Unit measurement word problem: weight (US customary)

WEBVTT
Kind: captions
Language: en

00:00:00.590 --> 00:00:03.970
A standard elevator in a
mid-rise building can hold a

00:00:03.970 --> 00:00:08.050
maximum weight of
1 and 1/2 tons.

00:00:08.050 --> 00:00:13.220
Assuming an average adult weight
of 160 pounds, what is

00:00:13.220 --> 00:00:15.170
the maximum number of
adults who could

00:00:15.170 --> 00:00:18.130
safely ride the elevator?

00:00:18.130 --> 00:00:21.480
So what we need to do is we have
to get the maximum weight

00:00:21.480 --> 00:00:23.760
that the elevator could hold
in terms of pounds.

00:00:23.760 --> 00:00:25.970
And then say, OK, well, how
many adults is that?

00:00:25.970 --> 00:00:28.930
So they gave us the maximum
weight in terms of tons.

00:00:28.930 --> 00:00:33.070
So they say it is
1 and 1/2 tons.

00:00:33.070 --> 00:00:36.870
And it's always easier to deal
with improper fractions than

00:00:36.870 --> 00:00:39.350
mixed numbers, so let's write
this as an improper fraction.

00:00:39.350 --> 00:00:43.500
1 and 1/2 tons is the same thing
as-- well, 1 ton is 2

00:00:43.500 --> 00:00:45.230
halves, and then you
add another 1

00:00:45.230 --> 00:00:46.870
half, that's 3 halves.

00:00:46.870 --> 00:00:49.990
So you get 3/2 tons.

00:00:49.990 --> 00:00:52.700
Or another way to think about
it is 2 times 1 is

00:00:52.700 --> 00:00:55.640
2, plus 1 is 3.

00:00:55.640 --> 00:00:58.550
So the maximum capacity
is 3/2 tons.

00:00:58.550 --> 00:01:00.000
Let's think about how
many pounds that is.

00:01:00.000 --> 00:01:03.000
And to do that, we have to
know that there are 2,000

00:01:03.000 --> 00:01:04.769
pounds per ton.

00:01:04.769 --> 00:01:05.870
Let me write this up here.

00:01:05.870 --> 00:01:11.260
We know that there are
2,000 pounds per ton.

00:01:11.260 --> 00:01:13.240
This wasn't given in the
problem anywhere.

00:01:13.240 --> 00:01:16.300
This is something I knew from
past experience, and it's a

00:01:16.300 --> 00:01:17.950
good thing to know,
in general, that a

00:01:17.950 --> 00:01:20.090
ton is 2,000 pounds.

00:01:20.090 --> 00:01:21.630
So I'm going to write
it right over here.

00:01:21.630 --> 00:01:25.280
Now, how do we convert these
3/2 tons into pounds?

00:01:25.280 --> 00:01:27.640
Well, we're going to multiply it
by something, and the units

00:01:27.640 --> 00:01:29.590
that we're going to multiply
by, we want the

00:01:29.590 --> 00:01:30.780
tons to cancel out.

00:01:30.780 --> 00:01:36.170
So we're going to want to have
tons in the denominator, so it

00:01:36.170 --> 00:01:38.520
cancels out with this
tons up here.

00:01:38.520 --> 00:01:41.760
And then we want pounds
in the numerator.

00:01:41.760 --> 00:01:43.900
And that's exactly what
we wrote up here.

00:01:43.900 --> 00:01:48.760
There are 2,000 pounds for every
1 ton, or you could just

00:01:48.760 --> 00:01:50.640
say 2,000 pounds per ton.

00:01:50.640 --> 00:01:52.880
You could put the 1 there, but
it doesn't really change the

00:01:52.880 --> 00:01:53.940
expression.

00:01:53.940 --> 00:02:00.260
Now, if we multiply 3/2 tons
times 2,000 pounds per ton,

00:02:00.260 --> 00:02:02.030
what'll happen is that
the tons cancel out.

00:02:02.030 --> 00:02:04.240
That was the whole point of
multiplying it by this.

00:02:04.240 --> 00:02:15.860
And we would be left with 3/2
times 2,000, and the only unit

00:02:15.860 --> 00:02:17.110
left is pounds.

00:02:19.620 --> 00:02:22.740
And if you do it this way,
you'll never get confused.

00:02:22.740 --> 00:02:25.420
You'll know that the units
cancel out so you're getting

00:02:25.420 --> 00:02:26.390
the right units.

00:02:26.390 --> 00:02:28.370
But if you just think about it
in your mind, it should also

00:02:28.370 --> 00:02:30.430
make sense.

00:02:30.430 --> 00:02:33.600
If there are 2,000 pounds per
ton and there are 1 and 1/2

00:02:33.600 --> 00:02:37.670
tons, I should multiply 1 and
1/2 times 2,000 to get the

00:02:37.670 --> 00:02:38.460
number of pounds.

00:02:38.460 --> 00:02:40.020
That makes sense.

00:02:40.020 --> 00:02:42.860
And we know 1 and 1/2 times
2,000 is 3,000, but we'll

00:02:42.860 --> 00:02:44.780
figure it out right here.

00:02:44.780 --> 00:02:46.110
So what is 3/2 times 2,000?

00:02:46.110 --> 00:02:47.590
Well, I just told you answer.

00:02:47.590 --> 00:02:50.130
We can actually simplify
it right over here.

00:02:50.130 --> 00:02:56.920
This is going to be 3 times
2,000/2 pounds.

00:02:56.920 --> 00:02:59.690
We can divide the numerator
and the denominator by 2.

00:02:59.690 --> 00:03:03.610
This will become 1,000, and this
will become 1, so it's 3

00:03:03.610 --> 00:03:09.010
times 1,000 pounds, or this
is equal to 3,000 pounds.

00:03:09.010 --> 00:03:11.980
So what we've done so far, we've
just figured out the

00:03:11.980 --> 00:03:13.870
maximum capacity of
the elevator.

00:03:13.870 --> 00:03:16.540
It can hold 1 and 1/2 tons,
which is the exact same thing

00:03:16.540 --> 00:03:18.440
as 3,000 pounds.

00:03:18.440 --> 00:03:22.010
Now, what we need to figure
out is 3,000 pounds is the

00:03:22.010 --> 00:03:26.030
equivalent to how many average
adults of 160 pounds?

00:03:26.030 --> 00:03:29.860
Or how many 160 pound people
would it take to weigh a total

00:03:29.860 --> 00:03:32.320
of 3,000 pounds?

00:03:32.320 --> 00:03:36.150
Well, we can just
divide by 160.

00:03:36.150 --> 00:03:38.660
And if you want to make sure
that the units work out,

00:03:38.660 --> 00:03:41.900
remember, we want our answer to
be in terms of people, and

00:03:41.900 --> 00:03:44.060
we want the pounds
to cancel out.

00:03:44.060 --> 00:03:46.130
So we have pounds in the
numerator here, so if we

00:03:46.130 --> 00:03:51.050
divide by pounds, the pounds
will cancel out.

00:03:51.050 --> 00:03:55.535
And then we want our leftover to
be people, or maybe person.

00:03:58.550 --> 00:03:59.820
Person, people, same thing.

00:03:59.820 --> 00:04:02.300
Let me do people.

00:04:02.300 --> 00:04:04.620
The grammar of it, singular,
plural, might make it a little

00:04:04.620 --> 00:04:06.260
confusing, but I think you
get the general idea.

00:04:06.260 --> 00:04:08.750
Now, if we were to write this
out, what does it tell us?

00:04:08.750 --> 00:04:14.130
1 person weighs 160 pounds, so
there's one person for every

00:04:14.130 --> 00:04:16.060
160 pounds.

00:04:16.060 --> 00:04:18.860
So notice, if we multiply these
two expressions, the

00:04:18.860 --> 00:04:20.250
pounds will cancel out.

00:04:20.250 --> 00:04:23.590
We'll be just left
with people.

00:04:23.590 --> 00:04:27.520
We're multiplying 3,000 times
1/160, but it's really just

00:04:27.520 --> 00:04:30.490
taking 3,000 and dividing by
160, which makes sense.

00:04:30.490 --> 00:04:32.060
We have a capacity of 3,000.

00:04:32.060 --> 00:04:34.370
Each of our people weighs
160 pounds.

00:04:34.370 --> 00:04:35.080
Divide by 160.

00:04:35.080 --> 00:04:36.240
It tells you how many people.

00:04:36.240 --> 00:04:38.750
But this way, you know that
the units are working out.

00:04:38.750 --> 00:04:47.620
So this is going to be equal
to 3,000/160 people.

00:04:47.620 --> 00:04:50.340
That is the maximum capacity
of the elevator in terms of

00:04:50.340 --> 00:04:51.550
average people.

00:04:51.550 --> 00:04:52.280
Now, what is this?

00:04:52.280 --> 00:04:54.170
Well, we can divide the
numerator and the

00:04:54.170 --> 00:04:56.940
denominator by 10.

00:04:56.940 --> 00:04:59.230
If we divide the numerator and
the denominator by 10, this

00:04:59.230 --> 00:05:04.510
becomes 300/16.

00:05:04.510 --> 00:05:08.990
If we divide 300 by 2,
this becomes 150.

00:05:08.990 --> 00:05:12.840
If we divide 16 by 2,
this becomes 8.

00:05:12.840 --> 00:05:14.620
Now, let's see, what can
we do more here?

00:05:14.620 --> 00:05:15.760
We could divide by 2 again.

00:05:15.760 --> 00:05:17.300
Let me rewrite it.

00:05:17.300 --> 00:05:22.070
So this is the same thing
as 150/8 people.

00:05:22.070 --> 00:05:24.290
150, we can divide by 2.

00:05:24.290 --> 00:05:25.860
It gives us 75.

00:05:25.860 --> 00:05:29.440
And if you take 8 divided
by 2, that is 4.

00:05:29.440 --> 00:05:32.830
So we have 75 divided
by 4 people.

00:05:32.830 --> 00:05:34.620
Let me just do that,
work it out.

00:05:34.620 --> 00:05:38.700
So you have 75 divided by 4.

00:05:38.700 --> 00:05:40.240
4 goes into 7 one time.

00:05:40.240 --> 00:05:42.900
1 times 4 is 4.

00:05:42.900 --> 00:05:44.200
You subtract.

00:05:44.200 --> 00:05:45.840
7 minus 4 is 3.

00:05:45.840 --> 00:05:47.620
Bring down this 5.

00:05:47.620 --> 00:05:50.070
4 goes into 35 eight times.

00:05:50.070 --> 00:05:52.560
8 times 4 is 32.

00:05:52.560 --> 00:05:53.810
Subtract.

00:05:53.810 --> 00:05:55.440
5 minutes 2 is 3.

00:05:55.440 --> 00:05:58.630
And then you have the decimal.

00:05:58.630 --> 00:06:00.520
We're going to the right
of the ones place.

00:06:00.520 --> 00:06:02.650
We're going to the
tenths place now.

00:06:02.650 --> 00:06:05.550
So we can bring down
a zero over here.

00:06:05.550 --> 00:06:08.730
4 goes into 30 seven times.

00:06:08.730 --> 00:06:11.890
7 times 4 is 28.

00:06:11.890 --> 00:06:12.670
You subtract.

00:06:12.670 --> 00:06:13.700
You get 2.

00:06:13.700 --> 00:06:16.560
Bring down another zero.

00:06:16.560 --> 00:06:19.250
4 goes into 20 exactly
five times.

00:06:19.250 --> 00:06:24.770
5 times 4 is 20, and
then we are done.

00:06:24.770 --> 00:06:28.610
So this expression is exactly--
the 3,000 divided by

00:06:28.610 --> 00:06:32.740
160, or the 150 divided by 8,
the 75 divided by 4, it all

00:06:32.740 --> 00:06:37.810
turns out to be 18.75
people is the

00:06:37.810 --> 00:06:39.110
capacity of the elevator.

00:06:39.110 --> 00:06:44.790
18.75 average 160-pound people
would weigh 3,000 pounds.

00:06:44.790 --> 00:06:45.990
Now, do they want a decimal?

00:06:45.990 --> 00:06:48.350
What is the maximum number of
adults who could safely ride

00:06:48.350 --> 00:06:48.730
the elevator?

00:06:48.730 --> 00:06:51.240
Well, if they're all going to
be average, then the maximum

00:06:51.240 --> 00:06:56.210
number of adults, since you
can't have 3/4 of a person, or

00:06:56.210 --> 00:06:58.860
75/100 of a person,
the maximum number

00:06:58.860 --> 00:07:00.560
is going to be 18.

00:07:00.560 --> 00:07:03.560
If you have 19 average-weight
adults, you are going to be

00:07:03.560 --> 00:07:07.270
too heavy, and the elevator
will fall or something.


Unit measurement word problem: volume (US customary)

WEBVTT
Kind: captions
Language: en

00:00:00.640 --> 00:00:03.940
A local hospital recently
conducted a blood drive where

00:00:03.940 --> 00:00:07.990
they collected a total of 80
pints of blood from donors.

00:00:07.990 --> 00:00:11.340
The hospital was hoping to
collect a total of 8 gallons

00:00:11.340 --> 00:00:13.170
of blood from the drive.

00:00:13.170 --> 00:00:14.890
Did they meet their goal?

00:00:14.890 --> 00:00:17.490
How much more or less
than their goal did

00:00:17.490 --> 00:00:19.030
the hospital collect?

00:00:19.030 --> 00:00:20.640
So really, they collected
80 pints.

00:00:20.640 --> 00:00:22.830
We just need to figure out how
many gallons that is, and then

00:00:22.830 --> 00:00:26.750
say, well, is that going to be
more or less than 8 gallons?

00:00:26.750 --> 00:00:31.000
So we start with 80 pints.

00:00:31.000 --> 00:00:32.770
And we can take it
step by step.

00:00:32.770 --> 00:00:35.090
You may or may not know how
many pints there are per

00:00:35.090 --> 00:00:37.415
gallon, so let's just go
straight to quarts first, and

00:00:37.415 --> 00:00:39.360
then from quarts we
can go to gallons.

00:00:39.360 --> 00:00:42.080
But if you know right from the
get go how many pints there

00:00:42.080 --> 00:00:43.620
are per gallon, you
could go there.

00:00:43.620 --> 00:00:45.310
So let's convert
this to quarts.

00:00:45.310 --> 00:00:48.430
So we have 80 pints, so what
are we going to multiply or

00:00:48.430 --> 00:00:50.120
divide by to get quarts?

00:00:50.120 --> 00:00:51.650
Well, one way to think about
it, you're going from a

00:00:51.650 --> 00:00:54.150
smaller unit, pints, to a larger
unit, so you're going

00:00:54.150 --> 00:00:56.020
to have less of that
larger unit.

00:00:56.020 --> 00:00:57.740
So you're going to divide.

00:00:57.740 --> 00:00:59.330
This number's going
to be smaller when

00:00:59.330 --> 00:01:00.640
it goes into quarts.

00:01:00.640 --> 00:01:03.610
And it's going to be smaller by
a factor of 2 because you

00:01:03.610 --> 00:01:06.850
have 2 pints per quart.

00:01:06.850 --> 00:01:08.260
You're not going to
multiply by 2.

00:01:08.260 --> 00:01:09.270
You're not going to
have more quarts.

00:01:09.270 --> 00:01:10.780
You're going to divide by 2.

00:01:10.780 --> 00:01:13.090
So you could say, times 1/2.

00:01:13.090 --> 00:01:15.540
This is the same thing as
dividing by 2, and we'll make

00:01:15.540 --> 00:01:16.560
sure that the units work out.

00:01:16.560 --> 00:01:23.190
We have one quart for every 2
pints, or you can view this as

00:01:23.190 --> 00:01:26.150
2 pints per quart or 1/2
of a quart per pint.

00:01:26.150 --> 00:01:28.950
Either way, the units work out,
and you're essentially

00:01:28.950 --> 00:01:32.560
taking 80 and dividing by 2, or
multiplying by 1/2, and you

00:01:32.560 --> 00:01:34.690
get 40 quarts.

00:01:34.690 --> 00:01:37.700
And I want to make sure that
your brain does it both ways.

00:01:37.700 --> 00:01:39.180
Because when you're just doing
it, you don't have paper, you

00:01:39.180 --> 00:01:41.640
don't have the units around, you
should just think, hey, 80

00:01:41.640 --> 00:01:43.540
pints, there's 2 pints
per quart.

00:01:43.540 --> 00:01:45.190
I'm going to have half
as many quarts.

00:01:45.190 --> 00:01:46.710
I'm going to have 40 quarts.

00:01:46.710 --> 00:01:48.980
But when problems get a little
bit more complicated, it is

00:01:48.980 --> 00:01:51.750
nice to make sure that the units
cancel out in this way,

00:01:51.750 --> 00:01:54.370
so that you know, OK,
1 quart is 2 pints.

00:01:54.370 --> 00:01:57.090
Pints in the denominator, pints
in the numerator, cancel

00:01:57.090 --> 00:02:00.080
them out, and I'm just left with
quarts, and 80 times 1/2,

00:02:00.080 --> 00:02:00.890
which is 40.

00:02:00.890 --> 00:02:05.840
So we have 40 quarts
now, and now we can

00:02:05.840 --> 00:02:07.170
convert this to gallons.

00:02:07.170 --> 00:02:10.620
We know that there are 4 quarts
per gallon or that 1

00:02:10.620 --> 00:02:12.120
gallon has 4 quarts.

00:02:12.120 --> 00:02:14.310
And once again, we're going to
go from a smaller unit to a

00:02:14.310 --> 00:02:15.920
larger unit, to gallons.

00:02:15.920 --> 00:02:18.070
So we know there's a factor
of 4 difference.

00:02:18.070 --> 00:02:20.090
Since you're going to a larger
unit, your brain should say,

00:02:20.090 --> 00:02:22.460
hey, I'm going to divide by 4.

00:02:22.460 --> 00:02:25.710
I'm going to have a factor 4
fewer gallons because it's a

00:02:25.710 --> 00:02:26.820
larger unit.

00:02:26.820 --> 00:02:29.540
And to make sure that units work
out, you just remember,

00:02:29.540 --> 00:02:32.070
well, we have quarts up here in
the numerator, you're going

00:02:32.070 --> 00:02:34.590
to want quarts down here
in the denominator.

00:02:34.590 --> 00:02:38.610
And we care about converting
into gallons, and

00:02:38.610 --> 00:02:40.820
1 gallon is 4 quarts.

00:02:40.820 --> 00:02:41.850
And this will work out.

00:02:41.850 --> 00:02:43.380
The quarts will cancel out.

00:02:43.380 --> 00:02:47.600
And notice, you're also
dividing by 4.

00:02:47.600 --> 00:02:52.110
40 times 1/4 is the exact same
thing as 40 divided by 4,

00:02:52.110 --> 00:02:52.900
which makes sense.

00:02:52.900 --> 00:02:54.730
We're going to a larger unit.

00:02:54.730 --> 00:03:01.270
So 40 times 1/4 is 10, and the
units left are gallons.

00:03:01.270 --> 00:03:06.620
So the 80 pints of blood
that the hospital

00:03:06.620 --> 00:03:08.320
collected is 10 gallons.

00:03:08.320 --> 00:03:10.480
Their goal was only 8 gallons.

00:03:13.020 --> 00:03:14.390
So did they meet their goal?

00:03:14.390 --> 00:03:15.920
Yes, they met their goal!

00:03:15.920 --> 00:03:17.460
How much more or less
than their goal did

00:03:17.460 --> 00:03:18.460
the hospital collect?

00:03:18.460 --> 00:03:21.220
Well, their goal was 8,
they collected 10.

00:03:21.220 --> 00:03:28.080
They collected 2 extra gallons
than their goal.


Unit conversion: gallons to quarts, pints, and cups

WEBVTT
Kind: captions
Language: en

00:00:00.510 --> 00:00:04.120
How many cups are in
3 and 1/2 gallons?

00:00:04.120 --> 00:00:06.870
So before even addressing this
question, let's just think

00:00:06.870 --> 00:00:08.640
about how large a cup is.

00:00:08.640 --> 00:00:09.990
Actually, I'll give you a little
bit of overview of how

00:00:09.990 --> 00:00:12.800
many cups there are in a pint,
how many pints in a quart, and

00:00:12.800 --> 00:00:14.870
how many quarts in a gallon.

00:00:14.870 --> 00:00:18.610
Let me just draw a cube here,
and let's imagine

00:00:18.610 --> 00:00:19.860
that this is a gallon.

00:00:23.290 --> 00:00:27.000
The most common time we see
a gallon is when you see a

00:00:27.000 --> 00:00:28.460
gallon of milk.

00:00:28.460 --> 00:00:30.340
So let's say that that whole
thing is a gallon.

00:00:30.340 --> 00:00:31.740
You can imagine if it had a
handle, it would be kind of a

00:00:31.740 --> 00:00:33.130
big gallon of milk.

00:00:33.130 --> 00:00:36.290
Now, there are 4 quarts
per gallon.

00:00:36.290 --> 00:00:37.160
Let me write this over here.

00:00:37.160 --> 00:00:43.730
There are 4 quarts per gallon.

00:00:43.730 --> 00:00:45.690
So if I were to draw the quarts
here, I could divide

00:00:45.690 --> 00:00:50.600
this gallon into 4 quarts, and
then each of these sections

00:00:50.600 --> 00:00:51.660
would be a quart.

00:00:51.660 --> 00:00:54.860
So you would have 4 quarts.

00:00:54.860 --> 00:00:58.350
So this right here that I've
just drawn in blue would be

00:00:58.350 --> 00:01:02.820
exactly 1 quart.

00:01:02.820 --> 00:01:05.880
And obviously, there's 4 of them
in this entire gallon.

00:01:05.880 --> 00:01:09.330
Now, you can divide the
quarts into pints.

00:01:09.330 --> 00:01:16.670
You have 2 pints per quart.

00:01:16.670 --> 00:01:21.120
So this quart that I drew here,
I can divide it into 2,

00:01:21.120 --> 00:01:24.380
like that, and this little
section that I'm highlighting

00:01:24.380 --> 00:01:27.550
in magenta is a pint.

00:01:27.550 --> 00:01:30.910
That is a pint right
over there.

00:01:30.910 --> 00:01:33.996
And then finally, there
are 2 cups per pint.

00:01:42.070 --> 00:01:45.190
So this pint right here, I can
divide it into 2, and each of

00:01:45.190 --> 00:01:46.370
these will be a cup.

00:01:46.370 --> 00:01:52.310
So this section right
here will be a cup.

00:01:52.310 --> 00:01:54.640
Now, we can go straight and
figure out exactly how many

00:01:54.640 --> 00:01:55.820
cups there are per gallon.

00:01:55.820 --> 00:01:57.300
Actually, that might be
an interesting way

00:01:57.300 --> 00:01:58.710
to think about it.

00:01:58.710 --> 00:02:01.940
If you have 4 quarts-- let's
multiply it right here.

00:02:01.940 --> 00:02:12.080
So you have 4 quarts per gallon

00:02:12.080 --> 00:02:13.705
times 2 pints per quart.

00:02:20.830 --> 00:02:21.750
What does this give you?

00:02:21.750 --> 00:02:26.160
This gives you 4 times
2 is equal to 8.

00:02:26.160 --> 00:02:28.720
And then the quarts cancel
out, and you

00:02:28.720 --> 00:02:31.730
have 8 pints per gallon.

00:02:35.510 --> 00:02:38.020
And that makes complete sense
because we had 4 quarts in

00:02:38.020 --> 00:02:40.120
this gallon, and then
each of those quarts

00:02:40.120 --> 00:02:41.700
have 2 pints in them.

00:02:41.700 --> 00:02:43.120
So 4 times 2.

00:02:43.120 --> 00:02:44.510
So 8 pints per gallon.

00:02:44.510 --> 00:02:47.790
And then we can multiply that
times 2 cups per pint.

00:02:47.790 --> 00:02:49.780
So I could just copy and
paste this right here.

00:02:55.650 --> 00:02:58.040
Actually, I should've
cut and paste.

00:02:58.040 --> 00:03:00.110
Let me select it again.

00:03:00.110 --> 00:03:02.190
I want to do that so I get
that real estate back.

00:03:02.190 --> 00:03:05.420
So edit, cut, edit, paste.

00:03:05.420 --> 00:03:06.250
There you go.

00:03:06.250 --> 00:03:09.660
So now you multiply this
times 2 cups per pint.

00:03:09.660 --> 00:03:12.710
And the reason why this will
work is because you have pints

00:03:12.710 --> 00:03:13.315
in the numerator.

00:03:13.315 --> 00:03:15.480
It cancels out with the pints
in the denominator.

00:03:15.480 --> 00:03:20.480
And you will be left with-- I'll
go back to the yellow-- 8

00:03:20.480 --> 00:03:23.120
times 2 is 16.

00:03:23.120 --> 00:03:27.790
In the numerator, we have
cups per gallon.

00:03:27.790 --> 00:03:29.410
Now, we just figured how many
cups there are per gallon.

00:03:29.410 --> 00:03:30.050
That makes sense.

00:03:30.050 --> 00:03:34.780
This section right here is
exactly 1/16 of this entire

00:03:34.780 --> 00:03:36.210
cube, this entire gallon.

00:03:36.210 --> 00:03:37.570
But we haven't even answered
our question.

00:03:37.570 --> 00:03:38.990
We want to figure out how
many cups there are

00:03:38.990 --> 00:03:41.160
in 3 and 1/2 gallons.

00:03:41.160 --> 00:03:42.240
So let's write it over here.

00:03:42.240 --> 00:03:46.840
So we're concerned with
3 and 1/2 gallons.

00:03:46.840 --> 00:03:48.900
I don't like working
with mixed numbers.

00:03:48.900 --> 00:03:51.150
I like to turn them into
improper fractions.

00:03:51.150 --> 00:03:56.200
3 and 1/2 is the same thing as
2 times 3 is 6, plus 1 is 7.

00:03:56.200 --> 00:03:58.440
This is the same thing as 7/2.

00:03:58.440 --> 00:04:02.000
If you divided 7 by 2, you would
get 3 with a remainder

00:04:02.000 --> 00:04:04.010
of 1, or this would be
3 and 1/2, so this is

00:04:04.010 --> 00:04:05.740
the exact same thing.

00:04:05.740 --> 00:04:10.140
So we want to know how many
cups are in 7/2 gallons.

00:04:10.140 --> 00:04:13.060
So what we want to do is end up
with cups, and we want the

00:04:13.060 --> 00:04:14.640
gallons to cancel out.

00:04:14.640 --> 00:04:17.450
So we have gallons in the
numerator right here.

00:04:17.450 --> 00:04:19.100
It's definitely not in
the denominator.

00:04:19.100 --> 00:04:23.180
And so we want to divide
by gallons.

00:04:23.180 --> 00:04:24.940
And then we're going to
have a numerator.

00:04:24.940 --> 00:04:26.700
We have cups in the numerator.

00:04:26.700 --> 00:04:28.490
And how many cups are
there per gallon?

00:04:28.490 --> 00:04:29.530
Well, we just figured
that out.

00:04:29.530 --> 00:04:33.310
There are 16 cups per gallon.

00:04:33.310 --> 00:04:36.080
When you multiply these two
quantities, the gallons will

00:04:36.080 --> 00:04:38.250
cancel out, and you'll just be
left with cups, and that's

00:04:38.250 --> 00:04:39.220
what we wanted.

00:04:39.220 --> 00:04:41.940
So it's going to be
7/2 times 16.

00:04:41.940 --> 00:04:51.040
So this is going to be
7 times 16/2 cups.

00:04:51.040 --> 00:04:52.900
You could divide 16
by 2 to get 8.

00:04:52.900 --> 00:04:54.140
2 divided by 2 is 1.

00:04:54.140 --> 00:04:57.580
So it just becomes 7 times 8
divided by 1, or just 7 times

00:04:57.580 --> 00:04:59.120
8, which is 56.

00:04:59.120 --> 00:05:03.200
So this is equal to 56 cups.

00:05:03.200 --> 00:05:04.700
And this should make sense.

00:05:04.700 --> 00:05:08.360
This should be a much larger
number because cups are a much

00:05:08.360 --> 00:05:09.710
smaller unit.

00:05:09.710 --> 00:05:11.820
So if you have 3 and 1/2
gallons, you will have many,

00:05:11.820 --> 00:05:14.400
many, many more cups in that
3 and 1/2 gallons,

00:05:14.400 --> 00:05:16.660
so this makes sense.


Unit measurement word problem: running laps (US customary)

WEBVTT
Kind: captions
Language: en

00:00:00.770 --> 00:00:03.420
Jamir is training for a
race and is running

00:00:03.420 --> 00:00:05.170
laps around a field.

00:00:05.170 --> 00:00:10.430
If the distance around the field
is 300 yards, how many

00:00:10.430 --> 00:00:17.930
complete laps would he need to
do to run at least 2 miles?

00:00:17.930 --> 00:00:21.272
So they tell us how far one lap
is, it's 300 yards, but we

00:00:21.272 --> 00:00:24.310
need to figure out how many
laps to go 2 miles.

00:00:24.310 --> 00:00:26.460
So a good starting point would
be to get everything into the

00:00:26.460 --> 00:00:27.190
same units.

00:00:27.190 --> 00:00:30.020
We have distance here in terms
of miles, we have it here in

00:00:30.020 --> 00:00:31.130
terms of yards.

00:00:31.130 --> 00:00:32.960
So let's just get everything
into yards.

00:00:32.960 --> 00:00:34.470
So he needs to run 2 miles.

00:00:37.730 --> 00:00:39.450
How do we convert
that to yards?

00:00:39.450 --> 00:00:41.820
Well, I don't have it memorized
how many yards there

00:00:41.820 --> 00:00:45.040
are per mile, but I do have it
memorized how many feet there

00:00:45.040 --> 00:00:45.710
are per mile.

00:00:45.710 --> 00:00:48.060
And it's a good thing to have
in the back of your brain

00:00:48.060 --> 00:00:55.040
someplace, that in general you
have 5,280 feet per mile.

00:00:55.040 --> 00:00:55.930
It's a good number to know.

00:00:55.930 --> 00:00:58.740
5,280 feet per mile.

00:00:58.740 --> 00:01:01.530
So if we want to convert, we can
first convert the miles to

00:01:01.530 --> 00:01:04.050
feet, and then we know that
there are 3 feet per yard, and

00:01:04.050 --> 00:01:06.770
then we'll have 2 miles
in terms of yards.

00:01:06.770 --> 00:01:09.930
So 2 miles, if we want it
converted to feet, we want

00:01:09.930 --> 00:01:15.650
miles in the denominator and we
want feet in the numerator.

00:01:15.650 --> 00:01:18.450
And the reason why I say that
is so that this miles will

00:01:18.450 --> 00:01:19.850
cancel out with that
miles, and we'll

00:01:19.850 --> 00:01:21.050
just have feet there.

00:01:21.050 --> 00:01:28.460
And I just wrote down, there's
5,280 feet per mile, or you

00:01:28.460 --> 00:01:31.810
say 5,280 feet for
every 1 mile.

00:01:31.810 --> 00:01:33.390
You can write it either
way, but let's just

00:01:33.390 --> 00:01:34.490
write it like that.

00:01:34.490 --> 00:01:35.770
And then we can multiply.

00:01:35.770 --> 00:01:37.460
So this is going to
give us what?

00:01:37.460 --> 00:01:44.340
If we just multiply the
numbers 2 times 5,280.

00:01:44.340 --> 00:01:45.310
So what is that going to be?

00:01:45.310 --> 00:01:46.820
Maybe I should get
a calculator out.

00:01:46.820 --> 00:01:50.130
Or we could do that
in our head.

00:01:50.130 --> 00:01:53.710
Let's think of it this way:
2 times 80 is 160.

00:01:53.710 --> 00:01:56.990
2 times 200 is 400.

00:01:56.990 --> 00:02:00.140
So it's going to be 400 plus
160 is going to be 560.

00:02:00.140 --> 00:02:02.940
And then 2 times 5,000
thousand is 10,000.

00:02:02.940 --> 00:02:07.140
So it's 10,560.

00:02:07.140 --> 00:02:12.590
And then the miles cancel
out, and we are

00:02:12.590 --> 00:02:14.020
just left with feet.

00:02:14.020 --> 00:02:15.630
And let me actually
multiply it out.

00:02:15.630 --> 00:02:17.900
I did it in my head that time,
but that's not always useful.

00:02:17.900 --> 00:02:23.350
Let me verify for
you that 5,280

00:02:23.350 --> 00:02:27.080
times 2 is indeed 10,560.

00:02:27.080 --> 00:02:29.010
So 2 times 0 is 0.

00:02:29.010 --> 00:02:31.400
2 times 8 is 16.

00:02:31.400 --> 00:02:32.500
Carry the 1.

00:02:32.500 --> 00:02:35.920
2 times 2 is 4, plus 1 is 5.

00:02:35.920 --> 00:02:37.840
2 times 5 is 10.

00:02:37.840 --> 00:02:40.190
10,560.

00:02:40.190 --> 00:02:43.670
So he needs to run
10,560 feet.

00:02:43.670 --> 00:02:48.070
Now, we want this in
terms of yards.

00:02:48.070 --> 00:02:52.320
So 10,560 feet.

00:02:52.320 --> 00:02:54.620
Let's convert this to yards.

00:02:54.620 --> 00:02:55.860
Well, we want it in yards.

00:02:55.860 --> 00:03:00.300
So we want yards in the
numerator, and we want feet in

00:03:00.300 --> 00:03:02.900
the denominator, so that the
feet cancel out with that feet

00:03:02.900 --> 00:03:04.210
right there.

00:03:04.210 --> 00:03:08.185
And we know that there are
3 feet for every 1 yard.

00:03:11.550 --> 00:03:14.450
Or another way to read this is
that you have 1/3 of a yard

00:03:14.450 --> 00:03:15.730
for every foot.

00:03:15.730 --> 00:03:17.760
And now we can multiply.

00:03:17.760 --> 00:03:18.590
And it makes sense.

00:03:18.590 --> 00:03:21.330
If you're going from feet to
yards, the number should get

00:03:21.330 --> 00:03:23.720
smaller because yards
is a bigger unit.

00:03:23.720 --> 00:03:26.970
You need fewer yards to go the
same distance as a certain

00:03:26.970 --> 00:03:27.730
number of feet.

00:03:27.730 --> 00:03:29.770
So it makes sense that
we're dividing.

00:03:29.770 --> 00:03:32.740
Same thing: 2 miles is a ton of
feet, so it made sense that

00:03:32.740 --> 00:03:34.760
we were multiplying
by a large number.

00:03:34.760 --> 00:03:36.720
Here it makes sense that
we're dividing.

00:03:36.720 --> 00:03:37.970
So let's do this.

00:03:37.970 --> 00:03:41.900
So this becomes 10,560
times 1 divided by 3.

00:03:41.900 --> 00:03:46.670
So it's 10,560/3.

00:03:46.670 --> 00:03:48.220
That's that and that part.

00:03:48.220 --> 00:03:52.570
And then the feet cancel
out, and we are

00:03:52.570 --> 00:03:55.170
just left with yards.

00:03:55.170 --> 00:04:02.760
So 2 miles is 10,560
divided by 3.

00:04:02.760 --> 00:04:05.310
And let's figure out
what that is.

00:04:05.310 --> 00:04:11.090
So 3 goes into 10,560.

00:04:11.090 --> 00:04:12.460
It doesn't go into 1.

00:04:12.460 --> 00:04:14.280
It goes into 10 three times.

00:04:14.280 --> 00:04:16.140
3 times 3 is 9.

00:04:16.140 --> 00:04:17.589
And we subtract.

00:04:17.589 --> 00:04:18.630
We get 1.

00:04:18.630 --> 00:04:19.910
Bring down this 5.

00:04:19.910 --> 00:04:21.209
It becomes a 15.

00:04:21.209 --> 00:04:24.190
3 goes into 15 five times.

00:04:24.190 --> 00:04:27.380
5 times 3 is 15.

00:04:27.380 --> 00:04:29.890
We have no remainder, or 0.

00:04:29.890 --> 00:04:32.220
You bring down the 6.

00:04:32.220 --> 00:04:34.290
3 goes into 6 two times.

00:04:34.290 --> 00:04:35.980
Let me scroll down
a little bit.

00:04:35.980 --> 00:04:37.740
2 times 3 is 6.

00:04:37.740 --> 00:04:38.590
Subtract.

00:04:38.590 --> 00:04:39.620
No remainder.

00:04:39.620 --> 00:04:41.430
Bring down this last 0.

00:04:41.430 --> 00:04:44.000
3 goes into 0 zero times.

00:04:44.000 --> 00:04:45.920
0 times 3 is 0.

00:04:45.920 --> 00:04:49.150
And we have no remainder.

00:04:49.150 --> 00:05:00.090
So 2 miles is the equivalent
to 3,520 yards.

00:05:00.090 --> 00:05:02.150
That's the total distance
he has to travel.

00:05:02.150 --> 00:05:04.680
That's the equivalent
of 2 miles.

00:05:04.680 --> 00:05:06.770
Now we want to figure out
how many laps there are.

00:05:06.770 --> 00:05:10.820
We want this in terms of laps,
not in terms of yards.

00:05:10.820 --> 00:05:15.070
So we want the yards
to cancel out.

00:05:15.070 --> 00:05:18.590
And we want laps in the
numerator, right?

00:05:18.590 --> 00:05:20.690
Because when you multiply, the
yards will cancel out, and

00:05:20.690 --> 00:05:22.630
we'll just be left with laps.

00:05:22.630 --> 00:05:25.910
Now, how many laps are there
per yard or yards per lap?

00:05:25.910 --> 00:05:29.600
Well, they say the distance
around the field is 300 yards.

00:05:29.600 --> 00:05:35.530
So we have 300 yards
for every 1 lap.

00:05:35.530 --> 00:05:37.900
So now, multiply this
right here.

00:05:37.900 --> 00:05:43.400
The yards will cancel out,
and we will get 3,520.

00:05:43.400 --> 00:05:45.480
Let me do that in a
different color.

00:05:45.480 --> 00:05:52.460
We will get 3,520, that right
there, times 1/300.

00:05:52.460 --> 00:05:54.020
When you multiply it times
1, it just becomes

00:05:54.020 --> 00:05:57.860
3,520 divided by 300.

00:05:57.860 --> 00:06:00.550
And in terms of the units,
the yards canceled out.

00:06:00.550 --> 00:06:03.430
We're just left with the laps.

00:06:03.430 --> 00:06:05.820
So this is how many laps
he needs to run.

00:06:05.820 --> 00:06:09.700
So 3,520 divided by 300.

00:06:09.700 --> 00:06:12.450
Well, we can eyeball
this right here.

00:06:12.450 --> 00:06:15.170
What is 11 times 300?

00:06:15.170 --> 00:06:16.830
Let's just approximate
this right here.

00:06:16.830 --> 00:06:22.100
So if we did 11 times
300, what is that

00:06:22.100 --> 00:06:23.580
going to be equal to?

00:06:23.580 --> 00:06:28.700
Well, 11 times 3 is 33, and then
we have two zeroes here.

00:06:28.700 --> 00:06:30.270
So this will be 3,300.

00:06:30.270 --> 00:06:32.250
So it's a little bit
smaller than that.

00:06:32.250 --> 00:06:35.850
If we have 12 times 300, what
is that going to be?

00:06:35.850 --> 00:06:41.110
12 times 3 is 36, and then we
have these two zeroes, so it's

00:06:41.110 --> 00:06:43.490
equal to 3,600.

00:06:43.490 --> 00:06:45.680
So this is going to be
11 point something.

00:06:45.680 --> 00:06:48.540
It's larger than 11, right?

00:06:48.540 --> 00:06:51.130
3,520 is larger than 3,300.

00:06:51.130 --> 00:06:53.140
So when you divide by 300 you're
going to get something

00:06:53.140 --> 00:06:54.740
larger than 11.

00:06:54.740 --> 00:06:58.280
But this number right here is
smaller than 3,600 so when you

00:06:58.280 --> 00:07:00.110
divide it by 300, you're going
to get something a little bit

00:07:00.110 --> 00:07:02.420
smaller than 12.

00:07:02.420 --> 00:07:05.800
So the exact number of laps is
going to be a little bit lower

00:07:05.800 --> 00:07:07.570
than 12 laps.

00:07:07.570 --> 00:07:10.620
So 2 miles is a little bit
lower than 12 laps.

00:07:10.620 --> 00:07:12.820
But let's make sure we're
answering their question.

00:07:12.820 --> 00:07:17.170
How many complete laps would
he need to do to

00:07:17.170 --> 00:07:18.560
run at least 2 miles?

00:07:18.560 --> 00:07:22.190
So they're telling us that,
look, this might be, 11 point

00:07:22.190 --> 00:07:23.870
something, something,
something laps.

00:07:23.870 --> 00:07:26.930
That would be the exact number
of laps to run 2 miles.

00:07:26.930 --> 00:07:30.170
But they say how many complete
laps does he have to run?

00:07:30.170 --> 00:07:33.240
11 complete laps would
not be enough.

00:07:33.240 --> 00:07:35.820
He would have to run 12.

00:07:35.820 --> 00:07:41.470
So our answer here is
12 complete laps.

00:07:41.470 --> 00:07:42.980
That complete tells us
that they want a

00:07:42.980 --> 00:07:44.310
whole number of laps.

00:07:44.310 --> 00:07:45.730
We can't just divide this.

00:07:45.730 --> 00:07:47.690
If we divide this, we're going
to get some 11 point

00:07:47.690 --> 00:07:48.310
something, something.

00:07:48.310 --> 00:07:50.420
You can do with the calculator
or do it by hand if you're

00:07:50.420 --> 00:07:51.070
interested.

00:07:51.070 --> 00:07:54.720
But we have to do at least 12
because that's the smallest

00:07:54.720 --> 00:07:58.280
whole number of laps that will
get us to at least this

00:07:58.280 --> 00:08:01.020
distance right here, or this
number of laps, or the

00:08:01.020 --> 00:08:03.400
equivalent of 2 miles.


Adding different units for weight

WEBVTT
Kind: captions
Language: en

00:00:00.550 --> 00:00:06.400
We have 11 ounces plus 29 ounces
plus 5 pounds is equal

00:00:06.400 --> 00:00:09.780
to how many pounds,
or blank pounds?

00:00:09.780 --> 00:00:12.350
So we need to add these three
quantities right here, and

00:00:12.350 --> 00:00:15.130
they want us to give the
answer in pounds.

00:00:15.130 --> 00:00:17.880
And we can only add quantities
that have the same units.

00:00:17.880 --> 00:00:20.040
So let's just add these ounces
first, just to get

00:00:20.040 --> 00:00:20.910
them out of the way.

00:00:20.910 --> 00:00:22.990
And then we could see, maybe we
can convert them to pounds,

00:00:22.990 --> 00:00:24.420
or convert the pounds
to ounces.

00:00:24.420 --> 00:00:26.330
We'll probably convert them to
pounds, so that our final

00:00:26.330 --> 00:00:27.520
answer is in pounds.

00:00:27.520 --> 00:00:31.300
So if we just add 11
ounces plus 29

00:00:31.300 --> 00:00:32.560
ounces, what do we get?

00:00:32.560 --> 00:00:38.150
Well, 11 plus 29 is 40.

00:00:38.150 --> 00:00:39.110
Let me write it like this.

00:00:39.110 --> 00:00:43.520
This right here is 40 ounces.

00:00:43.520 --> 00:00:46.380
So we need to add 40 ounces to
5 pounds to get a certain

00:00:46.380 --> 00:00:47.450
number of pounds.

00:00:47.450 --> 00:00:52.690
So let's convert this right here
to pounds, and then, once

00:00:52.690 --> 00:00:54.515
we have that in pounds, we can
just add it to that, and then

00:00:54.515 --> 00:00:56.510
we'll have our final answer.

00:00:56.510 --> 00:00:59.290
So 40 ounces, we want to
convert it to pounds.

00:00:59.290 --> 00:01:02.520
So we need to multiply it by
something where, in the units,

00:01:02.520 --> 00:01:10.780
we have ounces in the
denominator, and we have

00:01:10.780 --> 00:01:14.170
pounds in the numerator.

00:01:14.170 --> 00:01:16.960
And we need that so that these
ounces cancel out with these

00:01:16.960 --> 00:01:18.980
ounces, and we're just
left with pounds.

00:01:18.980 --> 00:01:22.430
And we know already that there
are 16 ounces per pound.

00:01:22.430 --> 00:01:26.650
So there are 16 ounces
per 1 pound.

00:01:26.650 --> 00:01:29.290
Or you could say there's 1 pound
per every 16 ounces.

00:01:29.290 --> 00:01:33.640
Or you could say there's 1/16
of a pound per ounce.

00:01:33.640 --> 00:01:36.900
Either way, if you multiply
these two quantities, the

00:01:36.900 --> 00:01:38.340
ounces cancel out.

00:01:38.340 --> 00:01:41.540
And this whole quantity becomes,
when you multiply it

00:01:41.540 --> 00:01:44.720
out, you're left with
40 divided by 16.

00:01:44.720 --> 00:01:46.980
40/16.

00:01:46.980 --> 00:01:49.610
It's really 40 times 1
over 16, but the 1

00:01:49.610 --> 00:01:50.840
doesn't change anything.

00:01:50.840 --> 00:01:56.990
And then 40/16 pounds.

00:01:56.990 --> 00:01:59.505
And let's see if we can write
this as a mixed number, or if

00:01:59.505 --> 00:02:01.100
we can simplify this
a little bit.

00:02:01.100 --> 00:02:08.160
Both of these numbers
are divisible by 8.

00:02:08.160 --> 00:02:09.449
So let's divide them
both by 8.

00:02:09.449 --> 00:02:12.220
If you divide 40 by
8, you get 5.

00:02:12.220 --> 00:02:15.620
You divide 16 by 8, you get 2.

00:02:15.620 --> 00:02:16.690
So it's 5/2.

00:02:16.690 --> 00:02:18.800
If we want to write this as a
mixed number-- or even better,

00:02:18.800 --> 00:02:21.880
let's write it as a decimal.

00:02:21.880 --> 00:02:24.040
This is 5 divided by 2.

00:02:24.040 --> 00:02:28.850
2 goes into 5 2 times.

00:02:28.850 --> 00:02:31.200
2 times 2 is 4.

00:02:31.200 --> 00:02:32.210
Subtract.

00:02:32.210 --> 00:02:33.630
You have a remainder, 1.

00:02:33.630 --> 00:02:36.110
We want a decimal, so let's put
the decimal right there

00:02:36.110 --> 00:02:37.780
and keep bringing down 0's.

00:02:37.780 --> 00:02:40.340
So let's bring down
a 0 right there.

00:02:40.340 --> 00:02:42.950
2 goes into 10 5 times.

00:02:42.950 --> 00:02:44.690
5 times 2 is 10.

00:02:44.690 --> 00:02:47.760
And we have no remainder.

00:02:47.760 --> 00:02:50.120
So this is exactly 2.5,
which makes sense.

00:02:50.120 --> 00:02:53.440
5 over 2 is the same thing as
2 and 1/2 as a mixed number,

00:02:53.440 --> 00:02:54.770
which is the exact same
thing as 2.5.

00:02:58.530 --> 00:03:02.970
This first part right here
simplified down to 5/2 pounds,

00:03:02.970 --> 00:03:04.430
or 2.5 pounds.

00:03:04.430 --> 00:03:10.285
So the problem becomes 2.5
pounds plus 5 pounds.

00:03:15.020 --> 00:03:19.980
And 2.5 plus 5, fairly
straightforward, it's 7.5.

00:03:19.980 --> 00:03:24.640
So this is equal
to 7.5 pounds.

00:03:24.640 --> 00:03:30.260
7.5 pounds is our answer,
and we're done.


Converting pounds to ounces

WEBVTT
Kind: captions
Language: en

00:00:00.580 --> 00:00:04.170
How many ounces are
in 6 pounds?

00:00:04.170 --> 00:00:06.670
So we have 6 pounds
and we need to

00:00:06.670 --> 00:00:09.130
convert them to ounces.

00:00:09.130 --> 00:00:12.110
And if you don't know it
already, you'll know it now,

00:00:12.110 --> 00:00:15.530
that there are 16 ounces
per pound.

00:00:15.530 --> 00:00:18.280
So what we want to do is we
want to have pounds in the

00:00:18.280 --> 00:00:19.680
denominator.

00:00:19.680 --> 00:00:21.250
It's in the numerator
right now.

00:00:21.250 --> 00:00:29.980
So we want to divide by pounds
and multiply by ounces.

00:00:29.980 --> 00:00:31.600
Maybe I'll write it out.

00:00:35.300 --> 00:00:36.990
And I just told you
that there are 16

00:00:36.990 --> 00:00:43.170
ounces for every 1 pound.

00:00:43.170 --> 00:00:46.420
So if we multiplied these two
expressions, this pounds will

00:00:46.420 --> 00:00:49.120
cancel with that pounds, and
we'll just be left with the

00:00:49.120 --> 00:00:52.040
unit of ounces, which is what we
want, and we just multiply

00:00:52.040 --> 00:00:53.410
6 times 16.

00:00:53.410 --> 00:00:56.120
So it works out unit-wise, and
it makes sense as well.

00:00:56.120 --> 00:01:00.880
If we have 16 ounces per pound,
and we have 6 pounds,

00:01:00.880 --> 00:01:02.960
we just have to multiply
6 times 16.

00:01:02.960 --> 00:01:05.840
That'll be the total number of
ounces we have. So this is

00:01:05.840 --> 00:01:09.270
going to be equal to--
what's 6 times 16?

00:01:09.270 --> 00:01:15.310
So if you take 16 times
6, 6 times 6 is 36.

00:01:15.310 --> 00:01:16.100
Carry the 3.

00:01:16.100 --> 00:01:19.400
6 times 1 is 6, plus 3 is 9.

00:01:19.400 --> 00:01:22.550
So 6 times 16 is 96.

00:01:22.550 --> 00:01:24.640
You have this divided by 1 here,
but that's not going to

00:01:24.640 --> 00:01:25.650
change anything.

00:01:25.650 --> 00:01:26.820
And then all we're
left with in the

00:01:26.820 --> 00:01:29.700
dimensions are the ounces.

00:01:29.700 --> 00:01:33.190
So 6 pounds are 96 ounces.


Converting yards into inches

WEBVTT
Kind: captions
Language: en

00:00:00.420 --> 00:00:04.830
We're asked how many inches
are in 4 and 1/2 yards?

00:00:04.830 --> 00:00:06.300
Let me write that down.

00:00:06.300 --> 00:00:09.110
4 and 1/2 yards.

00:00:09.110 --> 00:00:11.501
Now, whenever we're dealing with
fractions and we're going

00:00:11.501 --> 00:00:14.350
to multiply and divide by
fractions, it really

00:00:14.350 --> 00:00:16.400
complicates the issue to
have a mixed number.

00:00:16.400 --> 00:00:19.540
So right from the get go, I
want to turn this into an

00:00:19.540 --> 00:00:21.020
improper fraction.

00:00:21.020 --> 00:00:23.140
Let me do it over here
in the top right.

00:00:23.140 --> 00:00:25.640
4 and 1/2 written
as an improper

00:00:25.640 --> 00:00:27.010
fraction is equal to what?

00:00:27.010 --> 00:00:30.000
We're still going to have
2 as a denominator.

00:00:30.000 --> 00:00:31.900
So 2 times 4 is 8.

00:00:31.900 --> 00:00:35.680
So 8/2 is the same thing 4.

00:00:35.680 --> 00:00:38.140
Let me rewrite this, just
as a bit of review.

00:00:38.140 --> 00:00:41.640
4 is the same thing as 8/2.

00:00:41.640 --> 00:00:43.070
That's the same thing as 4.

00:00:43.070 --> 00:00:47.170
And then you have
that plus 1/2.

00:00:47.170 --> 00:00:49.670
That is going to give you 9/2.

00:00:49.670 --> 00:00:54.870
The quick way to do it: 2 times
4 is 8, 8 plus 1 is 9.

00:00:54.870 --> 00:00:58.070
So 4 and 1/2 is the
same thing as 9/2.

00:00:58.070 --> 00:01:01.760
So 4 and 1/2 yards is the same
thing as-- let me write it

00:01:01.760 --> 00:01:03.185
over here-- 9/2.

00:01:06.530 --> 00:01:07.450
yards.

00:01:07.450 --> 00:01:11.160
Now, we want to convert
this into inches.

00:01:11.160 --> 00:01:13.990
Just so we can take this in baby
steps, maybe we convert

00:01:13.990 --> 00:01:17.890
this into feet first, and then
once we have it in feet, then

00:01:17.890 --> 00:01:19.850
we can convert it into inches.

00:01:19.850 --> 00:01:22.620
So to convert it into feet, we
just have to remember that

00:01:22.620 --> 00:01:26.620
there are 3 feet for
every 1 yard.

00:01:26.620 --> 00:01:29.530
So let me write that down.

00:01:29.530 --> 00:01:36.330
There are 3 feet per yard.

00:01:36.330 --> 00:01:41.810
And if we were to multiply 9/2
yards times 3 feet, this yard

00:01:41.810 --> 00:01:42.900
would be in the numerator.

00:01:42.900 --> 00:01:45.670
It'd be divided by this yard,
and they would cancel out, and

00:01:45.670 --> 00:01:47.740
we'd just be left with feet.

00:01:47.740 --> 00:01:49.810
So we know we have
to multiply by 3.

00:01:49.810 --> 00:01:53.220
You can say this is 3 feet for
every 1 yard, if it makes it

00:01:53.220 --> 00:01:55.470
simple, or just 3
feet per yard.

00:01:55.470 --> 00:01:58.340
Another way to think about it
is however many yards you

00:01:58.340 --> 00:02:01.200
have, you're going to have
more feet, right?

00:02:01.200 --> 00:02:02.480
There are 3 feet per yard.

00:02:02.480 --> 00:02:04.170
So if I have 1 yard, I'm
going to have 3 feet.

00:02:04.170 --> 00:02:06.750
If I'm going to have 2 yards,
I'm going to have 6 feet.

00:02:06.750 --> 00:02:08.190
So you should always think about
it in your head, OK,,

00:02:08.190 --> 00:02:09.539
well, yeah, multiplying by 3.

00:02:09.539 --> 00:02:11.009
So that also makes sense.

00:02:11.009 --> 00:02:14.360
So if we multiply by 3
right over here the

00:02:14.360 --> 00:02:19.760
9 times 3 is 27/2.

00:02:19.760 --> 00:02:20.330
Let me write it out.

00:02:20.330 --> 00:02:22.760
Let me take it step by step,
not skipping any steps.

00:02:22.760 --> 00:02:33.290
So this is equal to 9/2
times 3/1 yards.

00:02:33.290 --> 00:02:35.590
This yards right here,
I'll do it in orange.

00:02:35.590 --> 00:02:40.040
Yards times feet per yards.

00:02:49.890 --> 00:02:53.790
The yards cancel out, and you're
left with 9 times 3 is

00:02:53.790 --> 00:03:04.210
equal to 27/2 feet.

00:03:04.210 --> 00:03:08.890
So we figured out 4 and 1/2
yards is 27/2 feet.

00:03:08.890 --> 00:03:11.070
And that makes sense because
we should have

00:03:11.070 --> 00:03:12.370
more feet than yards.

00:03:12.370 --> 00:03:14.180
And actually, this should
be three times more, so

00:03:14.180 --> 00:03:15.490
everything makes sense.

00:03:15.490 --> 00:03:19.290
27/2 is 3 times 9/2.

00:03:19.290 --> 00:03:26.710
So now we have 27/2 feet,
and now we want to

00:03:26.710 --> 00:03:28.050
convert this to inches.

00:03:28.050 --> 00:03:31.260
And we just have to remember
there are 12 inches per yard.

00:03:31.260 --> 00:03:35.260
And we're going to want to
multiply by 12, because

00:03:35.260 --> 00:03:38.300
however many feet we have, we're
going to have 12 times

00:03:38.300 --> 00:03:39.840
as many inches.

00:03:39.840 --> 00:03:41.290
If we have 1 foot, we're
going to have 12

00:03:41.290 --> 00:03:43.520
inches, 2 feet, 24 inches.

00:03:43.520 --> 00:03:46.440
27/2 feet, we're going to
multiply it by 12 to get the

00:03:46.440 --> 00:03:47.720
number of inches.

00:03:47.720 --> 00:03:52.300
Since this is going to be times
12, and we'll make sure

00:03:52.300 --> 00:03:58.840
the dimensions work out:
12 inches per foot.

00:03:58.840 --> 00:04:01.010
And the feet and the foot, this
is just the plural and

00:04:01.010 --> 00:04:02.440
the singular of the same word.

00:04:02.440 --> 00:04:03.790
It's the same dimension.

00:04:03.790 --> 00:04:05.135
This will cancel out.

00:04:05.135 --> 00:04:09.130
So this will be-- if we just
rearrange the multiplication,

00:04:09.130 --> 00:04:11.210
view it as everything is getting
multiplied, and when

00:04:11.210 --> 00:04:13.540
you just multiply a bunch of
things, order doesn't matter.

00:04:13.540 --> 00:04:20.519
So this is equal to 27/2
times 12 feet.

00:04:20.519 --> 00:04:22.540
I'm just swapping the order.

00:04:22.540 --> 00:04:31.540
Feet times inches divided by
feet, or foot, just the

00:04:31.540 --> 00:04:33.140
singular of the same word.

00:04:33.140 --> 00:04:35.720
The feet and the foot cancel
out, they're the same unit.

00:04:35.720 --> 00:04:39.710
And you have 27 times 12
divided by 2 inches.

00:04:39.710 --> 00:04:42.560
And what we could do here is
that our final answer is going

00:04:42.560 --> 00:04:51.660
to be 27 times 12/2 inches.

00:04:51.660 --> 00:04:55.770
And before we multiply the 27
times 12 and then divide by 2,

00:04:55.770 --> 00:04:59.460
you immediately see, well, I can
just divide 12 by 2, and 2

00:04:59.460 --> 00:05:02.400
by 2, and it makes our
computation simpler.

00:05:02.400 --> 00:05:06.200
12 divided by 2 is 6,
2 divided by 2 is 1.

00:05:06.200 --> 00:05:09.450
It becomes 27 times 6 inches,
and let's figure

00:05:09.450 --> 00:05:10.860
out what that is.

00:05:10.860 --> 00:05:15.050
27 times 6.

00:05:15.050 --> 00:05:18.340
7 times 6 is 42.

00:05:18.340 --> 00:05:24.770
2 times 6 is 12, plus 4 is 16.

00:05:24.770 --> 00:05:34.910
This is equal to 162 inches,
which makes sense.

00:05:34.910 --> 00:05:39.320
4 and 1/2 yards, that gets us to
this number right here: 27

00:05:39.320 --> 00:05:42.180
divided by 2 is 13
and 1/2 feet.

00:05:42.180 --> 00:05:44.440
You multiply that by
12, it makes sense.

00:05:44.440 --> 00:05:45.580
You're going to have
a bunch of inches.

00:05:45.580 --> 00:05:47.980
162 inches.


Adding different units of length

WEBVTT
Kind: captions
Language: en

00:00:00.460 --> 00:00:04.650
An electrician has the following
lengths of cable: 23

00:00:04.650 --> 00:00:08.130
inches, 49 inches, and 8 feet.

00:00:08.130 --> 00:00:10.760
How much cable does
he have in Feet?

00:00:10.760 --> 00:00:11.810
So these are the lengths.

00:00:11.810 --> 00:00:13.940
Each of these are the
length of a cable in

00:00:13.940 --> 00:00:15.120
inches, inches, and feet.

00:00:15.120 --> 00:00:17.150
And we want to know the total
length, if you add all of

00:00:17.150 --> 00:00:20.640
these up, and we need the
total length in feet.

00:00:20.640 --> 00:00:23.770
And so the best way to do that
is to convert each of these

00:00:23.770 --> 00:00:27.130
lengths into feet, and
then add them all up.

00:00:27.130 --> 00:00:34.680
So let's start with this one
right over here: 23 inches.

00:00:34.680 --> 00:00:37.940
So it's always important to
have your intuition give a

00:00:37.940 --> 00:00:41.050
little bit of a check on what
the answer should look like.

00:00:41.050 --> 00:00:44.470
There are many inches per foot,
so when you convert this

00:00:44.470 --> 00:00:46.790
into feet, you should have
a smaller number.

00:00:46.790 --> 00:00:49.250
There are 12 inches per foot.

00:00:49.250 --> 00:00:51.170
So this should be
a small number.

00:00:51.170 --> 00:00:52.770
This is not even 2 feet.

00:00:52.770 --> 00:00:54.420
24 inches would be 2 feet.

00:00:54.420 --> 00:00:56.760
So this should be less
than 2 feet.

00:00:56.760 --> 00:00:58.370
But let's do it mathematically.

00:00:58.370 --> 00:01:01.560
So to do it mathematically, we
want this inches to cancel out

00:01:01.560 --> 00:01:02.270
with inches.

00:01:02.270 --> 00:01:04.330
And the way you do that,
is you put that in the

00:01:04.330 --> 00:01:05.580
denominator.

00:01:10.510 --> 00:01:12.360
So it cancels out
with the inches.

00:01:12.360 --> 00:01:16.450
And so we want feet per inches,
or foot per inches.

00:01:16.450 --> 00:01:17.680
I guess I'll just write ft.

00:01:17.680 --> 00:01:19.580
It could be feet or
foot, singular or

00:01:19.580 --> 00:01:21.230
plural, it doesn't matter.

00:01:21.230 --> 00:01:23.680
So how many feet are
there per inches?

00:01:23.680 --> 00:01:25.380
Or another way to think about
it, how many inches

00:01:25.380 --> 00:01:26.710
are there per foot?

00:01:26.710 --> 00:01:32.120
1 foot is equal to 12 inches,
or you could say 1 foot for

00:01:32.120 --> 00:01:35.520
every 12 inches, or you could
read this as 1/12

00:01:35.520 --> 00:01:37.780
of a foot per inch.

00:01:37.780 --> 00:01:43.480
Either way, if we multiply this,
the inches cancel out.

00:01:43.480 --> 00:01:46.520
That's why we know, at least
mathematically, if we just did

00:01:46.520 --> 00:01:49.390
it mechanically, why we
shouldn't multiply by 12.

00:01:49.390 --> 00:01:51.070
But also it should make
complete sense.

00:01:51.070 --> 00:01:53.910
We should be dividing by 12
because when you express this

00:01:53.910 --> 00:01:56.770
distance in feet, it should be a
smaller number, so we should

00:01:56.770 --> 00:01:58.120
divide by 12.

00:01:58.120 --> 00:01:59.150
So what does this give us?

00:01:59.150 --> 00:02:09.470
This is equal to 23
times 1 is 23/12.

00:02:09.470 --> 00:02:11.820
This inches cancels out with
that inches, and we're just

00:02:11.820 --> 00:02:13.250
left with feet.

00:02:13.250 --> 00:02:15.840
So that is 23/12 feet.

00:02:15.840 --> 00:02:17.840
And this is an improper
fraction, but I'll leave it as

00:02:17.840 --> 00:02:20.090
an improper fraction for now
because they're actually

00:02:20.090 --> 00:02:22.370
easier to manipulate
than mixed numbers.

00:02:22.370 --> 00:02:23.660
So that's that first cable.

00:02:23.660 --> 00:02:27.190
Let's do the second one
right here: 49 inches.

00:02:27.190 --> 00:02:31.810
So the second cable
is 49 inches, and

00:02:31.810 --> 00:02:32.630
we do the same thing.

00:02:32.630 --> 00:02:34.160
We want to convert it to feet.

00:02:34.160 --> 00:02:35.760
We have inches in
the denominator.

00:02:35.760 --> 00:02:39.610
We should end up dividing by
something because we want a

00:02:39.610 --> 00:02:40.280
smaller number.

00:02:40.280 --> 00:02:43.050
49 inches will be a smaller
number of feet

00:02:43.050 --> 00:02:44.520
by a factor of 12.

00:02:44.520 --> 00:02:48.610
So what we care about is feet
per inches, and we know that

00:02:48.610 --> 00:02:51.840
there is 1 foot for every
12 inches, or 1/12

00:02:51.840 --> 00:02:52.940
of a foot per inch.

00:02:52.940 --> 00:02:54.290
It can be read either way.

00:02:54.290 --> 00:02:57.770
When you multiply, the inches
will cancel out, and we will

00:02:57.770 --> 00:03:04.590
be left with 49 times 1, which
is 49, over 12 feet.

00:03:04.590 --> 00:03:06.450
That is the second cable.

00:03:06.450 --> 00:03:08.310
And then we have this
last cable right

00:03:08.310 --> 00:03:12.390
here, this 8-foot cable.

00:03:12.390 --> 00:03:17.950
The very last one is 8 feet, and
if we want, we can convert

00:03:17.950 --> 00:03:19.710
that into an improper
fraction.

00:03:19.710 --> 00:03:21.500
At this point, there's two
ways we can do it.

00:03:21.500 --> 00:03:22.680
Everything is in feet.

00:03:22.680 --> 00:03:24.190
Here, it's improper fractions.

00:03:24.190 --> 00:03:28.360
We could, if we want, convert
these into mixed numbers and

00:03:28.360 --> 00:03:30.780
then add them up, or we can
convert this into an improper

00:03:30.780 --> 00:03:33.350
fraction that has the same
denominator, and

00:03:33.350 --> 00:03:34.280
then add them up.

00:03:34.280 --> 00:03:36.450
And the easiest way, I think, is
to just have this with the

00:03:36.450 --> 00:03:37.230
denominator 12.

00:03:37.230 --> 00:03:40.530
So 8 feet is the same thing
as what over 12?

00:03:40.530 --> 00:03:41.870
Well, what's 8 times 12?

00:03:41.870 --> 00:03:43.320
It's 96, right?

00:03:43.320 --> 00:03:45.580
96 divided by 12 is 8.

00:03:45.580 --> 00:03:48.340
8 is the same thing as 96/12.

00:03:48.340 --> 00:03:49.610
These are equivalent.

00:03:49.610 --> 00:03:53.320
Let me make sure this 8 and
96/12 is the exact same thing.

00:03:53.320 --> 00:03:56.850
I picked 12 because these have
12 in the denominator.

00:03:56.850 --> 00:03:59.900
And then I said, 12
times 8 is 96.

00:03:59.900 --> 00:04:04.560
So 8 feet is the same
thing as 96/12 feet.

00:04:04.560 --> 00:04:06.470
And now I can add
everything up.

00:04:06.470 --> 00:04:10.780
The total length of cable he has
is-- I'll do it over here.

00:04:10.780 --> 00:04:22.200
It's 96/12 plus 23/12 plus
49/12, and everything is in

00:04:22.200 --> 00:04:24.640
feet, so this answer will
give us in feet.

00:04:24.640 --> 00:04:26.650
We have all of the same
denominators.

00:04:26.650 --> 00:04:30.970
Our denominator is 12.

00:04:30.970 --> 00:04:38.080
And so our numerator's going
to be 96 plus 23 plus 49.

00:04:38.080 --> 00:04:39.360
Let's add that up over here.

00:04:39.360 --> 00:04:45.020
So 96, 23, 49, we have
to add it up.

00:04:45.020 --> 00:04:46.630
6 plus 3 is 9.

00:04:46.630 --> 00:04:50.010
9 plus 9 is 18.

00:04:50.010 --> 00:04:51.780
1 plus 9 is 10.

00:04:51.780 --> 00:04:53.630
10 plus 2 is 12.

00:04:53.630 --> 00:04:56.650
12 plus 4 is 16.

00:04:56.650 --> 00:04:57.930
So that's 168.

00:04:57.930 --> 00:05:04.120
So this expression right here is
equal to 168/12, which is a

00:05:04.120 --> 00:05:04.590
valid answer.

00:05:04.590 --> 00:05:05.840
And, of course, all of
these are in feet,

00:05:05.840 --> 00:05:08.090
so it's 168/12 feet.

00:05:08.090 --> 00:05:10.410
But let's write this now as a
mixed number, so that we have

00:05:10.410 --> 00:05:12.890
a better idea of really
how many feet it is.

00:05:12.890 --> 00:05:16.410
And to do that, we just
divide 168 by 12.

00:05:16.410 --> 00:05:20.790
So 12 goes into 168.

00:05:20.790 --> 00:05:22.140
It doesn't go into 1.

00:05:22.140 --> 00:05:24.400
It goes into 16 exactly
one time.

00:05:24.400 --> 00:05:26.520
1 times 12 is 12.

00:05:26.520 --> 00:05:27.400
We subtract.

00:05:27.400 --> 00:05:30.580
16 minus 12 is 4.

00:05:30.580 --> 00:05:32.110
Bring down the 8.

00:05:35.560 --> 00:05:38.270
12 goes into 48 four times.

00:05:38.270 --> 00:05:40.610
4 times 12 is 48.

00:05:40.610 --> 00:05:42.840
And we have no remainder.

00:05:42.840 --> 00:05:46.140
So 168/12 is exactly
14, so this is

00:05:46.140 --> 00:05:49.670
exactly equal to 14 feet.

00:05:49.670 --> 00:05:56.780
So our electrician has exactly
14 feet of cable.


Percent word problem example 4

WEBVTT
Kind: captions
Language: en

00:00:00.760 --> 00:00:04.050
100 is what percent of 80?

00:00:04.050 --> 00:00:07.080
These problems tend to kill
people because on some level

00:00:07.080 --> 00:00:09.260
they're kind of simple, they're
just 100 and an 80

00:00:09.260 --> 00:00:11.130
there, and they're asking
what percent.

00:00:11.130 --> 00:00:12.530
But then people get confused.

00:00:12.530 --> 00:00:14.210
They say, do I divide
the 100 by the 80?

00:00:14.210 --> 00:00:15.080
The 80 by 100?

00:00:15.080 --> 00:00:16.570
Or is it something
else going on?

00:00:16.570 --> 00:00:18.630
And you really just have to
think through what the

00:00:18.630 --> 00:00:19.660
language is saying.

00:00:19.660 --> 00:00:24.410
They're saying that this value
right here, this 100, is some

00:00:24.410 --> 00:00:27.480
percentage of 80, and that some
percentage is what we

00:00:27.480 --> 00:00:28.310
have to figure out.

00:00:28.310 --> 00:00:30.020
What percent?

00:00:30.020 --> 00:00:35.370
So if we multiply 80 by this
what percent, we will get 100.

00:00:35.370 --> 00:00:36.720
So let's view it this way.

00:00:39.380 --> 00:00:40.200
We have 80.

00:00:40.200 --> 00:00:43.510
If we multiply it by something,
let's call this

00:00:43.510 --> 00:00:45.700
something x.

00:00:45.700 --> 00:00:46.900
Let me do that in a
different color.

00:00:46.900 --> 00:00:50.350
If we multiply 80 by
something, we are

00:00:50.350 --> 00:00:52.180
going to get 100.

00:00:52.180 --> 00:00:53.960
And we need to figure out
what we need to multiply

00:00:53.960 --> 00:00:56.510
80 by to get 100.

00:00:56.510 --> 00:00:59.040
And if we just solve this
equation as it is, we're going

00:00:59.040 --> 00:01:01.920
to get a value for x.

00:01:01.920 --> 00:01:05.459
And what we need to do is then
convert it to a percent.

00:01:05.459 --> 00:01:08.540
Another way you could have
viewed this is 100 is what you

00:01:08.540 --> 00:01:10.670
get when you multiply
what by 80?

00:01:10.670 --> 00:01:12.750
And then you would have gotten
this number, and then you

00:01:12.750 --> 00:01:14.800
could convert it to a percent.

00:01:14.800 --> 00:01:16.540
So this is essentially
the equation and now

00:01:16.540 --> 00:01:17.520
we can solve it.

00:01:17.520 --> 00:01:21.280
If we divide both sides of this
equation by 80, so you

00:01:21.280 --> 00:01:24.210
divide the left-hand side by
80, the right-hand side

00:01:24.210 --> 00:01:26.615
by 80, you get x.

00:01:26.615 --> 00:01:30.950
x is equal to 100/80.

00:01:30.950 --> 00:01:36.150
They both share a common factor
of 20, so 100 divided

00:01:36.150 --> 00:01:44.010
by 20 is 5, and 80 divided
by 20 is 4.

00:01:44.010 --> 00:01:48.180
So in simplest form, x is equal
to 5/4, but I've only

00:01:48.180 --> 00:01:50.210
expressed it as a fraction.

00:01:50.210 --> 00:01:52.290
But they want to know
what percent of 80.

00:01:52.290 --> 00:01:54.720
If they just said 100
is what fraction of

00:01:54.720 --> 00:01:55.680
80, we would be done.

00:01:55.680 --> 00:01:58.570
We could say 100 is 5/4
of 80, and we would

00:01:58.570 --> 00:02:00.470
be absolutely correct.

00:02:00.470 --> 00:02:02.130
But they want to say
what percent?

00:02:02.130 --> 00:02:05.080
So we have to convert this to
a percent, and the easiest

00:02:05.080 --> 00:02:08.570
thing to do is to first convert
it into a decimal, so

00:02:08.570 --> 00:02:09.199
let's do that.

00:02:09.199 --> 00:02:16.700
5/4 is literally the same thing
as 5 divided by 4, so

00:02:16.700 --> 00:02:18.560
let's figure out what that is.

00:02:18.560 --> 00:02:22.010
Let me do it in magenta.

00:02:22.010 --> 00:02:25.950
So 5 divided by 4.

00:02:25.950 --> 00:02:28.190
You want to have all the
decimals there, so let's put

00:02:28.190 --> 00:02:29.860
some zeroes out here.

00:02:29.860 --> 00:02:32.200
4 goes into 5 one time.

00:02:32.200 --> 00:02:35.370
Let me switch up the colors.

00:02:35.370 --> 00:02:37.200
1 times 4 is 4.

00:02:37.200 --> 00:02:38.410
You subtract.

00:02:38.410 --> 00:02:40.690
You get 5 minus 4 is 1.

00:02:40.690 --> 00:02:42.290
Bring down the next zero.

00:02:42.290 --> 00:02:44.350
And of course, the decimal is
sitting right here, so we want

00:02:44.350 --> 00:02:45.880
to put it right over there.

00:02:45.880 --> 00:02:49.950
So you bring down
the next zero.

00:02:49.950 --> 00:02:53.170
4 goes into 10 two times.

00:02:53.170 --> 00:02:55.450
2 times 4 is 8.

00:02:55.450 --> 00:02:56.610
You subtract.

00:02:56.610 --> 00:02:58.690
10 minus 8 is 2.

00:02:58.690 --> 00:03:00.875
Bring down the next zero.

00:03:03.590 --> 00:03:06.700
4 goes into 20 five times.

00:03:06.700 --> 00:03:09.920
5 times 4 is 20.

00:03:09.920 --> 00:03:10.670
Subtract.

00:03:10.670 --> 00:03:11.820
No remainder.

00:03:11.820 --> 00:03:16.090
So this is equal to 1.25.

00:03:16.090 --> 00:03:18.820
5/4 is the same thing
as 5 divided by 4,

00:03:18.820 --> 00:03:21.050
which is equal to 1.25.

00:03:21.050 --> 00:03:28.220
So far, we could say, 100 is
1.25 times 80, or 1.25 of 80,

00:03:28.220 --> 00:03:31.170
you could even say, But we still
haven't expressed it as

00:03:31.170 --> 00:03:31.770
a percentage.

00:03:31.770 --> 00:03:34.650
This is really just
as a number.

00:03:34.650 --> 00:03:37.900
I guess you could call it a
decimal, but it's a whole

00:03:37.900 --> 00:03:38.680
number and a decimal.

00:03:38.680 --> 00:03:40.750
It would be a mixed number if we
didn't do it as a decimal.

00:03:40.750 --> 00:03:44.670
It's 1 and 1/4, or 1 and 25
hundredths, however you want

00:03:44.670 --> 00:03:45.580
to read it.

00:03:45.580 --> 00:03:50.500
So to write it as a percent,
you literally just have to

00:03:50.500 --> 00:03:55.450
multiply this times 100, or
shift the decimal over twice.

00:03:55.450 --> 00:03:58.530
So this is going to be equal to,
as a percent, if you just

00:03:58.530 --> 00:04:11.930
shift the decimal over twice,
this is equal to 125%.

00:04:11.930 --> 00:04:12.980
And that makes complete sense.

00:04:12.980 --> 00:04:17.470
100 is 125% of 80.

00:04:17.470 --> 00:04:19.890
80 is 100% of 80.

00:04:19.890 --> 00:04:21.779
100% percent is more than 80.

00:04:21.779 --> 00:04:24.660
It's actually 1 and 1/4 of 80,
and you see that right over

00:04:24.660 --> 00:04:25.510
there, so it makes sense.

00:04:25.510 --> 00:04:27.470
It's 125%.

00:04:27.470 --> 00:04:29.810
It's more than 100%.

00:04:29.810 --> 00:04:30.740
But we are done.

00:04:30.740 --> 00:04:31.950
We've solved the problem.

00:04:31.950 --> 00:04:35.850
It is a 125% of 80.


Solving percent problems

WEBVTT
Kind: captions
Language: en

00:00:00.420 --> 00:00:04.780
We're asked to identify the
percent, amount, and base in

00:00:04.780 --> 00:00:05.640
this problem.

00:00:05.640 --> 00:00:11.320
And they ask us, 150 is
25% of what number?

00:00:11.320 --> 00:00:13.650
They don't ask us to solve it,
but it's too tempting.

00:00:13.650 --> 00:00:16.800
So what I want to do is first
answer this question that

00:00:16.800 --> 00:00:18.390
they're not even asking
us to solve.

00:00:18.390 --> 00:00:20.140
But first, I want to answer
this question.

00:00:20.140 --> 00:00:23.090
And then we can think about what
the percent, the amount,

00:00:23.090 --> 00:00:25.620
and the base is, because
those are just words.

00:00:25.620 --> 00:00:26.680
Those are just definitions.

00:00:26.680 --> 00:00:28.330
The important thing is
to be able to solve a

00:00:28.330 --> 00:00:29.620
problem like this.

00:00:29.620 --> 00:00:36.640
So they're saying 150 is
25% of what number?

00:00:36.640 --> 00:00:44.030
Or another way to view this,
150 is 25% of some number.

00:00:44.030 --> 00:00:52.690
So let's let x, x is equal
to the number that

00:00:52.690 --> 00:00:58.080
150 is 25% of, right?

00:00:58.080 --> 00:00:59.150
That's what we need
to figure out.

00:00:59.150 --> 00:01:01.470
150 is 25% of what number?

00:01:01.470 --> 00:01:03.920
That number right here
we're seeing is x.

00:01:03.920 --> 00:01:07.270
So that tells us that if we
start with x, and if we were

00:01:07.270 --> 00:01:16.790
to take 25% of x, you could
imagine, that's the same thing

00:01:16.790 --> 00:01:21.500
as multiplying it by 25%, which
is the same thing as

00:01:21.500 --> 00:01:23.420
multiplying it, if you
view it as a decimal,

00:01:23.420 --> 00:01:27.920
times 0.25 times x.

00:01:27.920 --> 00:01:29.230
These two statements
are identical.

00:01:29.230 --> 00:01:32.290
So if you start with that
number, you take 25% of it, or

00:01:32.290 --> 00:01:41.870
you multiply it by 0.25, that
is going to be equal to 150.

00:01:41.870 --> 00:01:45.780
150 is 25% of this number.

00:01:45.780 --> 00:01:48.760
And then you can solve for x.

00:01:48.760 --> 00:01:52.280
So let's just start with
this one over here.

00:01:52.280 --> 00:01:54.110
Let me just write it separately,
so you understand

00:01:54.110 --> 00:01:54.780
what I'm doing.

00:01:54.780 --> 00:02:01.190
0.25 times some number
is equal to 150.

00:02:01.190 --> 00:02:02.910
Now there's two ways
we can do this.

00:02:02.910 --> 00:02:07.780
We can divide both sides of this
equation by 0.25, or if

00:02:07.780 --> 00:02:10.930
you recognize that four quarters
make a dollar, you

00:02:10.930 --> 00:02:14.230
could say, let's multiply both
sides of this equation by 4.

00:02:14.230 --> 00:02:15.200
You could do either one.

00:02:15.200 --> 00:02:17.550
I'll do the first, because
that's how we normally do

00:02:17.550 --> 00:02:20.370
algebra problems like this.

00:02:20.370 --> 00:02:28.590
So let's just multiply
both by 0.25.

00:02:28.590 --> 00:02:30.050
That will just be an x.

00:02:30.050 --> 00:02:35.040
And then the right-hand side
will be 150 divided by 0.25.

00:02:35.040 --> 00:02:36.790
And the reason why I wanted to
is really it's just good

00:02:36.790 --> 00:02:38.420
practice dividing
by a decimal.

00:02:38.420 --> 00:02:39.620
So let's do that.

00:02:39.620 --> 00:02:46.090
So we want to figure out what
150 divided by 0.25 is.

00:02:46.090 --> 00:02:47.610
And we've done this before.

00:02:47.610 --> 00:02:49.590
When you divide by a decimal,
what you can do is you can

00:02:49.590 --> 00:02:51.950
make the number that you're
dividing into the other

00:02:51.950 --> 00:02:54.660
number, you can turn this into
a whole number by essentially

00:02:54.660 --> 00:02:56.980
shifting the decimal
two to the right.

00:02:56.980 --> 00:02:58.715
But if you do that for the
number in the denominator, you

00:02:58.715 --> 00:03:00.700
also have to do that
to the numerator.

00:03:00.700 --> 00:03:04.150
So right now you can view
this as 150.00.

00:03:04.150 --> 00:03:07.360
If you multiply 0.25 times
100, you're shifting the

00:03:07.360 --> 00:03:09.070
decimal two to the right.

00:03:09.070 --> 00:03:11.220
Then you'd also have to do
that with 150, so then it

00:03:11.220 --> 00:03:13.290
becomes 15,000.

00:03:13.290 --> 00:03:15.250
Shift it two to the right.

00:03:15.250 --> 00:03:17.470
So our decimal place
becomes like this.

00:03:17.470 --> 00:03:20.510
So 150 divided by 0.25
is the same thing as

00:03:20.510 --> 00:03:23.840
15,000 divided by 25.

00:03:23.840 --> 00:03:26.520
And let's just work it
out really fast.

00:03:26.520 --> 00:03:31.960
So 25 doesn't go into 1, doesn't
go into 15, it goes

00:03:31.960 --> 00:03:34.650
into 150, what is that?

00:03:34.650 --> 00:03:36.020
Six times, right?

00:03:36.020 --> 00:03:37.890
If it goes into 100 four
times, then it goes

00:03:37.890 --> 00:03:41.290
into 150 six times.

00:03:41.290 --> 00:03:45.290
6 times 0.25 is-- or actually,
this is now a 25.

00:03:45.290 --> 00:03:46.170
We've shifted the decimal.

00:03:46.170 --> 00:03:47.920
This decimal is sitting
right over there.

00:03:47.920 --> 00:03:50.990
So 6 times 25 is 150.

00:03:50.990 --> 00:03:52.190
You subtract.

00:03:52.190 --> 00:03:53.270
You get no remainder.

00:03:53.270 --> 00:03:55.390
Bring down this 0 right here.

00:03:55.390 --> 00:03:58.180
25 goes into 0 zero times.

00:03:58.180 --> 00:03:59.990
0 times 25 is 0.

00:03:59.990 --> 00:04:00.810
Subtract.

00:04:00.810 --> 00:04:01.640
No remainder.

00:04:01.640 --> 00:04:03.620
Bring down this last 0.

00:04:03.620 --> 00:04:06.140
25 goes into 0 zero times.

00:04:06.140 --> 00:04:07.710
0 times 25 is 0.

00:04:07.710 --> 00:04:08.440
Subtract.

00:04:08.440 --> 00:04:09.640
No remainder.

00:04:09.640 --> 00:04:13.840
So 150 divided by 0.25
is equal to 600.

00:04:13.840 --> 00:04:15.470
And you might have been able
to do that in your head,

00:04:15.470 --> 00:04:20.220
because when we were at this
point in our equation, 0.25x

00:04:20.220 --> 00:04:23.790
is equal to 150, you could
have just multiplied both

00:04:23.790 --> 00:04:25.750
sides of this equation
times 4.

00:04:25.750 --> 00:04:29.170
4 times 0.25 is the same
thing as 4 times

00:04:29.170 --> 00:04:31.190
1/4, which is a whole.

00:04:31.190 --> 00:04:33.860
And 4 times 150 is 600.

00:04:33.860 --> 00:04:35.790
So you would have gotten
it either way.

00:04:35.790 --> 00:04:38.390
And this makes total sense.

00:04:38.390 --> 00:04:43.710
If 150 is 25% of some number,
that means 150 should be 1/4

00:04:43.710 --> 00:04:44.310
of that number.

00:04:44.310 --> 00:04:46.690
It should be a lot smaller than
that number, and it is.

00:04:46.690 --> 00:04:49.710
150 is 1/4 of 600.

00:04:49.710 --> 00:04:52.070
Now let's answer their
actual question.

00:04:52.070 --> 00:04:55.950
Identify the percent.

00:04:55.950 --> 00:05:00.800
Well, that looks like 25%,
that's the percent.

00:05:00.800 --> 00:05:03.820
The amount and the base
in this problem.

00:05:03.820 --> 00:05:05.990
And based on how they're wording
it, I assume amount

00:05:05.990 --> 00:05:10.330
means when you take the 25% of
the base, so they're saying

00:05:10.330 --> 00:05:14.335
that the amount-- as my best
sense of it-- is that the

00:05:14.335 --> 00:05:24.540
amount is equal to the percent
times the base.

00:05:24.540 --> 00:05:27.130
Let me do the base in green.

00:05:27.130 --> 00:05:29.410
So the base is the number you're
taking the percent of.

00:05:29.410 --> 00:05:32.650
The amount is the quantity
that that percentage

00:05:32.650 --> 00:05:33.610
represents.

00:05:33.610 --> 00:05:39.670
So here we already saw
the percent is 25%.

00:05:39.670 --> 00:05:40.960
That's the percent.

00:05:40.960 --> 00:05:52.910
The number that we're taking
25% of, or the base, is x.

00:05:52.910 --> 00:05:54.620
The value of it is 600.

00:05:54.620 --> 00:05:55.680
We figured it out.

00:05:55.680 --> 00:05:59.180
And the amount is 150.

00:05:59.180 --> 00:06:01.980
This right here is the amount.

00:06:01.980 --> 00:06:03.350
The amount is 150.

00:06:03.350 --> 00:06:07.630
150 is 25% of the
base, of 600.

00:06:07.630 --> 00:06:10.610
The important thing is how
you solve this problem.

00:06:10.610 --> 00:06:13.950
The words themselves, you know,
those are all really

00:06:13.950 --> 00:06:15.460
just definitions.


Percent word problem example 5

WEBVTT
Kind: captions
Language: en

00:00:00.580 --> 00:00:05.070
78 is 15% of what number?

00:00:05.070 --> 00:00:10.060
So there's some unknown number
out there, and if we take 15%

00:00:10.060 --> 00:00:13.000
of that number, we
will get 78.

00:00:13.000 --> 00:00:16.079
So let's just call that
unknown number x.

00:00:16.079 --> 00:00:24.510
And we know that if we take
15% of x, so multiply x by

00:00:24.510 --> 00:00:29.990
15%, we will get 78.

00:00:29.990 --> 00:00:34.330
And now we just literally
have to solve for x.

00:00:34.330 --> 00:00:37.880
Now, 15% mathematically, you
can deal directly with

00:00:37.880 --> 00:00:39.600
percentages, but it's
much easier if it's

00:00:39.600 --> 00:00:41.240
written as a decimal.

00:00:41.240 --> 00:00:48.350
And we know that 15% is the
same thing as 15 per 100.

00:00:48.350 --> 00:00:50.040
That's literally per cent.

00:00:50.040 --> 00:00:54.560
Cent means 100, which is
the same thing as 0.15.

00:00:54.560 --> 00:00:58.060
This is literally
15 hundredths.

00:00:58.060 --> 00:01:03.600
So we could rewrite this as
0.15 times some unknown

00:01:03.600 --> 00:01:11.510
number, times x,
is equal to 78.

00:01:11.510 --> 00:01:15.570
And now we can divide both sides
of this equation by 0.15

00:01:15.570 --> 00:01:17.460
to solve for x.

00:01:17.460 --> 00:01:21.130
So you divide the left side
by 0.15, and I'm literally

00:01:21.130 --> 00:01:24.140
picking 0.15 to divide both
sides because that's what I

00:01:24.140 --> 00:01:26.030
have out here in
front of the x.

00:01:26.030 --> 00:01:28.580
So if I'm multiplying something
by 0.15 and then I

00:01:28.580 --> 00:01:31.700
divided by 0.15, I'll just
be left with an x here.

00:01:31.700 --> 00:01:33.110
That's the whole motivation.

00:01:33.110 --> 00:01:35.680
If I do it to the left-hand
side, I have to do it to the

00:01:35.680 --> 00:01:36.930
right-hand side.

00:01:39.420 --> 00:01:43.460
These cancel out, and
I get x is equal to

00:01:43.460 --> 00:01:47.600
78 divided by 0.15.

00:01:47.600 --> 00:01:50.000
Now, we have to figure
out what that is.

00:01:50.000 --> 00:01:51.900
If we had a calculator, pretty
straightforward, but let's

00:01:51.900 --> 00:01:53.860
actually work it out.

00:01:53.860 --> 00:01:58.460
So we have 78 divided by,
and it's going to be

00:01:58.460 --> 00:02:01.840
some decimal number.

00:02:01.840 --> 00:02:03.870
It's going to be
larger than 78.

00:02:03.870 --> 00:02:05.790
But let's figure out what it
ends up being, so let's throw

00:02:05.790 --> 00:02:07.050
some zeroes out there.

00:02:07.050 --> 00:02:08.490
It's not going to be
a whole number.

00:02:08.490 --> 00:02:12.860
And we're dividing it by 0.15.

00:02:12.860 --> 00:02:16.030
Now, to simplify things, let's
multiply both this numerator

00:02:16.030 --> 00:02:19.330
and this denominator by 100,
and that's so that 0.15

00:02:19.330 --> 00:02:20.720
becomes 15.

00:02:20.720 --> 00:02:25.530
So 0.15 times 100 is 15.

00:02:25.530 --> 00:02:28.220
We're just moving the decimal
to the right.

00:02:28.220 --> 00:02:30.500
Let me put that in
a new color.

00:02:30.500 --> 00:02:32.470
Right there, that's where
our decimals goes.

00:02:32.470 --> 00:02:34.600
Let me erase the other one,
so we don't get confused.

00:02:34.600 --> 00:02:36.480
If we did that for the 15,
we also have to do

00:02:36.480 --> 00:02:37.520
that for the 78.

00:02:37.520 --> 00:02:42.810
So if you move the decimal two
to the right, one, two, it

00:02:42.810 --> 00:02:48.350
becomes 7,800.

00:02:48.350 --> 00:02:52.530
So one way to think about it, 78
divided by 0.15 is the same

00:02:52.530 --> 00:02:56.880
thing as 7,800 divided by 15,
multiplying the numerator and

00:02:56.880 --> 00:02:59.240
the denominator by 100.

00:02:59.240 --> 00:03:01.890
So let's figure out
what this is.

00:03:01.890 --> 00:03:06.140
15 does not go into 7, So you
could do it zero times and you

00:03:06.140 --> 00:03:07.920
can do all that, or you can just
say, OK, that's not going

00:03:07.920 --> 00:03:08.960
to give us anything.

00:03:08.960 --> 00:03:12.210
So then how many times
does 15 go into 78?

00:03:12.210 --> 00:03:13.040
So let's think about it.

00:03:13.040 --> 00:03:18.640
15 goes into 60 four times.

00:03:18.640 --> 00:03:20.770
15 times 5 is 75.

00:03:20.770 --> 00:03:23.470
That looks about right,
so we say five times.

00:03:23.470 --> 00:03:24.550
5 times 15.

00:03:24.550 --> 00:03:27.810
5 times 5 is 25.

00:03:27.810 --> 00:03:29.150
Put the 2 up there.

00:03:29.150 --> 00:03:31.920
5 times 1 is 5, plus 2 is 7.

00:03:31.920 --> 00:03:34.040
75, you subtract.

00:03:34.040 --> 00:03:36.890
78 minus 75 five is 3.

00:03:36.890 --> 00:03:38.260
Bring down a zero.

00:03:41.220 --> 00:03:44.220
15 goes into 30 exactly
two times.

00:03:44.220 --> 00:03:46.430
2 times 15 is 30.

00:03:46.430 --> 00:03:47.310
Subtract.

00:03:47.310 --> 00:03:48.480
No remainder.

00:03:48.480 --> 00:03:51.040
Bring down the next zero.

00:03:51.040 --> 00:03:52.750
We're still to the left
of the decimal point.

00:03:52.750 --> 00:03:54.470
The decimal point is
right over here.

00:03:54.470 --> 00:03:57.170
If we write it up here, which
we should, it's right over

00:03:57.170 --> 00:03:58.670
there, so we have one
more place to go.

00:03:58.670 --> 00:04:00.730
So we bring down
this next zero.

00:04:00.730 --> 00:04:03.330
15 goes into 0 zero times.

00:04:03.330 --> 00:04:05.520
0 times 15 is 0.

00:04:05.520 --> 00:04:06.640
Subtract.

00:04:06.640 --> 00:04:08.030
No remainder.

00:04:08.030 --> 00:04:13.670
So 78 divided by 0.15
is exactly 520.

00:04:13.670 --> 00:04:16.510
So x is equal to 520.

00:04:16.510 --> 00:04:21.170
So 78 is 15% of 520.

00:04:21.170 --> 00:04:23.500
And if we want to use some of
the terminology that you might

00:04:23.500 --> 00:04:26.945
see in a math class, the 15%
is obviously the percent.

00:04:31.990 --> 00:04:36.420
520, or what number before we
figured out it was 520, that's

00:04:36.420 --> 00:04:38.220
what we're taking the
percentage of.

00:04:38.220 --> 00:04:40.410
This is sometimes referred
to as the base.

00:04:43.520 --> 00:04:46.370
And then when you take some
percentage of the base, you

00:04:46.370 --> 00:04:48.850
get what's sometimes referred
to as the amount.

00:04:48.850 --> 00:04:53.350
So in this circumstance,
78 would be the amount.

00:04:53.350 --> 00:04:56.160
You could view it as the amount
is the percentage of

00:04:56.160 --> 00:04:58.540
the base, but we were able
to figure that out.

00:04:58.540 --> 00:05:01.040
It's nice to know those, if
that's the terminology you use

00:05:01.040 --> 00:05:01.570
in your class.

00:05:01.570 --> 00:05:02.790
But the important thing
is to be able

00:05:02.790 --> 00:05:03.960
just answer this question.

00:05:03.960 --> 00:05:09.750
And it makes sense, because
15% is a very small

00:05:09.750 --> 00:05:10.350
percentage.

00:05:10.350 --> 00:05:13.230
If 78 is a small percentage of
some number, that means that

00:05:13.230 --> 00:05:18.020
number has to be pretty big, and
our answer gels with that.

00:05:18.020 --> 00:05:19.530
This looks about right.

00:05:19.530 --> 00:05:25.030
78 is exactly 15% of 520.


Representing a number as a decimal, percent, and fraction 2

WEBVTT
Kind: captions
Language: en

00:00:00.550 --> 00:00:06.870
We're asked to write 7/8 as a
decimal and as a percent.

00:00:06.870 --> 00:00:08.620
We'll start off with a decimal,
and we'll see it's

00:00:08.620 --> 00:00:12.260
pretty easy to go from a
decimal to a percent.

00:00:12.260 --> 00:00:14.660
Now, whenever you see a problem
like this, it's

00:00:14.660 --> 00:00:15.510
sometimes confusing.

00:00:15.510 --> 00:00:18.000
It's like, how do I even get
it into a decimal, or as a

00:00:18.000 --> 00:00:20.380
fraction over 100, or
as a percentage?

00:00:20.380 --> 00:00:24.160
And you always have to remember
7 over 8, or 7/8, is

00:00:24.160 --> 00:00:25.490
the exact same thing.

00:00:28.120 --> 00:00:33.090
This means literally
7 divided by 8.

00:00:33.090 --> 00:00:34.830
Not 8 divided by 7.

00:00:34.830 --> 00:00:37.180
7 divided by 8.

00:00:37.180 --> 00:00:40.580
The numerator divided
by the denominator.

00:00:40.580 --> 00:00:42.260
And you say, well, how do I
turn that into a decimal?

00:00:42.260 --> 00:00:45.010
Well, we just literally do a
long division problem, but we

00:00:45.010 --> 00:00:48.410
keep going behind the decimal
point, so that we don't end up

00:00:48.410 --> 00:00:50.860
with a remainder, or until we
end up with things repeating.

00:00:50.860 --> 00:00:51.540
You'll see what we mean.

00:00:51.540 --> 00:00:54.330
In this case, we won't end up
with anything repeating.

00:00:54.330 --> 00:00:55.790
So let's try this out.

00:00:55.790 --> 00:00:57.555
So it's 7 divided by 8.

00:01:03.070 --> 00:01:06.910
So how many times does
8 go into 7?

00:01:06.910 --> 00:01:08.530
Well, 8 does not go into 7.

00:01:08.530 --> 00:01:10.250
It goes zero times.

00:01:10.250 --> 00:01:12.180
And actually, just so that we
make sure that everything's

00:01:12.180 --> 00:01:14.280
clean, let's put our decimal.

00:01:14.280 --> 00:01:19.020
You can view this as
8 going into 7.000.

00:01:19.020 --> 00:01:21.940
You can keep adding as many
zeroes as you need until

00:01:21.940 --> 00:01:23.130
you're done dividing.

00:01:23.130 --> 00:01:26.970
So we have our decimal point
right here, right behind the 7

00:01:26.970 --> 00:01:27.640
where it was up here.

00:01:27.640 --> 00:01:30.230
So we say 8 goes into
7 zero times.

00:01:30.230 --> 00:01:33.090
0 times 8 is 0.

00:01:33.090 --> 00:01:34.410
You subtract.

00:01:34.410 --> 00:01:36.520
7 minus 0 is 7.

00:01:36.520 --> 00:01:38.980
Now we can bring down a 0.

00:01:38.980 --> 00:01:40.230
We bring down a 0.

00:01:40.230 --> 00:01:41.570
It becomes 70.

00:01:41.570 --> 00:01:45.010
And then you say 8 goes into
70 how many times?

00:01:45.010 --> 00:01:47.370
Well, 8 times 8 is 64,
so that works.

00:01:47.370 --> 00:01:48.950
8 times 9 is 72.

00:01:48.950 --> 00:01:49.980
That's too big.

00:01:49.980 --> 00:01:51.230
So it goes into it
eight times.

00:01:54.730 --> 00:01:57.250
8 times 8 is 64.

00:01:57.250 --> 00:02:03.060
When you subtract,
70 minus 64 is 6.

00:02:03.060 --> 00:02:05.080
You still have a remainder,
so let's keep going.

00:02:05.080 --> 00:02:07.260
Let's bring down another 0.

00:02:07.260 --> 00:02:11.580
So you bring down another 0
right over there, and so you

00:02:11.580 --> 00:02:13.520
say, how many times
does 8 go into 60?

00:02:13.520 --> 00:02:16.480
8 times 8 is 64, so
that's too big.

00:02:16.480 --> 00:02:20.670
8 times 7 is 56, so
that'll work.

00:02:20.670 --> 00:02:24.680
So it goes into 60
seven times.

00:02:24.680 --> 00:02:27.800
7 times 8 is 56.

00:02:27.800 --> 00:02:29.010
You subtract.

00:02:29.010 --> 00:02:32.300
60 minus 56 is 4.

00:02:32.300 --> 00:02:34.780
So we still have a remainder,
so let's keep bringing down

00:02:34.780 --> 00:02:35.970
some zeroes.

00:02:35.970 --> 00:02:39.210
So let's bring this
0 down here.

00:02:39.210 --> 00:02:41.710
And 8 goes into 40
how many times?

00:02:41.710 --> 00:02:45.690
Well, 8 times 5 is 40, so it
goes in nice and evenly.

00:02:45.690 --> 00:02:47.400
So it goes into it five times.

00:02:47.400 --> 00:02:50.880
5 times 8 is 40.

00:02:50.880 --> 00:02:51.890
Subtract.

00:02:51.890 --> 00:02:53.200
No remainder.

00:02:53.200 --> 00:02:56.450
So as a decimal, we just figured
out that 7/8, which is

00:02:56.450 --> 00:03:04.820
equal to 7 divided by
8, is exactly 0.875.

00:03:04.820 --> 00:03:11.390
So 7/8 as a decimal
is equal to 0.875.

00:03:11.390 --> 00:03:13.490
Now we've done the
decimal part.

00:03:13.490 --> 00:03:15.200
Now the next thing is
to do a percent.

00:03:15.200 --> 00:03:17.520
And if you have it as a decimal,
doing it as a percent

00:03:17.520 --> 00:03:19.160
is very easy.

00:03:19.160 --> 00:03:22.440
You literally shift the decimal
place two to the

00:03:22.440 --> 00:03:24.280
right, and you put a
percent sign there.

00:03:24.280 --> 00:03:25.930
And I think it makes
sense why it works.

00:03:25.930 --> 00:03:28.520
Now you're going to say,
how many per hundred?

00:03:28.520 --> 00:03:33.600
You can view this as
875 thousandths.

00:03:33.600 --> 00:03:34.430
Let me write this down.

00:03:34.430 --> 00:03:35.800
You can view this
as a fraction.

00:03:35.800 --> 00:03:41.050
You could say, well, this is the
same thing as 875/1,000.

00:03:41.050 --> 00:03:42.620
That's how we've read it in
the past. This is the

00:03:42.620 --> 00:03:45.950
thousandths spot right here.

00:03:45.950 --> 00:03:53.340
Or you could read this
as 87.5/100.

00:03:53.340 --> 00:03:56.570
If you just go two decimal
places, it's 87.5/100.

00:03:56.570 --> 00:03:59.060
Or if you just took this, and
you divide the numerator and

00:03:59.060 --> 00:04:01.170
the denominator by 10,
you would get this.

00:04:01.170 --> 00:04:06.700
And this is literally saying
87.5 per 100, So this second

00:04:06.700 --> 00:04:12.195
statement right here, this is
literally saying 87.5 per

00:04:12.195 --> 00:04:15.560
hundred, or per cent.

00:04:15.560 --> 00:04:21.440
So this is equal to 87.5%.

00:04:21.440 --> 00:04:23.560
So that gives you the reasoning
for why it works,

00:04:23.560 --> 00:04:26.300
but the really easy way, if you
have a decimal, to make it

00:04:26.300 --> 00:04:30.710
into a percent, you literally
multiply the number by 100 and

00:04:30.710 --> 00:04:32.820
put the percent there, which
is essentially telling you

00:04:32.820 --> 00:04:35.090
that you're going to divide by
100, so you're multiplying and

00:04:35.090 --> 00:04:36.040
dividing by 100.

00:04:36.040 --> 00:04:39.460
So if you multiply this by 100,
which is equivalent to

00:04:39.460 --> 00:04:42.520
shifting the decimal place two
places to the right, that

00:04:42.520 --> 00:04:47.570
literally would become
87.5, then you

00:04:47.570 --> 00:04:48.630
want to put the percent.

00:04:48.630 --> 00:04:51.310
This says this is going
to be over 100.

00:04:51.310 --> 00:04:53.360
So you multiply by 100, and
then divide by 100.

00:04:53.360 --> 00:04:55.510
You're not really changing
the number.

00:04:55.510 --> 00:04:57.010
Hopefully, that makes sense.

00:04:57.010 --> 00:04:58.820
Another way to remember, because
sometimes you might

00:04:58.820 --> 00:05:02.280
get confused-- Do I put the
decimal to the right?

00:05:02.280 --> 00:05:04.550
Do I take it to the left--
is that the decimal

00:05:04.550 --> 00:05:07.890
representation will always be
smaller than the percent

00:05:07.890 --> 00:05:08.940
representation.

00:05:08.940 --> 00:05:10.820
And not only will it be smaller,
but it will be

00:05:10.820 --> 00:05:15.060
smaller by exactly
a factor of 100.

00:05:15.060 --> 00:05:17.870
This is 100 times smaller
of a number right here

00:05:17.870 --> 00:05:19.910
than just the 87.5.

00:05:19.910 --> 00:05:21.980
Obviously, when you put this
percent here, these become the

00:05:21.980 --> 00:05:24.390
exact same number.


Converting percent to decimal and fraction

WEBVTT
Kind: captions
Language: en

00:00:00.670 --> 00:00:06.150
Write 18% as a decimal and as
a fraction in simplest form.

00:00:06.150 --> 00:00:12.550
So let's do it as a decimal
first. So 18% is the same

00:00:12.550 --> 00:00:18.050
thing as 18 per 100,
or 18 per cent.

00:00:18.050 --> 00:00:20.230
I'm actually separating out the
percent, it's only going

00:00:20.230 --> 00:00:21.460
to be one word, but
I'm writing it as,

00:00:21.460 --> 00:00:23.120
literally, per cent.

00:00:23.120 --> 00:00:25.120
Cent means the same
thing as 100.

00:00:25.120 --> 00:00:29.130
So this literally means
18 per 100.

00:00:29.130 --> 00:00:31.580
Actually, I said I would do the
decimal first, but we can

00:00:31.580 --> 00:00:35.180
start putting it into a fraction
first. 18 per 100 as

00:00:35.180 --> 00:00:39.790
a fraction literally
means 18/100.

00:00:39.790 --> 00:00:42.235
We're literally doing the
fraction first. This literally

00:00:42.235 --> 00:00:48.270
means 18 per 100, or
18 hundredths.

00:00:48.270 --> 00:00:50.830
From here we can go straight
to a decimal or we could do

00:00:50.830 --> 00:00:52.570
this fraction in
simplest form.

00:00:52.570 --> 00:00:54.470
Let's do the decimal first, just
because that's actually

00:00:54.470 --> 00:00:57.800
what I said I would do first.
Let's do that first. This is

00:00:57.800 --> 00:01:06.710
the same thing as
18 hundredths.

00:01:06.710 --> 00:01:09.100
And we know how to write
that in decimal form.

00:01:09.100 --> 00:01:12.230
It's 0.18.

00:01:12.230 --> 00:01:16.030
You could view this as 1 tenth
and 8 hundredths, which is the

00:01:16.030 --> 00:01:19.410
same thing, or 10 hundredths and
8 hundredths, which is 18

00:01:19.410 --> 00:01:20.260
hundredths.

00:01:20.260 --> 00:01:22.470
So this is written
in decimal form.

00:01:22.470 --> 00:01:24.795
And if we write it as a
simplified fraction, we need

00:01:24.795 --> 00:01:29.800
to see if there is a common
factor for 18 and 100.

00:01:29.800 --> 00:01:31.750
And they're both even numbers,
so we know they're both

00:01:31.750 --> 00:01:34.300
divisible by 2, so let's divide
both the numerator and

00:01:34.300 --> 00:01:35.300
the denominator by 2.

00:01:35.300 --> 00:01:41.260
So we have 18 divided by 2
over 100 divided by 2.

00:01:41.260 --> 00:01:44.390
And we're going to get
18 divided by 2 is 9.

00:01:44.390 --> 00:01:47.840
100 divided by 2 is 50.

00:01:47.840 --> 00:01:51.700
And I don't think these guys
share any common factors.

00:01:51.700 --> 00:01:53.310
50 is not divisible by 3.

00:01:53.310 --> 00:01:55.880
9 is only divisible
by 3 and 1 and 9.

00:01:55.880 --> 00:01:59.050
So this is the fraction
in simplest form.

00:01:59.050 --> 00:02:05.420
So we have 18% is the same thing
as 0.18, which is the

00:02:05.420 --> 00:02:08.889
same thing, in simplest
form, as 9/50.

00:02:08.889 --> 00:02:12.780
Now, I went through a lot of
pain here to show you that

00:02:12.780 --> 00:02:14.520
this really just comes
from the word, from

00:02:14.520 --> 00:02:16.440
percent, from per 100.

00:02:16.440 --> 00:02:18.990
But if you ever were to see this
in a problem, the fast

00:02:18.990 --> 00:02:23.010
way to do this is to immediately
say, OK, if I have

00:02:23.010 --> 00:02:26.910
18%, you should immediately say,
anything in front of the

00:02:26.910 --> 00:02:28.950
percent-- that's that anything,
whatever this

00:02:28.950 --> 00:02:32.060
anything is-- it should be
equal to that anything.

00:02:32.060 --> 00:02:36.250
In this case it's 18/100.

00:02:36.250 --> 00:02:38.180
And another way to think
about it, you could

00:02:38.180 --> 00:02:45.920
view this as 18.0%.

00:02:45.920 --> 00:02:49.530
I just added a trailing zero
there, just so that you see

00:02:49.530 --> 00:02:50.970
the decimal, really.

00:02:50.970 --> 00:02:54.810
But if you want to express this
as a decimal without the

00:02:54.810 --> 00:02:59.770
percent, you just move
the decimal to

00:02:59.770 --> 00:03:01.720
the left two spaces.

00:03:01.720 --> 00:03:06.200
So if we move the decimal to the
left two spaces, one, two,

00:03:06.200 --> 00:03:11.400
this becomes 0.18.

00:03:11.400 --> 00:03:13.700
Or you could immediately
say that 18% as

00:03:13.700 --> 00:03:15.640
a fraction is 18/100.

00:03:15.640 --> 00:03:18.240
When you put it in simplified
form, it's 9/50.

00:03:18.240 --> 00:03:21.060
But you should also see that
18/100, and we have seen this,

00:03:21.060 --> 00:03:27.180
is the exact same thing as
18 hundredths, or 0.18.

00:03:27.180 --> 00:03:29.770
Hopefully, this made some
connections for you and didn't

00:03:29.770 --> 00:03:31.490
confuse you.


The meaning of percent over 100

WEBVTT
Kind: captions
Language: en

00:00:00.660 --> 00:00:04.430
Show 109% by shading.

00:00:04.430 --> 00:00:09.760
So just as a bit of review, 109%
if we were to write it

00:00:09.760 --> 00:00:16.910
out, would literally be 109
percent, which is the same

00:00:16.910 --> 00:00:25.330
thing as 109 per-- and I could
write cent again, but that's

00:00:25.330 --> 00:00:26.270
getting old.

00:00:26.270 --> 00:00:28.540
Cent means 100, so it literally

00:00:28.540 --> 00:00:32.850
means 109 per hundred.

00:00:32.850 --> 00:00:35.400
If you had 100 per 100, you're
dealing with the whole, but

00:00:35.400 --> 00:00:37.040
now we have more than a whole.

00:00:37.040 --> 00:00:38.850
We have 109 per 100.

00:00:38.850 --> 00:00:41.460
We can actually write this as
a ratio, or as a fraction.

00:00:41.460 --> 00:00:45.730
This is the same thing
as 109 per 100.

00:00:45.730 --> 00:00:48.220
It's the the same thing
as 109/100.

00:00:48.220 --> 00:00:50.260
So let's shade that in.

00:00:50.260 --> 00:00:53.720
So we have a whole here,
so we could consider

00:00:53.720 --> 00:00:55.300
this square a whole.

00:00:55.300 --> 00:00:57.150
In the last video, we counted.

00:00:57.150 --> 00:00:58.830
This is a 10 by 10 square.

00:00:58.830 --> 00:01:01.460
It is cut up into 100 pieces.

00:01:01.460 --> 00:01:05.510
So if we want 109 of those
100 pieces, what

00:01:05.510 --> 00:01:06.660
are we talking about?

00:01:06.660 --> 00:01:08.130
That means we're going to
shade in all of the

00:01:08.130 --> 00:01:09.350
100 right over here.

00:01:09.350 --> 00:01:10.950
Let me do that in a new color.

00:01:10.950 --> 00:01:13.090
So we'll shade in all of this.

00:01:17.550 --> 00:01:20.740
If you just shaded that in,
that would be 100%.

00:01:20.740 --> 00:01:28.410
That would be 100/100, or
100 per 100, or 100%.

00:01:28.410 --> 00:01:30.540
I think you're getting the
meaning of all of this.

00:01:30.540 --> 00:01:31.940
I don't just want you just
memorize this stuff.

00:01:31.940 --> 00:01:34.970
This really just means 100
out of 100, or a whole.

00:01:34.970 --> 00:01:37.540
And you can see that this
is the whole square.

00:01:37.540 --> 00:01:39.010
That's 100 out of
100 right there.

00:01:39.010 --> 00:01:43.200
The question is saying show
us 109% by shading.

00:01:43.200 --> 00:01:46.610
We already did 100 per 100, but
we need to do another 9,

00:01:46.610 --> 00:01:48.170
so let's shade in another 9.

00:01:48.170 --> 00:01:55.380
So now we have one, two, three,
four, five, six, seven,

00:01:55.380 --> 00:01:57.030
eight, nine.

00:01:57.030 --> 00:01:59.350
So this piece right here, you
could almost view that is--

00:01:59.350 --> 00:02:02.090
well, that is!

00:02:02.090 --> 00:02:04.320
That is 9% of an
entire square.

00:02:04.320 --> 00:02:06.700
This is 100% of an
entire square.

00:02:06.700 --> 00:02:10.620
If you considered this whole
thing plus this blue area

00:02:10.620 --> 00:02:16.920
right over here, you are talking
about 109% of one

00:02:16.920 --> 00:02:18.690
whole square.

00:02:18.690 --> 00:02:21.430
Hopefully, that made sense.