.640 --> 00:00:54.550
these are both divisible by 5,
so let's divide the numerator

00:00:54.550 --> 00:00:57.230
and the denominator by 5.

00:00:57.230 --> 00:01:01.950
So if we divide the numerator by
5 and the denominator by 5,

00:01:01.950 --> 00:01:06.480
the numerator, 5 divided
by 5 is 1, and then 35

00:01:06.480 --> 00:01:08.420
divided by 5 is 7.

00:01:08.420 --> 00:01:14.170
So this thing is equivalent to
saying that 1/4 is equal to

00:01:14.170 --> 00:01:18.930
1/7, which is clearly
not true.

00:01:18.930 --> 00:01:23.880
This is clearly not true, so
the proportion is false.


Find an Unknown in a Proportion 2

WEBVTT
Kind: captions
Language: en

00:00:00.660 --> 00:00:05.500
A recipe for oatmeal cookies
calls for 2 cups of flour for

00:00:05.500 --> 00:00:08.670
every 3 cups of oatmeal.

00:00:08.670 --> 00:00:13.180
How much flour is needed for a
big batch of cookies that uses

00:00:13.180 --> 00:00:15.270
9 cups of oatmeal?

00:00:15.270 --> 00:00:19.810
So they tell us that we
have 2 cups of flour.

00:00:19.810 --> 00:00:21.060
Let me write that down.

00:00:27.480 --> 00:00:30.775
You need 2 cups of flour for
every 3 cups of oatmeal.

00:00:39.980 --> 00:00:42.810
Now, what we need to figure
out is how much flour is

00:00:42.810 --> 00:00:46.290
needed for a big batch that
uses 9 cups of oatmeal.

00:00:50.330 --> 00:00:51.700
We need to figure
out how much.

00:00:51.700 --> 00:00:54.910
So let's just call that amount
of flour we need for this

00:00:54.910 --> 00:00:56.510
larger batch, let's call it x.

00:00:56.510 --> 00:01:07.875
That's equal to x cups of flour
for 9 cups of oatmeal.

00:01:18.140 --> 00:01:20.830
All we're saying, look, we need
2 cups of flour for every

00:01:20.830 --> 00:01:21.810
3 cups of oatmeal.

00:01:21.810 --> 00:01:25.800
That has to be the same
as x for every 9 cups.

00:01:25.800 --> 00:01:27.630
The proportion has to hold.

00:01:27.630 --> 00:01:32.010
These ratios have to simplify
to the same fraction.

00:01:32.010 --> 00:01:34.550
Now, the easiest way to do this,
we can just get rid of

00:01:34.550 --> 00:01:37.090
the cups of flour and the cups
of oatmeal for now, and we can

00:01:37.090 --> 00:01:39.930
just view this as a simple
proportion problem where it's

00:01:39.930 --> 00:01:44.700
2/3 is equal to x/9.

00:01:44.700 --> 00:01:48.010
And the simplest way to solve
this is to multiply both sides

00:01:48.010 --> 00:01:51.770
of this equation by 9, and the
reason why we're multiplying

00:01:51.770 --> 00:01:54.730
by 9 is so it cancels out with
this 9 in the denominator.

00:01:54.730 --> 00:01:56.680
You can view it as multiplying
both sides of

00:01:56.680 --> 00:01:59.390
the equation by 9/1.

00:01:59.390 --> 00:02:05.050
So if you multiply both sides
by 9/1, the left-hand side,

00:02:05.050 --> 00:02:06.680
you'll have a 9 in the
numerator, 3 in the

00:02:06.680 --> 00:02:07.300
denominator.

00:02:07.300 --> 00:02:09.090
You can divide them both by 3.

00:02:09.090 --> 00:02:11.640
So 9 divided by 3 is 3.

00:02:11.640 --> 00:02:13.810
3 divided by 3 is 1.

00:02:13.810 --> 00:02:16.700
So your left side of the
equation is 3 times

00:02:16.700 --> 00:02:18.525
2/1, so it's 6/1.

00:02:21.870 --> 00:02:24.650
Well, this 9 in the numerator
and this 9 in the denominator,

00:02:24.650 --> 00:02:25.500
they cancel out.

00:02:25.500 --> 00:02:27.870
They can both be divided by 9.

00:02:27.870 --> 00:02:30.120
So they cancel out, so
that is equal to x/1.

00:02:33.570 --> 00:02:37.550
6/1 is the same thing as 6. x/1
is the same thing as x.

00:02:37.550 --> 00:02:41.680
So we get x is equal to 6.

00:02:41.680 --> 00:02:44.610
So we've just figured out, if
the recipe calls for 2 cups of

00:02:44.610 --> 00:02:47.870
flour for every 3 cups of
oatmeal, that means that we

00:02:47.870 --> 00:02:52.700
need 6 cups of flour for every
9 cups of oatmeal.

00:02:52.700 --> 00:02:56.050
So we figured out that
x is equal to 6.


Adding and subtracting decimals word problem

WEBVTT
Kind: captions
Language: en

00:00:00.780 --> 00:00:07.080
Leo has $4,522.08 in
his bank account.

00:00:07.080 --> 00:00:11.890
He deposits another
$875.50 and then

00:00:11.890 --> 00:00:14.380
withdraws $300 in cash.

00:00:14.380 --> 00:00:16.300
How much is left
in his account?

00:00:16.300 --> 00:00:20.280
So he's starting
with $4,522.08.

00:00:20.280 --> 00:00:21.830
Let's write that down.

00:00:21.830 --> 00:00:27.560
$4,522.08.

00:00:27.560 --> 00:00:35.680
And then he deposits, or he
adds, another $875.50.

00:00:35.680 --> 00:00:41.810
So he's going to add $875.50.

00:00:41.810 --> 00:00:43.500
When you deposit into an
account, you're putting

00:00:43.500 --> 00:00:46.090
something into the account, or
you're adding to the account.

00:00:46.090 --> 00:00:51.270
So after he adds that $875.50,
what does he have?

00:00:51.270 --> 00:00:54.030
We go back to the penny spot,
or we could view that as the

00:00:54.030 --> 00:00:54.760
hundredths.

00:00:54.760 --> 00:00:57.790
A penny is one hundredth
of a dollar.

00:00:57.790 --> 00:00:58.830
Let me switch colors.

00:00:58.830 --> 00:01:01.210
We have 8 plus 0 is 8.

00:01:01.210 --> 00:01:03.120
0 plus 5 is 5.

00:01:03.120 --> 00:01:05.150
We have the decimal
right there.

00:01:05.150 --> 00:01:07.630
2 plus 5 is 7.

00:01:07.630 --> 00:01:09.920
2 plus 7 is 9.

00:01:09.920 --> 00:01:12.240
5 plus 8 is 13.

00:01:12.240 --> 00:01:15.930
Put the 3 down here and regroup
the 1, or carry the 1.

00:01:15.930 --> 00:01:17.710
1 plus 4 is 5.

00:01:17.710 --> 00:01:26.030
So after the $875.50 deposit,
he has $5,397.58.

00:01:26.030 --> 00:01:32.670
Then he withdraws $300 in cash,
or he takes out $300, so

00:01:32.670 --> 00:01:34.340
we'll have to subtract that.

00:01:34.340 --> 00:01:43.320
So then he withdraws $300 and
I just added some trailing

00:01:43.320 --> 00:01:45.310
zeroes after the decimal.

00:01:45.310 --> 00:01:49.210
$300 is the same thing as
$300.00 and zero cents.

00:01:49.210 --> 00:01:50.475
And then we subtract.

00:01:53.260 --> 00:01:56.120
8 minus 0 is 8.

00:01:56.120 --> 00:01:58.370
5 minus 0 is 5.

00:01:58.370 --> 00:02:00.000
We have our decimal
right there.

00:02:00.000 --> 00:02:02.460
7 minus 0 is 7.

00:02:02.460 --> 00:02:04.640
9 minus 0 is 9.

00:02:04.640 --> 00:02:10.919
3 minus 3 is 0, and then 5
minus nothing here is 5.

00:02:10.919 --> 00:02:14.830
So he's the left with, in
his account, $5,097.58.


Subtracting decimals example 1

WEBVTT
Kind: captions
Language: en

00:00:00.500 --> 00:00:07.540
We need to calculate 9.005 minus
3.6, or we could view it

00:00:07.540 --> 00:00:13.130
as 9 and 5 thousandths
minus 3 and 6 tenths.

00:00:13.130 --> 00:00:15.630
Whenever you do a subtracting
decimals problem, the most

00:00:15.630 --> 00:00:17.310
important thing, and this is
true when you're adding

00:00:17.310 --> 00:00:20.180
decimals as well, is you have
to line up the decimals.

00:00:20.180 --> 00:00:31.880
So this is 9.005 minus 3.6.

00:00:31.880 --> 00:00:34.870
So we've lined up the decimals,
and now we're ready

00:00:34.870 --> 00:00:36.270
to subtract.

00:00:36.270 --> 00:00:38.110
Now we can subtract.

00:00:38.110 --> 00:00:39.210
So we start up here.

00:00:39.210 --> 00:00:41.110
We have 5 minus nothing.

00:00:41.110 --> 00:00:44.860
You can imagine this 3.6, or
this 3 and 6 tenths, we could

00:00:44.860 --> 00:00:47.750
add two zeroes right here, and
it would be the same thing as

00:00:47.750 --> 00:00:52.210
3 and 600 thousandths, which is
the same thing as 6 tenths.

00:00:52.210 --> 00:00:54.860
And when you look at it that
way, you'd say, OK, 5 minus 0

00:00:54.860 --> 00:00:56.820
is nothing, and you just
write a 5 right there.

00:00:56.820 --> 00:00:58.585
Or you could have said, if
there's nothing there, it

00:00:58.585 --> 00:01:00.640
would have been 5 minus
nothing is 5.

00:01:00.640 --> 00:01:04.230
Then you have 0 minus
0, which is just 0.

00:01:04.230 --> 00:01:07.480
And then you have a 0 minus 6.

00:01:07.480 --> 00:01:10.070
And you can't subtract
6 from 0.

00:01:10.070 --> 00:01:12.620
So we need to get something into
this space right here,

00:01:12.620 --> 00:01:15.410
and what we essentially are
going to do is regroup.

00:01:15.410 --> 00:01:20.190
We're going to take one 1 from
the 9, so let's do that.

00:01:20.190 --> 00:01:24.680
So let's take one 1 from the
9, so it becomes an 8.

00:01:24.680 --> 00:01:26.310
And we need to do something
with that one 1.

00:01:26.310 --> 00:01:28.580
We're going to put it
in the tenths place.

00:01:28.580 --> 00:01:32.340
Now remember, one whole
is equal to 10 tenths.

00:01:32.340 --> 00:01:33.980
This is the tenths place.

00:01:33.980 --> 00:01:36.890
So then this will become 10.

00:01:36.890 --> 00:01:39.070
Sometimes it's taught that
you're borrowing the 1, but

00:01:39.070 --> 00:01:41.730
you're really taking it, and
you're actually taking 10 from

00:01:41.730 --> 00:01:43.440
the place to your left.

00:01:43.440 --> 00:01:46.940
So one whole is 10 tenths, we're
in the tenths place.

00:01:46.940 --> 00:01:48.835
So you have 10 minus 6.

00:01:48.835 --> 00:01:50.220
Let me switch colors.

00:01:50.220 --> 00:01:52.430
10 minus 6 is 4.

00:01:52.430 --> 00:01:55.550
You have your decimal right
there, and then you have 8

00:01:55.550 --> 00:01:58.390
minus 3 is 5.

00:01:58.390 --> 00:02:03.675
So 9.005 minus 3.6 is 5.405.


Multiplying decimals example

WEBVTT
Kind: captions
Language: en

00:00:00.430 --> 00:00:06.980
We're asked to multiply 32.12,
or 32 and 12 hundredths, times

00:00:06.980 --> 00:00:10.620
0.5, or just 5 tenths.

00:00:10.620 --> 00:00:12.630
Now when you multiply decimals,
you multiply them

00:00:12.630 --> 00:00:15.700
the exact same way you would
multiply whole numbers, and

00:00:15.700 --> 00:00:18.380
then you count the number of
spaces behind the decimal you

00:00:18.380 --> 00:00:21.330
have in your two numbers you're
multiplying, and you're

00:00:21.330 --> 00:00:23.720
going to have that many spaces
in your product.

00:00:23.720 --> 00:00:25.340
Let me show you what
I'm talking about.

00:00:25.340 --> 00:00:27.320
So let's just multiply
these two characters.

00:00:27.320 --> 00:00:35.720
So we have 32.12 times 0.5.

00:00:35.720 --> 00:00:38.670
And when you write them out, you
can just push both of them

00:00:38.670 --> 00:00:39.710
all the way to the right.

00:00:39.710 --> 00:00:41.530
You could almost ignore
the decimal.

00:00:41.530 --> 00:00:44.285
Right now, you should write the
decimal where they belong,

00:00:44.285 --> 00:00:48.660
but you can almost pretend that
this is 3,212 times 5,

00:00:48.660 --> 00:00:51.580
and then we'll worry about
the decimals in a second.

00:00:51.580 --> 00:00:52.920
So let's get started.

00:00:52.920 --> 00:00:56.390
So if we were just multiplying
5 times 3,212, we would say,

00:00:56.390 --> 00:00:59.540
well, 5 times 2 is 10.

00:00:59.540 --> 00:01:01.030
Regroup the 1.

00:01:01.030 --> 00:01:08.860
5 times 1 is 5, plus 1 is 6.

00:01:08.860 --> 00:01:14.260
5 times 2 is 10.

00:01:14.260 --> 00:01:15.720
Regroup the 1.

00:01:15.720 --> 00:01:23.400
And then finally, you have 5
times 3 is 15, plus 1 is 16.

00:01:23.400 --> 00:01:26.800
And then we don't have
any other places.

00:01:26.800 --> 00:01:29.800
If we were just doing this as
05, we wouldn't multiply 0

00:01:29.800 --> 00:01:30.480
times this whole thing.

00:01:30.480 --> 00:01:32.240
We would just get 0 anyway.

00:01:32.240 --> 00:01:36.000
So just 5 times 3,212 gives
us this number.

00:01:36.000 --> 00:01:38.700
But now we want to care
about the decimals.

00:01:38.700 --> 00:01:42.740
We just have to count the total
number of spaces or

00:01:42.740 --> 00:01:45.710
places we have behind the
decimal point in the two

00:01:45.710 --> 00:01:46.750
numbers we're multiplying.

00:01:46.750 --> 00:01:52.380
So we have one, two, three
spaces, or three numbers, to

00:01:52.380 --> 00:01:55.090
the right of the decimals in
the two numbers that we're

00:01:55.090 --> 00:01:55.970
multiplying.

00:01:55.970 --> 00:01:58.990
So we need that many numbers to
the right of the decimal in

00:01:58.990 --> 00:01:59.530
our answer.

00:01:59.530 --> 00:02:04.910
So we go one, two, three, put
the decimal right over there.

00:02:04.910 --> 00:02:11.080
So 32.12 times 0.5 is 16.060.

00:02:11.080 --> 00:02:13.220
And this trailing zero right
here we can ignore, because

00:02:13.220 --> 00:02:15.390
it's really not adding any
information there.

00:02:15.390 --> 00:02:19.200
So we could just write
this as 16.06.

00:02:19.200 --> 00:02:21.780
The last thing you want to do
is just make sure that this

00:02:21.780 --> 00:02:22.670
makes sense.

00:02:22.670 --> 00:02:26.530
You have a number that's
almost 32, and we're

00:02:26.530 --> 00:02:27.990
multiplying it by 0.5.

00:02:27.990 --> 00:02:33.860
Remember, 0.5 is the same thing
as 5 over 10, which is

00:02:33.860 --> 00:02:36.090
the same thing as 1/2.

00:02:36.090 --> 00:02:39.670
So we're really multiplying
32.12 times 1/2.

00:02:39.670 --> 00:02:43.100
We're trying to figure out what
one half of 32.12 is.

00:02:43.100 --> 00:02:49.640
And half of 32 is 16, and half
of 0.12 0.06, so this makes

00:02:49.640 --> 00:02:51.450
complete sense.


Multiplying Decimals 2

WEBVTT
Kind: captions
Language: en

00:00:00.550 --> 00:00:04.010
A single postage stamp
costs $0.44.

00:00:04.010 --> 00:00:07.930
How much would a roll of
1,000 stamps cost?

00:00:07.930 --> 00:00:13.570
So we're going to have 1,000
stamps, and each of them costs

00:00:13.570 --> 00:00:16.480
$0.44, so we can multiply
the 1,000 stamps

00:00:16.480 --> 00:00:24.680
times $0.44 per stamp.

00:00:24.680 --> 00:00:26.680
And then we just have to
multiply the two numbers.

00:00:26.680 --> 00:00:30.000
Now when you first multiply
decimals, you can just pretend

00:00:30.000 --> 00:00:32.229
like they're whole numbers,
and then worry about the

00:00:32.229 --> 00:00:33.840
decimals later.

00:00:33.840 --> 00:00:38.500
So we can view this as 1,000
times 44, and then worry about

00:00:38.500 --> 00:00:38.970
the decimals.

00:00:38.970 --> 00:00:40.560
What's 1,000 times 44?

00:00:40.560 --> 00:00:41.310
You could work it out.

00:00:41.310 --> 00:00:43.040
You could say, OK,
4 times 0 is 0.

00:00:43.040 --> 00:00:43.970
4 times 0 is 0.

00:00:43.970 --> 00:00:45.220
4 times 0 is 0.

00:00:47.470 --> 00:00:48.680
4 times 1 is 4.

00:00:48.680 --> 00:00:50.920
You get 4,000 here, And you
put a zero here, and you

00:00:50.920 --> 00:00:52.610
multiply that, you get 40,000.

00:00:52.610 --> 00:00:53.650
You'd add it all up.

00:00:53.650 --> 00:00:57.010
But I think we know from
experience, dealing with

00:00:57.010 --> 00:01:01.010
multiplying by powers of ten,
or by multiples of ten, that

00:01:01.010 --> 00:01:05.379
really, 44 times 1,000 is just
44,000, so we can just write

00:01:05.379 --> 00:01:06.270
it out here.

00:01:06.270 --> 00:01:12.220
So 44 times 1,000 is 44,000.

00:01:12.220 --> 00:01:13.620
Let me not put a comma
there just yet.

00:01:16.510 --> 00:01:18.360
That's 44 times 1,000.

00:01:18.360 --> 00:01:19.560
Now this isn't 44.

00:01:19.560 --> 00:01:21.200
This is 0.44.

00:01:21.200 --> 00:01:26.120
So in both numbers that we're
multiplying, we have exactly

00:01:26.120 --> 00:01:29.540
one, two numbers to the
right of the decimal.

00:01:29.540 --> 00:01:33.540
So our answer, our product, has
to have two numbers to the

00:01:33.540 --> 00:01:35.190
right of the decimal.

00:01:35.190 --> 00:01:36.640
So we count from the right.

00:01:36.640 --> 00:01:38.370
We count one, two.

00:01:38.370 --> 00:01:40.510
Stick the decimal right there.

00:01:40.510 --> 00:01:44.640
So our answer is 440.00, and
these trailing zeroes really

00:01:44.640 --> 00:01:45.960
add nothing there.

00:01:45.960 --> 00:01:49.120
So 1,000 times 0.44,
or forty-four

00:01:49.120 --> 00:01:52.700
cents really, is 440.

00:01:52.700 --> 00:01:57.850
Or it's going to cost us $440
to buy 1,000 stamps, which

00:01:57.850 --> 00:01:59.030
makes sense.

00:01:59.030 --> 00:02:02.080
Because 0.44, think about it.

00:02:02.080 --> 00:02:04.240
It's a little bit
less than half.

00:02:04.240 --> 00:02:05.720
0.5 would be half.

00:02:05.720 --> 00:02:08.780
So this is a little bit less
than half of $1,000.

00:02:08.780 --> 00:02:09.960
A half would be $500.

00:02:09.960 --> 00:02:12.229
This is a little bit less.


Dividing Decimals 2

WEBVTT
Kind: captions
Language: en

00:00:00.530 --> 00:00:06.550
We need to figure out what
99.061 divided by 100 is.

00:00:06.550 --> 00:00:17.210
So we are figuring out what
99.061 divided by 100.

00:00:17.210 --> 00:00:19.150
So in this situation,
our divisor is

00:00:19.150 --> 00:00:20.260
already a whole number.

00:00:20.260 --> 00:00:25.200
So we don't have to do any of
that multiplying by 10 or 100

00:00:25.200 --> 00:00:26.570
to move the decimal
over to the right.

00:00:26.570 --> 00:00:29.060
It's already a whole number,
so we're ready to divide.

00:00:29.060 --> 00:00:31.130
But the first thing we want to
do in this, just to make sure

00:00:31.130 --> 00:00:33.850
we don't make any mistakes, is
make sure we put the decimal

00:00:33.850 --> 00:00:34.580
in the right place.

00:00:34.580 --> 00:00:36.720
So the decimal is going to
sit right over here.

00:00:36.720 --> 00:00:38.600
This is where it was sitting
before, so this is where it

00:00:38.600 --> 00:00:40.480
will sit in our quotient.

00:00:40.480 --> 00:00:43.310
And now we are ready
to divide.

00:00:43.310 --> 00:00:44.780
So the first thing we want
to say is, well,

00:00:44.780 --> 00:00:46.770
does 100 go into 9?

00:00:46.770 --> 00:00:47.560
Well, no it doesn't.

00:00:47.560 --> 00:00:49.890
So does 100 go into 99?

00:00:49.890 --> 00:00:51.090
No, it doesn't.

00:00:51.090 --> 00:00:53.190
And if we want, we could put a
zero here, or we could just

00:00:53.190 --> 00:00:53.670
keep going.

00:00:53.670 --> 00:00:55.030
We'll add the 0 at the end.

00:00:55.030 --> 00:00:58.210
So 100 doesn't go into 9,
it doesn't go into 99.

00:00:58.210 --> 00:01:03.520
Does 100 go into 990?

00:01:03.520 --> 00:01:04.280
Sure!

00:01:04.280 --> 00:01:06.220
It'll go nine times.

00:01:06.220 --> 00:01:09.310
It goes into 990 nine times.

00:01:09.310 --> 00:01:12.060
So that's why we put the 9 above
the 0, because we had to

00:01:12.060 --> 00:01:14.730
get all the way to the 0 for the
100 to be divisible into

00:01:14.730 --> 00:01:15.560
the number.

00:01:15.560 --> 00:01:18.610
100 goes into 990 nine times.

00:01:18.610 --> 00:01:22.050
9 times 100 is 900.

00:01:22.050 --> 00:01:24.020
And then we can subtract.

00:01:24.020 --> 00:01:27.080
So 990 minus 900 is 90.

00:01:27.080 --> 00:01:28.520
We can do that in our heads.

00:01:28.520 --> 00:01:29.690
You can say, 0 minus 0 is 0.

00:01:29.690 --> 00:01:31.460
9 minus 0 is 9.

00:01:31.460 --> 00:01:33.040
These guys cancel out.

00:01:33.040 --> 00:01:37.840
Now we can bring down this 6.

00:01:37.840 --> 00:01:43.580
100 goes into 906 nine times.

00:01:43.580 --> 00:01:48.440
9 times 100 is 900, and
then we can subtract.

00:01:48.440 --> 00:01:51.780
906 minus 900 is
going to be 6.

00:01:51.780 --> 00:01:53.675
And then we bring down the 1.

00:02:00.260 --> 00:02:02.240
100 goes into 61.

00:02:02.240 --> 00:02:02.730
It doesn't!

00:02:02.730 --> 00:02:04.135
It goes into it zero times.

00:02:06.930 --> 00:02:09.210
0 times 100 is 0.

00:02:09.210 --> 00:02:12.920
And then when you subtract, you
have a remainder of 61.

00:02:12.920 --> 00:02:16.340
Now, you might be tempted to
say, OK, it goes into it--

00:02:16.340 --> 00:02:20.670
well, we could always put a
leading 0 here-- 0.990 times

00:02:20.670 --> 00:02:23.490
with a remainder of 61.

00:02:23.490 --> 00:02:25.940
First of all, that's
not right.

00:02:25.940 --> 00:02:29.890
The remainder isn't 61, because
we're now to the right

00:02:29.890 --> 00:02:30.960
of the decimal point.

00:02:30.960 --> 00:02:32.880
But in general, whenever you're
dividing to decimals,

00:02:32.880 --> 00:02:34.140
you want to keep dividing.

00:02:34.140 --> 00:02:35.910
You don't want to
have remainder.

00:02:35.910 --> 00:02:38.160
And the best way to keep
dividing is to remember that

00:02:38.160 --> 00:02:40.680
this has as many trailing zeroes
on it as you want.

00:02:40.680 --> 00:02:42.320
They're not really changing
the number.

00:02:42.320 --> 00:02:45.340
So we can throw a bunch of
zeroes to the right of here,

00:02:45.340 --> 00:02:46.710
as many as we need.

00:02:46.710 --> 00:02:48.700
So let's throw a
zero right now.

00:02:48.700 --> 00:02:49.950
Bring it down.

00:02:53.210 --> 00:02:58.750
100 goes into 610 six times.

00:02:58.750 --> 00:03:01.860
6 times 100 is 600.

00:03:01.860 --> 00:03:03.460
And then we subtract.

00:03:03.460 --> 00:03:06.060
610 minus 600 is 10.

00:03:06.060 --> 00:03:09.350
We don't want to have a
remainder, so we keep going.

00:03:09.350 --> 00:03:15.190
So let's throw another zero
here and bring it down.

00:03:15.190 --> 00:03:16.940
So we have another zero there.

00:03:16.940 --> 00:03:22.400
100 goes into 100 exactly
one time.

00:03:22.400 --> 00:03:25.210
1 times 100 is 100.

00:03:25.210 --> 00:03:27.670
And then now when you
subtract, we have no

00:03:27.670 --> 00:03:30.000
remainder, and we
are satisfied.

00:03:30.000 --> 00:03:30.840
And we're done.

00:03:30.840 --> 00:03:32.140
And sometimes you're going to
see that you're going to have

00:03:32.140 --> 00:03:34.100
to keep doing it, and you're
going to start having repeated

00:03:34.100 --> 00:03:35.910
numbers up here, and strange
things up here.

00:03:35.910 --> 00:03:37.720
And there's other ways
we'll deal with that.

00:03:37.720 --> 00:03:41.030
But in this circumstance, you
just want to keep going.

00:03:41.030 --> 00:03:44.050
You want to keep going until
you have no remainder.

00:03:44.050 --> 00:03:51.820
So our final answer is
99.061 divided by

00:03:51.820 --> 00:04:00.650
100 is equal to 0.99061.

00:04:00.650 --> 00:04:02.770
And I just put a leading
zero here.

00:04:02.770 --> 00:04:04.680
Sometimes it makes it easier
to read, and you make sure

00:04:04.680 --> 00:04:06.970
people understand that there's
a decimal there.

00:04:06.970 --> 00:04:09.890
It just makes it less
prone to errors.

00:04:09.890 --> 00:04:11.840
And we are done.

00:04:11.840 --> 00:04:14.080
And just to make the point,
this actually makes sense.

00:04:14.080 --> 00:04:18.690
99 is a little bit less than
100, so 99 divided by 100 is

00:04:18.690 --> 00:04:20.620
going to be a little
bit less than 1.

00:04:20.620 --> 00:04:24.590
And this number is a little
bit less than 1.


Dividing by a multi-digit decimal

WEBVTT
Kind: captions
Language: en

00:00:00.490 --> 00:00:07.760
We need to divide 0.25
into 1.03075.

00:00:07.760 --> 00:00:11.260
Now the first thing you want to
do when your divisor, the

00:00:11.260 --> 00:00:13.690
number that you're dividing into
the other number, is a

00:00:13.690 --> 00:00:17.850
decimal, is to multiply it by
10 enough times so that it

00:00:17.850 --> 00:00:19.990
becomes a whole number
so you can shift the

00:00:19.990 --> 00:00:21.220
decimal to the right.

00:00:21.220 --> 00:00:23.620
So every time you multiply
something by 10, you're

00:00:23.620 --> 00:00:26.170
shifting the decimal over
to the right once.

00:00:26.170 --> 00:00:27.620
So in this case, we want
to switch it over the

00:00:27.620 --> 00:00:29.310
right once and twice.

00:00:29.310 --> 00:00:34.690
So 0.25 times 10 twice is the
same thing as 0.25 times 100,

00:00:34.690 --> 00:00:38.190
and we'll turn the
0.25 into 25.

00:00:38.190 --> 00:00:41.250
Now if you do that with the
divisor, you also have to do

00:00:41.250 --> 00:00:42.860
that with the dividend,
the number that

00:00:42.860 --> 00:00:43.920
you're dividing into.

00:00:43.920 --> 00:00:47.220
So we also have to multiply this
by 10 twice, or another

00:00:47.220 --> 00:00:49.190
way of doing it is shift
the decimal over

00:00:49.190 --> 00:00:50.560
to the right twice.

00:00:50.560 --> 00:00:52.680
So we shift it over
once, twice.

00:00:52.680 --> 00:00:55.440
It will sit right over here.

00:00:55.440 --> 00:00:57.180
And to see why that makes
sense, you just have to

00:00:57.180 --> 00:01:00.700
realize that this expression
right here, this division

00:01:00.700 --> 00:01:14.840
problem, is the exact same
thing as having 1.03075

00:01:14.840 --> 00:01:21.310
divided by 0.25.

00:01:21.310 --> 00:01:25.650
And so we're multiplying
the 0.25 by 10 twice.

00:01:25.650 --> 00:01:28.590
We're essentially multiplying
it by 100.

00:01:28.590 --> 00:01:30.960
Let me do that in a
different color.

00:01:30.960 --> 00:01:34.750
We're multiplying it by 100
in the denominator.

00:01:34.750 --> 00:01:35.760
This is the divisor.

00:01:35.760 --> 00:01:38.670
We're multiplying it by 100, so
we also have to do the same

00:01:38.670 --> 00:01:41.040
thing to the numerator, if we
don't want to change this

00:01:41.040 --> 00:01:42.720
expression, if we don't want
to change the number.

00:01:42.720 --> 00:01:45.400
So we also have to multiply
that by 100.

00:01:45.400 --> 00:01:48.050
And when you do that,
this becomes 25, and

00:01:48.050 --> 00:01:52.200
this becomes 103.075.

00:01:52.200 --> 00:01:53.400
Now let me just rewrite this.

00:01:53.400 --> 00:01:55.520
Sometimes if you're doing this
in a workbook or something,

00:01:55.520 --> 00:01:57.240
you don't have to rewrite it as
long as you remember where

00:01:57.240 --> 00:01:57.910
the decimal is.

00:01:57.910 --> 00:01:59.340
But I'm going to rewrite
it, just so it's

00:01:59.340 --> 00:02:00.480
a little bit neater.

00:02:00.480 --> 00:02:03.330
So we multiplied both
the divisor and

00:02:03.330 --> 00:02:05.040
the dividend by 100.

00:02:05.040 --> 00:02:17.590
This problem becomes 25
divided into 103.075.

00:02:17.590 --> 00:02:20.130
These are going to result in
the exact same quotient.

00:02:20.130 --> 00:02:22.160
They're the exact same fraction,
if you want to view

00:02:22.160 --> 00:02:22.580
it that way.

00:02:22.580 --> 00:02:26.430
We've just multiplied both the
numerator and the denominator

00:02:26.430 --> 00:02:29.720
by 100 to shift the decimal
over to the right twice.

00:02:29.720 --> 00:02:32.560
Now that we've done that,
we're ready to divide.

00:02:32.560 --> 00:02:35.520
So the first thing, we have 25
here, and there's always a

00:02:35.520 --> 00:02:38.160
little bit of an art to dividing
something by a

00:02:38.160 --> 00:02:41.660
multiple-digit number, so we'll
see how well we can do.

00:02:41.660 --> 00:02:43.810
So 25 does not go into 1.

00:02:43.810 --> 00:02:45.750
25 does not go into 10.

00:02:45.750 --> 00:02:48.410
25 does go into 103.

00:02:48.410 --> 00:02:51.400
We know that 4 times 25
is 100, so 25 goes

00:02:51.400 --> 00:02:53.880
into 100 four times.

00:02:53.880 --> 00:02:56.540
4 times 5 is 20.

00:02:56.540 --> 00:02:59.840
4 times 2 is 8, plus 2 is 100.

00:02:59.840 --> 00:03:00.990
We knew that.

00:03:00.990 --> 00:03:02.600
Four quarters is $1.00.

00:03:02.600 --> 00:03:04.130
It's 100 cents.

00:03:04.130 --> 00:03:05.590
And now we subtract.

00:03:05.590 --> 00:03:11.920
103 minus 100 is going to
be 3, and now we can

00:03:11.920 --> 00:03:14.100
bring down this 0.

00:03:14.100 --> 00:03:16.640
So we bring down that 0 there.

00:03:16.640 --> 00:03:20.710
25 goes into 30 one time.

00:03:20.710 --> 00:03:22.210
And if we want, we could
immediately put

00:03:22.210 --> 00:03:23.070
this decimal here.

00:03:23.070 --> 00:03:25.400
We don't have to wait until
the end of the problem.

00:03:25.400 --> 00:03:27.930
This decimal sits right in that
place, so we could always

00:03:27.930 --> 00:03:30.730
have that decimal sitting right
there in our quotient or

00:03:30.730 --> 00:03:31.980
in our answer.

00:03:34.010 --> 00:03:36.690
So we were at 25 goes
into 30 one time.

00:03:36.690 --> 00:03:43.970
1 times 25 is 25, and then
we can subtract.

00:03:43.970 --> 00:03:46.550
30 minus 25, well,
that's just 5.

00:03:46.550 --> 00:03:48.510
I mean, we can do all this
borrowing business, or

00:03:48.510 --> 00:03:49.140
regrouping.

00:03:49.140 --> 00:03:50.410
This can become a 10.

00:03:50.410 --> 00:03:51.570
This becomes a 2.

00:03:51.570 --> 00:03:53.350
10 minus 5 is 5.

00:03:53.350 --> 00:03:55.200
2 minus 2 is nothing.

00:03:55.200 --> 00:03:59.250
But anyway, 30 minus 25 is 5.

00:03:59.250 --> 00:04:02.860
Now we can bring down this 7.

00:04:02.860 --> 00:04:06.270
25 goes into 57 two
times, right?

00:04:06.270 --> 00:04:08.780
25 times 2 is 50.

00:04:08.780 --> 00:04:11.940
25 goes into 57 two times.

00:04:11.940 --> 00:04:15.130
2 times 25 is 50.

00:04:15.130 --> 00:04:16.940
And now we subtract again.

00:04:16.940 --> 00:04:19.950
57 minus 50 is 7.

00:04:19.950 --> 00:04:21.760
And now we're almost done.

00:04:24.360 --> 00:04:28.280
We bring down that 5
right over there.

00:04:28.280 --> 00:04:34.150
25 goes into 75 three times.

00:04:34.150 --> 00:04:36.610
3 times 25 is 75.

00:04:36.610 --> 00:04:39.390
3 times 5 is 15.

00:04:39.390 --> 00:04:40.240
Regroup the 1.

00:04:40.240 --> 00:04:40.980
We can ignore that.

00:04:40.980 --> 00:04:41.920
That was from before.

00:04:41.920 --> 00:04:44.960
3 times 2 is 6, plus 1 is 7.

00:04:44.960 --> 00:04:46.260
So you can see that.

00:04:46.260 --> 00:04:51.540
And then we subtract, and then
we have no remainder.

00:04:51.540 --> 00:04:59.110
So 25 goes into 103.075 exactly
4.123 times, which

00:04:59.110 --> 00:05:02.100
makes sense, because 25 goes
into 100 about four times.

00:05:02.100 --> 00:05:04.080
This is a little bit larger than
100, so it's going to be

00:05:04.080 --> 00:05:05.740
a little bit more
than four times.

00:05:05.740 --> 00:05:07.920
And that's going to be the
exact same answer as the

00:05:07.920 --> 00:05:16.600
number of times that 0.25
goes into 1.03075.

00:05:16.600 --> 00:05:21.520
This will also be 4.123.

00:05:21.520 --> 00:05:24.580
So this fraction, or this
expression, is the exact same

00:05:24.580 --> 00:05:29.730
thing as 4.123.

00:05:29.730 --> 00:05:31.340
And we're done!


Multiplying decimals word problem

WEBVTT
Kind: captions
Language: en

00:00:00.490 --> 00:00:07.030
What is the cost of 14.6 gallons
of gasoline at $2.70

00:00:07.030 --> 00:00:08.290
per gallon?

00:00:08.290 --> 00:00:15.600
So we have 14.6 gallons,
and each gallon's

00:00:15.600 --> 00:00:17.300
going to cost $2.70.

00:00:17.300 --> 00:00:21.530
Or we can even view $2.70
as 2.7 dollars.

00:00:21.530 --> 00:00:25.040
Let's just multiply times 2.7.

00:00:25.040 --> 00:00:26.870
It makes things a little
bit simpler.

00:00:26.870 --> 00:00:30.490
I think you'll appreciate $2.70
is the same thing as 2.7

00:00:30.490 --> 00:00:32.340
dollars per gallon.

00:00:32.340 --> 00:00:35.030
So let's multiply this out.

00:00:35.030 --> 00:00:38.620
So first we have, and just as a
reminder, when you multiply

00:00:38.620 --> 00:00:42.280
decimals, you just have to treat
the numbers like whole

00:00:42.280 --> 00:00:44.760
numbers and then worry about
the decimals later.

00:00:44.760 --> 00:00:49.370
So right now, we can just view
this as 146 times 27, and then

00:00:49.370 --> 00:00:51.060
we'll worry about
the decimals.

00:00:51.060 --> 00:00:53.950
So first we have
a 7 times a 6.

00:00:53.950 --> 00:00:57.040
7 times 6 is 42.

00:00:57.040 --> 00:00:58.530
Regroup the 4.

00:00:58.530 --> 00:01:03.210
7 times 4 is 28, plus 4 is 32.

00:01:03.210 --> 00:01:04.730
Regroup the 3.

00:01:04.730 --> 00:01:08.730
7 times 1 is 7, plus 3 is 10.

00:01:08.730 --> 00:01:13.790
So we get 7 times
146 is 1,022.

00:01:13.790 --> 00:01:15.840
Now we're going to
deal with this 2.

00:01:15.840 --> 00:01:18.380
But this 2, at least before we
consider the decimal, is

00:01:18.380 --> 00:01:19.160
really a 20.

00:01:19.160 --> 00:01:22.310
So we're going to
put a 0 here.

00:01:22.310 --> 00:01:24.600
We're doing it exactly the same
way we do a traditional

00:01:24.600 --> 00:01:25.520
multiplication problem.

00:01:25.520 --> 00:01:27.620
We're ignoring the
decimals for now.

00:01:27.620 --> 00:01:29.430
2 times 6 is 12.

00:01:29.430 --> 00:01:31.660
Carry the 1, or regroup the 1.

00:01:31.660 --> 00:01:33.580
We can ignore these
guys right now.

00:01:33.580 --> 00:01:37.800
2 times 4 is 8, plus 1 is 9.

00:01:37.800 --> 00:01:41.360
2 times 1 is 2, and
now we can add.

00:01:44.600 --> 00:01:47.410
And we get 2 plus 0 is 2.

00:01:47.410 --> 00:01:49.390
2 plus 2 is 4.

00:01:49.390 --> 00:01:51.720
0 plus 9 is 9.

00:01:51.720 --> 00:01:55.170
1 plus 2 is 3.

00:01:55.170 --> 00:01:58.650
Now we've figured out what
146 times 27 is.

00:01:58.650 --> 00:02:00.950
It's 3,942.

00:02:00.950 --> 00:02:03.070
But this wasn't 146 times 27.

00:02:03.070 --> 00:02:06.030
It was 14.6 times 2.7.

00:02:06.030 --> 00:02:07.980
So now we have to worry
about the decimals.

00:02:07.980 --> 00:02:11.130
We just count how many numbers
are sitting behind decimals.

00:02:11.130 --> 00:02:14.200
We have one right there and
a second one right there.

00:02:14.200 --> 00:02:16.710
So our product has to have
two numbers to the

00:02:16.710 --> 00:02:17.670
right of the decimal.

00:02:17.670 --> 00:02:21.160
So one, two, stick it
right over there.

00:02:21.160 --> 00:02:25.860
So for 14.6 gallons of gas at
$2.70 per gallon, it's going

00:02:25.860 --> 00:02:28.110
to cost $39.42.


Estimation with Decimals

WEBVTT
Kind: captions
Language: en

00:00:00.520 --> 00:00:02.840
Janelle is training
for a road race.

00:00:02.840 --> 00:00:06.090
Her pedometer tracks how
far she runs every day.

00:00:06.090 --> 00:00:08.350
Here are the pedometer readings
for the past four

00:00:08.350 --> 00:00:13.190
days: on Saturday, she went
3.89 miles; Sunday, 5.1;

00:00:13.190 --> 00:00:18.190
Monday, 10.21; Tuesday, 3.35.

00:00:18.190 --> 00:00:21.750
Estimate the total distance she
ran over the four days,

00:00:21.750 --> 00:00:23.640
and then calculate
the exact amount.

00:00:23.640 --> 00:00:26.460
Let's estimate first. So I'm
just going to round them to

00:00:26.460 --> 00:00:27.380
the nearest mile.

00:00:27.380 --> 00:00:30.190
So 3.89, let's round
it up to 4 miles.

00:00:30.190 --> 00:00:32.600
And I'm doing that because in
the tenths place, we have an

00:00:32.600 --> 00:00:34.730
8, which is 5 or greater.

00:00:34.730 --> 00:00:38.370
So let's just make that
roughly 4 miles.

00:00:38.370 --> 00:00:39.770
Let's make this 5.1.

00:00:39.770 --> 00:00:43.040
We round that down because
this 1 is less than 5.

00:00:43.040 --> 00:00:45.350
So let's make this 5 miles.

00:00:45.350 --> 00:00:50.960
10.21, let's make that
10 miles because

00:00:50.960 --> 00:00:51.950
2 would round down.

00:00:51.950 --> 00:00:53.480
It's less than 5.

00:00:53.480 --> 00:00:57.470
And 3.35, let's make that 3
miles, because 3 is less than

00:00:57.470 --> 00:00:58.740
5, so we'd round down.

00:00:58.740 --> 00:01:00.610
So that is 3 miles.

00:01:00.610 --> 00:01:04.090
And if we were to add them
up, 4 plus 5 is 9.

00:01:04.090 --> 00:01:07.110
9 plus 10 is 19.

00:01:07.110 --> 00:01:11.040
19 plus 3 is 22.

00:01:11.040 --> 00:01:20.040
So my estimate is that she ran
22 miles over the four days.

00:01:20.040 --> 00:01:21.080
That's my estimate.

00:01:21.080 --> 00:01:24.200
Now let's figure out the exact
amount that she ran.

00:01:24.200 --> 00:01:25.670
Let me scroll down
a little bit.

00:01:25.670 --> 00:01:32.940
So we're going to have to add
3.89 to 5.1-- and remember,

00:01:32.940 --> 00:01:34.870
when you're adding decimals,
you want to line up the

00:01:34.870 --> 00:01:44.390
decimal-- 10.21 and
then finally 3.35.

00:01:44.390 --> 00:01:47.900
And let's add all of these up.

00:01:47.900 --> 00:01:52.500
Now we'll start in the
hundredths place.

00:01:52.500 --> 00:01:56.820
There's nothing here, so 9 plus
nothing plus 1 is 10,

00:01:56.820 --> 00:01:59.340
plus 5 is 15.

00:01:59.340 --> 00:02:04.910
So let's write the 5, and then
carry, or regroup, the 1.

00:02:04.910 --> 00:02:06.360
Let me do this in
another color.

00:02:06.360 --> 00:02:10.030
1 plus 8 is 9.

00:02:10.030 --> 00:02:12.090
9 plus 1 is 10.

00:02:12.090 --> 00:02:14.190
10 plus 2 is 12.

00:02:14.190 --> 00:02:17.240
12 plus 3 is 15.

00:02:17.240 --> 00:02:18.750
Put the 5 down.

00:02:18.750 --> 00:02:21.045
Carry, or regroup, the 1.

00:02:21.045 --> 00:02:22.810
1 plus 3 is 4.

00:02:22.810 --> 00:02:25.140
4 plus 5 is 9.

00:02:25.140 --> 00:02:26.790
9 plus 0 is still 9.

00:02:26.790 --> 00:02:33.480
9 plus 3 is 12.

00:02:33.480 --> 00:02:33.960
Write the 2.

00:02:33.960 --> 00:02:35.800
Regroup this 1 right here.

00:02:35.800 --> 00:02:38.530
I'll do it out here just so it's
not part of any of these

00:02:38.530 --> 00:02:42.340
numbers, and then
1 plus 1 is 2.

00:02:42.340 --> 00:02:43.770
And then we have to remember
the decimal

00:02:43.770 --> 00:02:46.010
sitting right over there.

00:02:46.010 --> 00:02:52.760
So the exact distance she
ran was 22.55 miles.

00:02:52.760 --> 00:02:54.160
So our estimate wasn't
too bad.

00:02:54.160 --> 00:02:55.630
It was 22 miles.

00:02:55.630 --> 00:02:58.760
We got reasonably close, within
about little over a

00:02:58.760 --> 00:03:00.310
half a mile.


Dividing a decimal by a power of 10: shortcut

WEBVTT
Kind: captions
Language: en

00:00:00.420 --> 00:00:05.960
In the last video, we divided
100 into 99.061, and we did it

00:00:05.960 --> 00:00:06.770
the manual way.

00:00:06.770 --> 00:00:08.510
We did it the long
division way.

00:00:08.510 --> 00:00:10.690
In this video, I just want to
show you a quick shortcut

00:00:10.690 --> 00:00:14.900
because we're dividing something
by a power of ten.

00:00:14.900 --> 00:00:21.690
If I have 99.061, if I multiply
by a power of ten,

00:00:21.690 --> 00:00:23.080
I'm going to make the
number bigger.

00:00:23.080 --> 00:00:26.770
Every time I multiply by 10, the
decimal would shift to the

00:00:26.770 --> 00:00:31.250
right by one spot.

00:00:31.250 --> 00:00:36.320
So we could say, 99.061
times 10 is going

00:00:36.320 --> 00:00:40.770
to be equal to 990.61.

00:00:40.770 --> 00:00:43.060
Notice we just moved
the decimal over to

00:00:43.060 --> 00:00:44.670
the right by one.

00:00:44.670 --> 00:00:47.590
If I were to do-- I'll just
arbitrarily switch colors--

00:00:47.590 --> 00:00:53.670
99.061 divided by 10, we're
going to shift the decimal in

00:00:53.670 --> 00:00:54.830
the other direction.

00:00:54.830 --> 00:01:00.600
This is going to be 9.9061.

00:01:00.600 --> 00:01:04.180
So when we divide by 100, we're
dividing by 10 twice.

00:01:04.180 --> 00:01:06.340
We're shifting to
the left twice.

00:01:06.340 --> 00:01:17.150
So if we start with 99.061
divided by 100-- let me just

00:01:17.150 --> 00:01:17.760
write it like this.

00:01:17.760 --> 00:01:18.960
We've already written
the problem.

00:01:18.960 --> 00:01:22.570
If we want to divide this by
100, moving it one spot to the

00:01:22.570 --> 00:01:27.340
left will divide it by 10, and
then moving another spot to

00:01:27.340 --> 00:01:31.930
the left will divide
it by 10 again.

00:01:31.930 --> 00:01:41.400
So 99.061 divided by 100 is
going to be equal to 0.99061.

00:01:41.400 --> 00:01:44.560
We're just going to shift the
decimal to the left by two.

00:01:44.560 --> 00:01:46.920
And we might want to put a
leading zero here, just so it

00:01:46.920 --> 00:01:50.220
makes it a little bit
easier to read.