Categorizing triangles

WEBVTT
Kind: captions
Language: en

00:00:00.520 --> 00:00:03.180
Categorize the following
triangles according to

00:00:03.180 --> 00:00:07.120
whether or not they
are obtuse triangles.

00:00:07.120 --> 00:00:10.010
So an obtuse triangle
is a triangle

00:00:10.010 --> 00:00:12.990
that has an obtuse
angle in it, or an angle

00:00:12.990 --> 00:00:15.970
that is larger than 90 degrees.

00:00:15.970 --> 00:00:18.320
So it's pretty clear
that this one does not

00:00:18.320 --> 00:00:19.470
have any obtuse angles.

00:00:19.470 --> 00:00:20.970
This is a 90 degree
angle, and these

00:00:20.970 --> 00:00:23.010
are going to have to be
less than 90 degrees.

00:00:23.010 --> 00:00:24.950
So this is not obtuse.

00:00:24.950 --> 00:00:27.225
This one right over here,
just by looking at it,

00:00:27.225 --> 00:00:29.400
you see that all of them
are less than 90 degrees,

00:00:29.400 --> 00:00:32.100
so I'll put this not obtuse.

00:00:32.100 --> 00:00:33.860
Now, these two are interesting.

00:00:33.860 --> 00:00:37.960
Angle JKL looks like it
is larger than 90 degrees,

00:00:37.960 --> 00:00:39.960
and we can assume that
these are drawn to scale,

00:00:39.960 --> 00:00:42.880
so we can base it on
our visual judgment.

00:00:42.880 --> 00:00:44.930
So I would say that
this is obtuse,

00:00:44.930 --> 00:00:49.880
and angle BAC also looks like
it is larger than 90 degrees.

00:00:49.880 --> 00:00:51.980
So that's an obtuse
angle, so I would

00:00:51.980 --> 00:00:54.050
throw that in the
obtuse bucket as well.

00:00:54.050 --> 00:00:56.530
So we had two not
obtuse, two obtuse.

00:00:56.530 --> 00:00:57.500
Check our answer.

00:00:57.500 --> 00:00:59.980
Let's do a couple more of these.

00:00:59.980 --> 00:01:02.080
Which of the following
are correct descriptions

00:01:02.080 --> 00:01:03.742
of triangle PIG?

00:01:03.742 --> 00:01:06.100
Or I guess triangle pig?

00:01:06.100 --> 00:01:07.900
Select all that apply.

00:01:07.900 --> 00:01:09.994
PIG is equilateral.

00:01:09.994 --> 00:01:10.910
Well, that's not true.

00:01:10.910 --> 00:01:13.410
To be equilateral, all the sides
have to be the same length.

00:01:13.410 --> 00:01:14.990
And we see here two
sides are seven,

00:01:14.990 --> 00:01:16.380
but one side has length 4.

00:01:16.380 --> 00:01:17.860
So that's not true.

00:01:17.860 --> 00:01:20.424
Angle PIG has two equal angles.

00:01:20.424 --> 00:01:21.840
Well, we see that
right over here,

00:01:21.840 --> 00:01:24.120
these two angles
that are 74 degrees.

00:01:24.120 --> 00:01:26.880
So that's true.

00:01:26.880 --> 00:01:30.040
Triangle PIG, I guess,
has an obtuse angle.

00:01:30.040 --> 00:01:32.796
Well, an obtuse angle is one
that's larger than 90 degrees.

00:01:32.796 --> 00:01:34.170
None of these are
larger than 90.

00:01:34.170 --> 00:01:35.650
That's not true.

00:01:35.650 --> 00:01:37.899
Triangle PIG has
three acute angles.

00:01:37.899 --> 00:01:38.690
Well, that is true.

00:01:38.690 --> 00:01:41.980
All of these angles are
less than 90 degrees.

00:01:41.980 --> 00:01:44.420
Triangle PIG has a right angle.

00:01:44.420 --> 00:01:46.880
No, none of these angles
are exactly 90 degrees,

00:01:46.880 --> 00:01:50.390
so it does not
have a right angle.

00:01:50.390 --> 00:01:51.477
So let's check our answer.

00:01:51.477 --> 00:01:52.560
Let's do one more of this.

00:01:52.560 --> 00:01:54.620
This is actually kind of fun.

00:01:54.620 --> 00:01:56.760
Categorize the following
triangles according to

00:01:56.760 --> 00:01:58.380
whether or not they
are equilateral.

00:01:58.380 --> 00:02:00.230
So to be equilateral,
all of the sides

00:02:00.230 --> 00:02:01.890
have to have the same length.

00:02:01.890 --> 00:02:03.239
So this is equilateral.

00:02:03.239 --> 00:02:05.530
This one, the sides are
definitely not the same length.

00:02:05.530 --> 00:02:07.821
In fact, not even two of the
sides are the same length.

00:02:07.821 --> 00:02:09.491
That's really a
scalene triangle.

00:02:09.491 --> 00:02:11.490
Here we have two sides
that are the same length,

00:02:11.490 --> 00:02:12.410
but the third is different.

00:02:12.410 --> 00:02:14.030
This would be an
isosceles triangle,

00:02:14.030 --> 00:02:16.600
but it's not equilateral.

00:02:16.600 --> 00:02:18.300
And here they're
all the same length,

00:02:18.300 --> 00:02:20.600
so we have an
equilateral triangle.

00:02:20.600 --> 00:02:22.560
We got it right.


Triangles: categorization by angle or equal sides

WEBVTT
Kind: captions
Language: en

00:00:00.715 --> 00:00:03.340
What I want to do in this video
is talk about the two main ways

00:00:03.340 --> 00:00:05.380
that triangles are categorized.

00:00:05.380 --> 00:00:07.600
The first way is based
on whether or not

00:00:07.600 --> 00:00:11.410
the triangle has equal sides,
or at least a few equal sides.

00:00:11.410 --> 00:00:13.180
Then the other way is
based on the measure

00:00:13.180 --> 00:00:15.760
of the angles of the triangle.

00:00:15.760 --> 00:00:18.000
So the first
categorization right here,

00:00:18.000 --> 00:00:19.990
and all of these are
based on whether or not

00:00:19.990 --> 00:00:23.340
the triangle has equal
sides, is scalene.

00:00:23.340 --> 00:00:25.560
And a scalene
triangle is a triangle

00:00:25.560 --> 00:00:28.010
where none of the
sides are equal.

00:00:28.010 --> 00:00:30.730
So for example, if I have
a triangle like this, where

00:00:30.730 --> 00:00:37.140
this side has length 3,
this side has length 4,

00:00:37.140 --> 00:00:42.960
and this side has
length 5, then this

00:00:42.960 --> 00:00:46.100
is going to be a
scalene triangle.

00:00:46.100 --> 00:00:49.780
None of the sides
have an equal length.

00:00:49.780 --> 00:00:53.560
Now an isosceles triangle is
a triangle where at least two

00:00:53.560 --> 00:00:56.240
of the sides have equal lengths.

00:00:56.240 --> 00:01:01.450
So for example, this would
be an isosceles triangle.

00:01:01.450 --> 00:01:05.780
Maybe this has length
3, this has length 3,

00:01:05.780 --> 00:01:06.970
and this has length 2.

00:01:06.970 --> 00:01:10.920
Notice, this side and
this side are equal.

00:01:10.920 --> 00:01:15.310
So it meets the constraint of
at least two of the three sides

00:01:15.310 --> 00:01:18.350
are have the same length.

00:01:18.350 --> 00:01:21.340
Now an equilateral
triangle, you might imagine,

00:01:21.340 --> 00:01:23.170
and you'd be right,
is a triangle

00:01:23.170 --> 00:01:26.530
where all three sides
have the same length.

00:01:26.530 --> 00:01:30.800
So for example, this would
be an equilateral triangle.

00:01:30.800 --> 00:01:36.756
And let's say that this
has side 2, 2, and 2.

00:01:36.756 --> 00:01:41.900
Or if I have a triangle like
this where it's 3, 3, and 3.

00:01:41.900 --> 00:01:45.110
Any triangle where all three
sides have the same length

00:01:45.110 --> 00:01:47.330
is going to be equilateral.

00:01:47.330 --> 00:01:49.020
Now you might say,
well Sal, didn't you

00:01:49.020 --> 00:01:50.800
just say that an
isosceles triangle is

00:01:50.800 --> 00:01:54.270
a triangle has at least
two sides being equal.

00:01:54.270 --> 00:01:57.460
Wouldn't an equilateral
triangle be a special case

00:01:57.460 --> 00:01:59.340
of an isosceles triangle?

00:01:59.340 --> 00:02:02.230
And I would say yes,
you're absolutely right.

00:02:02.230 --> 00:02:05.110
An equilateral triangle
has all three sides equal,

00:02:05.110 --> 00:02:07.900
so it meets the constraints
for an isosceles.

00:02:07.900 --> 00:02:11.440
So by that definition,
all equilateral triangles

00:02:11.440 --> 00:02:13.730
are also isosceles triangles.

00:02:13.730 --> 00:02:16.480
But not all isosceles
triangles are equilateral.

00:02:16.480 --> 00:02:18.300
So for example, this
one right over here,

00:02:18.300 --> 00:02:21.560
this isosceles triangle,
clearly not equilateral.

00:02:21.560 --> 00:02:23.120
All three sides
are not the same.

00:02:23.120 --> 00:02:24.260
Only two are.

00:02:24.260 --> 00:02:26.140
But both of these
equilateral triangles

00:02:26.140 --> 00:02:29.380
meet the constraint that
at least two of the sides

00:02:29.380 --> 00:02:30.940
are equal.

00:02:30.940 --> 00:02:35.010
Now down here, we're going
to classify based on angles.

00:02:35.010 --> 00:02:39.620
An acute triangle is a triangle
where all of the angles

00:02:39.620 --> 00:02:41.480
are less than 90 degrees.

00:02:44.090 --> 00:02:53.590
So for example, a triangle
like this-- maybe this is 60,

00:02:53.590 --> 00:02:55.090
let me draw a little
bit bigger so I

00:02:55.090 --> 00:02:56.500
can draw the angle measures.

00:03:01.730 --> 00:03:03.290
That's a little bit less.

00:03:03.290 --> 00:03:05.650
I want to make it a
little bit more obvious.

00:03:05.650 --> 00:03:11.210
So let's say a
triangle like this.

00:03:11.210 --> 00:03:15.460
If this angle is 60 degrees,
maybe this one right over here

00:03:15.460 --> 00:03:18.040
is 59 degrees.

00:03:18.040 --> 00:03:21.290
And then this angle right
over here is 61 degrees.

00:03:21.290 --> 00:03:24.900
Notice they all add
up to 180 degrees.

00:03:24.900 --> 00:03:26.470
This would be an acute triangle.

00:03:26.470 --> 00:03:30.235
Notice all of the angles
are less than 90 degrees.

00:03:35.480 --> 00:03:38.290
A right triangle
is a triangle that

00:03:38.290 --> 00:03:41.630
has one angle that is
exactly 90 degrees.

00:03:41.630 --> 00:03:48.700
So for example, this right over
here would be a right triangle.

00:03:48.700 --> 00:03:52.260
Maybe this angle or this angle
is one that's 90 degrees.

00:03:52.260 --> 00:03:54.120
And the normal way
that this is specified,

00:03:54.120 --> 00:03:56.328
people wouldn't just do the
traditional angle measure

00:03:56.328 --> 00:03:57.580
and write 90 degrees here.

00:04:00.680 --> 00:04:02.540
They would draw the
angle like this.

00:04:02.540 --> 00:04:06.040
They would put a little, the
edge of a box-looking thing.

00:04:06.040 --> 00:04:08.230
And that tells you that
this angle right over here

00:04:08.230 --> 00:04:09.570
is 90 degrees.

00:04:09.570 --> 00:04:12.450
And because this triangle
has a 90 degree angle,

00:04:12.450 --> 00:04:14.870
and it could only have
one 90 degree angle,

00:04:14.870 --> 00:04:17.029
this is a right triangle.

00:04:17.029 --> 00:04:19.512
So that is equal to 90 degrees.

00:04:19.512 --> 00:04:21.970
Now you could imagine an obtuse
triangle, based on the idea

00:04:21.970 --> 00:04:24.880
that an obtuse angle is
larger than 90 degrees,

00:04:24.880 --> 00:04:27.180
an obtuse triangle
is a triangle that

00:04:27.180 --> 00:04:30.720
has one angle that is
larger than 90 degrees.

00:04:30.720 --> 00:04:34.275
So let's say that you have a
triangle that looks like this.

00:04:40.520 --> 00:04:44.820
Maybe this is 120 degrees.

00:04:44.820 --> 00:04:46.736
And then let's see,
let me make sure

00:04:46.736 --> 00:04:47.860
that this would make sense.

00:04:47.860 --> 00:04:53.260
Maybe this is 25 degrees.

00:04:53.260 --> 00:04:56.760
Or maybe that is 35 degrees.

00:04:56.760 --> 00:04:59.170
And this is 25 degrees.

00:04:59.170 --> 00:05:02.860
Notice, they still add up to
180, or at least they should.

00:05:02.860 --> 00:05:07.276
25 plus 35 is 60, plus
120, is 180 degrees.

00:05:07.276 --> 00:05:08.900
But the important
point here is that we

00:05:08.900 --> 00:05:11.950
have an angle that
is a larger, that

00:05:11.950 --> 00:05:16.150
is greater, than 90 degrees.

00:05:16.150 --> 00:05:17.570
Now, you might be
asking yourself,

00:05:17.570 --> 00:05:21.530
hey Sal, can a triangle be
multiple of these things.

00:05:21.530 --> 00:05:24.620
Can it be a right
scalene triangle?

00:05:24.620 --> 00:05:27.544
Absolutely, you could have
a right scalene triangle.

00:05:27.544 --> 00:05:28.960
In this situation
right over here,

00:05:28.960 --> 00:05:31.560
actually a 3, 4, 5
triangle, a triangle

00:05:31.560 --> 00:05:35.140
that has lengths of 3, 4, and
5 actually is a right triangle.

00:05:35.140 --> 00:05:39.350
And this right over here
would be a 90 degree angle.

00:05:39.350 --> 00:05:42.670
You could have an
equilateral acute triangle.

00:05:42.670 --> 00:05:45.520
In fact, all
equilateral triangles,

00:05:45.520 --> 00:05:48.390
because all of the angles
are exactly 60 degrees,

00:05:48.390 --> 00:05:51.630
all equilateral triangles
are actually acute.

00:05:51.630 --> 00:05:53.530
So there's multiple
combinations that you

00:05:53.530 --> 00:05:56.100
could have between
these situations

00:05:56.100 --> 00:05:59.170
and these situations
right over here.


Solving for an angle

WEBVTT
Kind: captions
Language: en

00:00:00.730 --> 00:00:03.890
What is the measure
of angle COB?

00:00:03.890 --> 00:00:08.230
So this is C. This
is O. And this is B.

00:00:08.230 --> 00:00:10.770
So they're telling us, what
is the measure of this angle

00:00:10.770 --> 00:00:12.770
right over here?

00:00:12.770 --> 00:00:14.698
This is angle COB.

00:00:14.698 --> 00:00:16.239
And they clearly
don't give it to us.

00:00:16.239 --> 00:00:17.890
We need to figure it out.

00:00:17.890 --> 00:00:19.620
And what they do give
us is they give us

00:00:19.620 --> 00:00:21.900
the measure of an
adjacent angle.

00:00:21.900 --> 00:00:24.020
This angle is 45-degree angled.

00:00:24.020 --> 00:00:30.200
Angle DOC is adjacent
because it shares this arm,

00:00:30.200 --> 00:00:34.720
this segment OC with angle COB.

00:00:34.720 --> 00:00:36.640
And then they give us
the combined angle.

00:00:36.640 --> 00:00:39.300
If you take the two outer
arms of the two angles,

00:00:39.300 --> 00:00:43.230
these two outer segments,
if you look at angle BOD,

00:00:43.230 --> 00:00:45.880
they tell us that
that is 70 degrees.

00:00:45.880 --> 00:00:48.800
So if the measure of the angle
made from the two outer arms

00:00:48.800 --> 00:00:51.130
of these two adjacent
angles, the two outer rays,

00:00:51.130 --> 00:00:53.980
if you kept going out
like this, if that's

00:00:53.980 --> 00:00:57.660
70 degrees and one of the
adjacent angles is 45,

00:00:57.660 --> 00:01:00.960
then this one right over
here must be 70 minus 45.

00:01:00.960 --> 00:01:04.160
Or another way of thinking about
it is this angle, the question

00:01:04.160 --> 00:01:11.280
mark angle, plus 45 degrees
must be equal to 70 degrees.

00:01:14.140 --> 00:01:21.020
Or that question mark must
be equal to 70 degrees

00:01:21.020 --> 00:01:22.345
minus 45 degrees.

00:01:26.160 --> 00:01:27.800
So what's this going to be?

00:01:27.800 --> 00:01:31.570
Well, if it was 70 minus
40, we'd get to 30.

00:01:31.570 --> 00:01:33.540
But then we have to
subtract another 5.

00:01:33.540 --> 00:01:36.480
So it's going to be 25 degrees.

00:01:36.480 --> 00:01:41.457
So the measure of angle
COB is 25 degrees.


Identify the angle example

WEBVTT
Kind: captions
Language: en

00:00:00.770 --> 00:00:02.974
Match these angles
with their measures.

00:00:02.974 --> 00:00:04.765
There should be one
angle in each category.

00:00:04.765 --> 00:00:08.720
We have 30 degrees, 60 degrees,
90 degrees, and 180 degrees.

00:00:08.720 --> 00:00:11.720
So there's a few that are
very easy to spot out.

00:00:11.720 --> 00:00:16.110
This angle right over here,
it makes a complete line.

00:00:16.110 --> 00:00:19.170
So this is clearly 180 degrees.

00:00:19.170 --> 00:00:20.794
So this one's 180 degrees.

00:00:20.794 --> 00:00:22.460
The other one that
might jump out at you

00:00:22.460 --> 00:00:23.626
is this one right over here.

00:00:23.626 --> 00:00:27.420
This is clearly a right
angle, or a 90-degree angle

00:00:27.420 --> 00:00:28.140
right over here.

00:00:28.140 --> 00:00:29.887
So this is 90 degrees.

00:00:29.887 --> 00:00:31.720
And so we have to think
which of these is 30

00:00:31.720 --> 00:00:33.110
and which is 60 degrees?

00:00:33.110 --> 00:00:34.610
Well, just by
comparing it that way,

00:00:34.610 --> 00:00:36.318
you know that the one
that opens out more

00:00:36.318 --> 00:00:38.800
is going to be 60 degrees and
the one that opens out less

00:00:38.800 --> 00:00:41.450
is going to be 30 degrees.

00:00:41.450 --> 00:00:43.530
And you can see that
this, the opening here,

00:00:43.530 --> 00:00:46.160
is half the size of the
opening right over here.

00:00:46.160 --> 00:00:48.700
So it makes sense that
this is 30, this is 60,

00:00:48.700 --> 00:00:53.610
and it also makes sense
that this angle is 1/3

00:00:53.610 --> 00:00:56.830
the measure of this
angle right over here,

00:00:56.830 --> 00:00:57.860
that this is 90 degrees.

00:00:57.860 --> 00:00:59.520
And then if you
were to double this,

00:00:59.520 --> 00:01:03.040
then this part of the angle
would go all the way out,

00:01:03.040 --> 00:01:06.544
and you would get
to the 180 degrees.

00:01:06.544 --> 00:01:07.960
So let's check our
answer and make

00:01:07.960 --> 00:01:10.210
sure we actually
got this one right.

00:01:10.210 --> 00:01:12.290
Let's do one more, just for fun.

00:01:12.290 --> 00:01:15.950
Which of these angles has
a measure of 60 degrees?

00:01:15.950 --> 00:01:18.600
So there's a couple that we
can immediately rule out.

00:01:18.600 --> 00:01:21.530
This angle here is clearly
more than 90 degrees.

00:01:21.530 --> 00:01:23.220
It's an obtuse angle.

00:01:23.220 --> 00:01:25.830
This angle here is
180 degrees, so we're

00:01:25.830 --> 00:01:27.840
going to have to pick
between these two.

00:01:27.840 --> 00:01:30.950
And we can assume that
these are all at scale.

00:01:30.950 --> 00:01:34.500
So if we know that a right angle
would have this line straight

00:01:34.500 --> 00:01:38.260
up and down, this looks like
it's 2/3 of the way there.

00:01:38.260 --> 00:01:41.394
So I would go with this
one right over there.

00:01:41.394 --> 00:01:43.310
Now, you might say, well,
what about this one?

00:01:43.310 --> 00:01:45.960
Well, this one looks like it's
about 1/3 of a right angle.

00:01:45.960 --> 00:01:48.022
If we were to do
2/3, then 3/3, it

00:01:48.022 --> 00:01:49.730
looks like we would
get to a right angle.

00:01:49.730 --> 00:01:52.635
So this one looks much
closer to 30 degrees.

00:01:52.635 --> 00:01:54.510
So which of these angles
has a measure of 60?

00:01:54.510 --> 00:01:55.430
That one right over there.

00:01:55.430 --> 00:01:57.638
You could immediately rule
out that one and that one,

00:01:57.638 --> 00:02:00.690
and then these take a little
bit closer inspection.


Drawing acute, right and obtuse angles

WEBVTT
Kind: captions
Language: en

00:00:00.690 --> 00:00:05.730
Put the vertex of the angle
at point A. So let me do that.

00:00:05.730 --> 00:00:07.280
Make one of the rays
go through point

00:00:07.280 --> 00:00:09.613
B. Make the other ray go
through one of the other points

00:00:09.613 --> 00:00:11.300
to make an acute angle.

00:00:11.300 --> 00:00:15.040
So an acute angle is an
angle less than 90 degrees.

00:00:15.040 --> 00:00:18.340
So we could make one of these
rays go through point B.

00:00:18.340 --> 00:00:22.100
And then we have to pick where
to put the other ray to make

00:00:22.100 --> 00:00:23.650
it go to one of
the other points.

00:00:23.650 --> 00:00:25.280
And we have to be
very careful here

00:00:25.280 --> 00:00:28.300
because we have to look at
this arc that shows which

00:00:28.300 --> 00:00:30.290
angle the tool is
actually measuring.

00:00:30.290 --> 00:00:34.019
Because we might be tempted
to do something like this,

00:00:34.019 --> 00:00:35.810
thinking that, hey,
maybe this is the angle

00:00:35.810 --> 00:00:37.010
that we're thinking about.

00:00:37.010 --> 00:00:39.890
But the tool thinks we're
referring to this outer angle

00:00:39.890 --> 00:00:42.660
right over here, this
larger huge angle.

00:00:42.660 --> 00:00:46.270
This angle right over here
is well over 180 degrees.

00:00:46.270 --> 00:00:48.610
So we have to pay
attention to this arc

00:00:48.610 --> 00:00:51.540
to make sure that the tool
is looking at the same angle

00:00:51.540 --> 00:00:52.640
that we are.

00:00:52.640 --> 00:00:54.670
So once again, we
want an acute angle.

00:00:54.670 --> 00:00:57.610
So this right over here
looks like an acute angle.

00:00:57.610 --> 00:01:00.100
It looks like it is
less than 90 degrees.

00:01:00.100 --> 00:01:02.470
And we have to be very
careful that we go exactly

00:01:02.470 --> 00:01:03.520
through that point.

00:01:03.520 --> 00:01:05.019
So that looks about right.

00:01:05.019 --> 00:01:07.630
This is an acute angle
because its measure

00:01:07.630 --> 00:01:10.140
is less than 90 degrees.

00:01:10.140 --> 00:01:11.800
Let's do a few more of these.

00:01:11.800 --> 00:01:14.470
Make an obtuse angle
using the black points.

00:01:14.470 --> 00:01:16.280
Choose one of the
points as the vertex

00:01:16.280 --> 00:01:18.910
and make the rays go through
the other two points.

00:01:18.910 --> 00:01:22.510
The angle should also be
less than 180 degrees.

00:01:22.510 --> 00:01:24.670
So you could think
of it several ways.

00:01:24.670 --> 00:01:26.290
You could just try
to pick that point.

00:01:26.290 --> 00:01:29.440
But then when you go through
these other two points,

00:01:29.440 --> 00:01:33.120
this right over here
is an acute angle.

00:01:33.120 --> 00:01:35.160
This is less than 90 degrees.

00:01:35.160 --> 00:01:37.780
You could do something
like this where now when

00:01:37.780 --> 00:01:42.760
I switch the rays, the tool is
now thinking about this angle,

00:01:42.760 --> 00:01:45.930
not this outer angle
right over here.

00:01:45.930 --> 00:01:47.770
But this is larger
than 180 degrees.

00:01:47.770 --> 00:01:49.240
So this also doesn't apply.

00:01:49.240 --> 00:01:52.210
So we really picked the
wrong point for the vertex.

00:01:52.210 --> 00:01:54.470
If you just move this out
of the way and eyeball it,

00:01:54.470 --> 00:01:56.800
it looks like you get
the largest angle that's

00:01:56.800 --> 00:02:00.190
less than 180 degrees if you
put the vertex right over here.

00:02:00.190 --> 00:02:01.590
So let me do that.

00:02:01.590 --> 00:02:03.930
Put the vertex right over there.

00:02:03.930 --> 00:02:07.537
And now it looks like I have
constructed a 180-degree angle.

00:02:07.537 --> 00:02:09.120
And we have to be
very careful that we

00:02:09.120 --> 00:02:11.203
go right through those
points because otherwise it

00:02:11.203 --> 00:02:13.330
might mark us wrong.

00:02:13.330 --> 00:02:14.540
So that looks pretty good.

00:02:14.540 --> 00:02:16.480
That's an obtuse angle
because its measure

00:02:16.480 --> 00:02:20.030
is greater than 90 degrees.

00:02:20.030 --> 00:02:21.720
Let's do one more of these.

00:02:21.720 --> 00:02:24.350
So another obtuse
angle using the points.

00:02:24.350 --> 00:02:31.870
Same general idea so that would
be an exactly 180-degree angle.

00:02:31.870 --> 00:02:34.217
And there we go.

00:02:34.217 --> 00:02:35.800
And this is an obtuse
angle because it

00:02:35.800 --> 00:02:38.920
is greater than 90 degrees.


Recognizing angles

WEBVTT
Kind: captions
Language: en

00:00:00.540 --> 00:00:04.570
Look at the diagram below, then
answer the following question.

00:00:04.570 --> 00:00:07.970
What type of angle is the angle
highlighted in the green below?

00:00:07.970 --> 00:00:09.810
So it looks like
two anteaters going

00:00:09.810 --> 00:00:11.520
after an ant right over here.

00:00:11.520 --> 00:00:13.695
And this anteater is
going straight down,

00:00:13.695 --> 00:00:15.070
or at least on my
screen it looks

00:00:15.070 --> 00:00:16.320
like it's going straight down.

00:00:16.320 --> 00:00:18.840
And this anteater's going
straight to the left.

00:00:18.840 --> 00:00:21.454
And so it looks like this
one's going straight down,

00:00:21.454 --> 00:00:22.870
this one's going
straight to left.

00:00:22.870 --> 00:00:26.474
It looks like this is a right
angle or a 90-degree angle.

00:00:26.474 --> 00:00:28.390
And so if I have to pick
between any of these,

00:00:28.390 --> 00:00:30.640
it looks most like
a right angle.

00:00:30.640 --> 00:00:32.360
It looks like this is
exactly going down,

00:00:32.360 --> 00:00:34.000
and this is going
exactly to the left,

00:00:34.000 --> 00:00:36.370
that this is a
90-degree angle here.

00:00:36.370 --> 00:00:38.770
If this was an acute angle,
then the angle between them

00:00:38.770 --> 00:00:39.870
would be smaller.

00:00:39.870 --> 00:00:41.420
So maybe this top
one would be coming

00:00:41.420 --> 00:00:43.760
in from this direction
right over here.

00:00:43.760 --> 00:00:46.567
If it was obtuse, this
angle would be larger.

00:00:46.567 --> 00:00:48.150
So let's just check
our answer and try

00:00:48.150 --> 00:00:50.770
to do a few more of these.

00:00:50.770 --> 00:00:53.450
Which of the angles labeled
in the diagram below

00:00:53.450 --> 00:00:55.200
are acute angles?

00:00:55.200 --> 00:01:00.340
So just as a reminder, an acute
angle is less than 90 degrees.

00:01:00.340 --> 00:01:07.670
So let's see, A and C both
look larger than 90 degrees.

00:01:07.670 --> 00:01:11.910
But B and D both look
less than 90 degrees.

00:01:11.910 --> 00:01:18.380
So I'll go with B and D
are the acute angles here.

00:01:18.380 --> 00:01:20.830
Let's do another one of these.

00:01:20.830 --> 00:01:24.280
What type of angle is the angle
highlighted in green below?

00:01:24.280 --> 00:01:26.990
Well, this angle is
less than 90 degrees.

00:01:26.990 --> 00:01:28.830
If it was equal to 90
degrees, this thing

00:01:28.830 --> 00:01:30.170
would come out like this.

00:01:30.170 --> 00:01:32.680
So this is clearly
less than 90 degrees.

00:01:32.680 --> 00:01:34.801
This is an acute angle.

00:01:34.801 --> 00:01:35.800
Let me just do one more.

00:01:35.800 --> 00:01:36.674
This is a lot of fun.

00:01:39.720 --> 00:01:42.000
Select a symbol from
the drop-down menu

00:01:42.000 --> 00:01:43.710
to complete the
following statement.

00:01:43.710 --> 00:01:45.540
Then answer the question below.

00:01:45.540 --> 00:01:49.135
Angle A is less than 90 degrees.

00:01:52.640 --> 00:01:55.480
What type of angle is angle A?

00:01:55.480 --> 00:01:59.130
So angle A, it's
less than 90 degrees.

00:01:59.130 --> 00:02:02.390
So an angle less than 90
degrees is an acute angle.

00:02:02.390 --> 00:02:05.070
If it was exactly 90 degrees,
it would be a right angle.

00:02:05.070 --> 00:02:07.320
If it was larger
than 90 degrees,

00:02:07.320 --> 00:02:09.590
it would be an obtuse angle.

00:02:09.590 --> 00:02:12.840
So I will go with acute angle.

00:02:12.840 --> 00:02:14.780
And we got it right.


Constructing angles

WEBVTT
Kind: captions
Language: en

00:00:00.710 --> 00:00:04.290
We're asked to construct
a 10 degree angle.

00:00:04.290 --> 00:00:06.830
So we have this
little angle tool

00:00:06.830 --> 00:00:11.110
here that we can use
to construct an angle.

00:00:11.110 --> 00:00:12.520
So just like that.

00:00:12.520 --> 00:00:14.105
And then they give
us a protractor

00:00:14.105 --> 00:00:16.390
to actually measure the angle.

00:00:16.390 --> 00:00:18.970
So let's set it up.

00:00:18.970 --> 00:00:20.966
Let's put the protractor here.

00:00:20.966 --> 00:00:22.340
Let's put the
vertex of the angle

00:00:22.340 --> 00:00:24.790
at the center of the protractor,
in other words, center

00:00:24.790 --> 00:00:26.642
the protractor at the
center of the vertex.

00:00:26.642 --> 00:00:28.600
Looks like the protractor's
a little bit easier

00:00:28.600 --> 00:00:29.310
to manipulate.

00:00:29.310 --> 00:00:31.020
So let's do that there.

00:00:31.020 --> 00:00:36.230
Now let's put one of the
rays here at 0 degrees.

00:00:36.230 --> 00:00:40.000
And now I'm going to put
the other ray at 10 degrees.

00:00:40.000 --> 00:00:41.630
And it looks like I am done.

00:00:41.630 --> 00:00:43.320
I have constructed
a 10 degree angle.

00:00:43.320 --> 00:00:44.820
And you want to be
careful here when

00:00:44.820 --> 00:00:47.160
you use this tool because
the angle in question--

00:00:47.160 --> 00:00:49.660
let me move the protractor show
you what I'm talking about--

00:00:49.660 --> 00:00:53.020
that this right over here is the
angle that we're talking about.

00:00:53.020 --> 00:00:56.080
If I'd switched these two rays,
the way the tool is set up,

00:00:56.080 --> 00:00:57.950
it might have
interpreted the angle

00:00:57.950 --> 00:00:59.940
as this outer angle
right over here.

00:00:59.940 --> 00:01:03.160
So be careful to look at which
angle we're actually measuring.

00:01:03.160 --> 00:01:05.349
But this looks like I
did the 10 degree angle.

00:01:05.349 --> 00:01:06.677
So let me check my answer.

00:01:06.677 --> 00:01:08.510
And just to be clear
what I'm talking about.

00:01:08.510 --> 00:01:12.060
If you did the 10
degree angle like this,

00:01:12.060 --> 00:01:15.150
then it definitely would
have marked it wrong

00:01:15.150 --> 00:01:19.440
even though the interior angle
right over here or this angle

00:01:19.440 --> 00:01:21.150
right here might be 10 degrees.

00:01:21.150 --> 00:01:23.490
The way the tool is set up,
you see from this circle,

00:01:23.490 --> 00:01:25.980
that it thinks that you're
looking at this outer angle.

00:01:25.980 --> 00:01:27.690
So it's important to
make sure, at least

00:01:27.690 --> 00:01:31.600
for the sake of this
exercise, that the system,

00:01:31.600 --> 00:01:34.110
that the computer
program knows which

00:01:34.110 --> 00:01:35.860
angle you're going
to talk about.

00:01:35.860 --> 00:01:37.480
Let's do one more of these.

00:01:37.480 --> 00:01:39.055
155 degree angle.

00:01:39.055 --> 00:01:40.680
And this one's
interesting because this

00:01:40.680 --> 00:01:42.320
is an obtuse angle.

00:01:42.320 --> 00:01:47.060
So once again, let
us put the protractor

00:01:47.060 --> 00:01:49.670
at the vertex of the angle.

00:01:49.670 --> 00:01:52.350
So just like that.

00:01:52.350 --> 00:01:55.810
And now that seems pretty good.

00:01:55.810 --> 00:02:00.560
Now let's take one ray
and put it at 0 degrees,

00:02:00.560 --> 00:02:03.980
and then let's take the
other one and put it at 155.

00:02:03.980 --> 00:02:08.330
So once again, 10, 20,
30, 40, 50, 60, 70, 80,

00:02:08.330 --> 00:02:10.729
90-- that gets us
to a right angle.

00:02:10.729 --> 00:02:13.804
Then we'll start getting into
obtuse angles, 100, 110, 120,

00:02:13.804 --> 00:02:17.030
130, 140, 150.

00:02:17.030 --> 00:02:19.340
And just to make
sure that blue arc

00:02:19.340 --> 00:02:22.355
is measuring this angle right
over here, not the outer one.

00:02:22.355 --> 00:02:24.230
And let me move the
protractor out of the way

00:02:24.230 --> 00:02:25.820
so we can get a good look at it.

00:02:25.820 --> 00:02:28.700
And we got it wrong.

00:02:28.700 --> 00:02:32.785
So let's see what we--
oh, 155 degree angle, not

00:02:32.785 --> 00:02:34.250
150 degree angle.

00:02:34.250 --> 00:02:35.310
Let me fix that.

00:02:35.310 --> 00:02:38.180
155 degree angle.

00:02:38.180 --> 00:02:40.065
Now we got it right.


Naming angles exercise example

WEBVTT
Kind: captions
Language: en

00:00:00.520 --> 00:00:04.230
What is another
name for angle CPA?

00:00:04.230 --> 00:00:07.900
So we have C, we have
P, and we have A.

00:00:07.900 --> 00:00:12.480
So angle CPA is going to be
this angle right over here.

00:00:12.480 --> 00:00:14.070
So what's another name for it?

00:00:14.070 --> 00:00:19.730
Well, I could start off with A,
and I could call it angle APC.

00:00:19.730 --> 00:00:24.110
So this is the same
thing as angle APC.

00:00:24.110 --> 00:00:26.130
Now is that any
one of my choices?

00:00:26.130 --> 00:00:30.070
Yeah, that's this
choice right over here.

00:00:30.070 --> 00:00:32.200
If someone said angle P,
that wouldn't give you

00:00:32.200 --> 00:00:33.190
a lot of information.

00:00:33.190 --> 00:00:36.744
That kind of says, well, that's
only giving me one point.

00:00:36.744 --> 00:00:38.160
I don't know, maybe
it's referring

00:00:38.160 --> 00:00:40.599
to that angle, that angle,
that angle, that angle.

00:00:40.599 --> 00:00:42.640
So that's really not giving
me enough information

00:00:42.640 --> 00:00:45.030
to specify this angle
right over here.

00:00:45.030 --> 00:00:51.450
Angle PAC would be an angle
formed if you actually

00:00:51.450 --> 00:00:55.640
had a line here, if you
had a line between AC.

00:00:55.640 --> 00:00:57.990
Angle PAC would be
this angle right

00:00:57.990 --> 00:01:00.060
over here, which is
clearly a different angle.

00:01:00.060 --> 00:01:04.629
Angle FPA would be
this angle right

00:01:04.629 --> 00:01:07.150
over here, which is also
clearly a different angle.

00:01:07.150 --> 00:01:10.389
So the only choice that
makes sense is angle APC.


How to read a line plot that uses fractions

WEBVTT
Kind: captions
Language: en

00:00:00.670 --> 00:00:03.870
The amount of rain that falls
in various cities in France

00:00:03.870 --> 00:00:04.740
varies.

00:00:04.740 --> 00:00:08.340
The line plot below shows
the average monthly rainfall

00:00:08.340 --> 00:00:10.360
in 13 different cities.

00:00:10.360 --> 00:00:13.830
Measurements are rounded to the
nearest 1/4 of a centimeter.

00:00:13.830 --> 00:00:15.900
How much more rain
falls in the rainiest

00:00:15.900 --> 00:00:18.210
city than the second
rainiest city?

00:00:18.210 --> 00:00:20.310
So let's make sure we
understand what they're

00:00:20.310 --> 00:00:22.800
calling a line plot
right over here.

00:00:22.800 --> 00:00:25.690
Each of these dots
represents one

00:00:25.690 --> 00:00:29.520
of the cities whose average
monthly rainfall was measured.

00:00:29.520 --> 00:00:31.620
And so, for example,
putting this dot here

00:00:31.620 --> 00:00:33.950
shows that this is
the only city that

00:00:33.950 --> 00:00:38.940
had 6 centimeters of
average monthly rainfall.

00:00:38.940 --> 00:00:43.210
Here, this shows that
there were two cities that

00:00:43.210 --> 00:00:45.840
had an average monthly
rainfall of-- looks

00:00:45.840 --> 00:00:50.090
like 8 and 3/4 centimeters.

00:00:50.090 --> 00:00:53.500
There are two cities that had
an average monthly rainfall

00:00:53.500 --> 00:00:56.150
of 12 and 3/4 centimeters.

00:00:56.150 --> 00:00:58.639
So at any given
amount of rainfall,

00:00:58.639 --> 00:01:00.180
it's essentially
showing you how many

00:01:00.180 --> 00:01:06.430
cities had that amount of
rainfall on average per month.

00:01:06.430 --> 00:01:08.850
Now that we understand
this diagram,

00:01:08.850 --> 00:01:10.440
let's answer the question.

00:01:10.440 --> 00:01:13.834
How much more rain falls
in the rainiest city?

00:01:13.834 --> 00:01:15.500
So the rainiest city
here, well, there's

00:01:15.500 --> 00:01:21.840
only one city that's up here
at 13 and 1/2 centimeters

00:01:21.840 --> 00:01:23.000
of rainfall.

00:01:23.000 --> 00:01:24.970
So this right over here,
let me mark this off.

00:01:24.970 --> 00:01:28.616
This is 13 and 1/2 centimeters.

00:01:28.616 --> 00:01:30.490
How much more rain falls
in the rainiest city

00:01:30.490 --> 00:01:32.600
than in the second
rainiest city?

00:01:32.600 --> 00:01:34.560
Well, this is the
second rainiest city,

00:01:34.560 --> 00:01:36.530
is this city right over here.

00:01:36.530 --> 00:01:41.560
This is 13 and 1/4 centimeter.

00:01:41.560 --> 00:01:45.830
So the difference between the
two is just one notch here.

00:01:45.830 --> 00:01:50.522
It's just one notch, going
from 13 and 1/4 to 13 and 1/2,

00:01:50.522 --> 00:01:51.730
so one notch right over here.

00:01:51.730 --> 00:01:53.730
We see that there's four
notches per centimeter.

00:01:53.730 --> 00:01:56.890
One notch over here is
1/4 of a centimeter.

00:01:56.890 --> 00:01:58.620
So just looking at
it, you could say

00:01:58.620 --> 00:02:06.790
that the difference is
1/4 of a centimeter.

00:02:06.790 --> 00:02:09.140
Now, if it wasn't so
clear, because here we're

00:02:09.140 --> 00:02:10.870
just looking one
notch right over here,

00:02:10.870 --> 00:02:12.810
you could take the
larger of the two

00:02:12.810 --> 00:02:15.940
and subtract from that
the smaller of the two.

00:02:15.940 --> 00:02:20.340
So you could take 13
and 1/2, and from that,

00:02:20.340 --> 00:02:23.320
subtract 13 and 1/4.

00:02:23.320 --> 00:02:25.240
And there's multiple
ways of doing this.

00:02:25.240 --> 00:02:28.520
You could subtract
the 13 from the 13,

00:02:28.520 --> 00:02:31.000
and then subtract
the 1/4 from the 1/2,

00:02:31.000 --> 00:02:32.147
and then you would get 1/4.

00:02:32.147 --> 00:02:33.730
Another way is you
could convert these

00:02:33.730 --> 00:02:36.180
both into improper fractions.

00:02:36.180 --> 00:02:39.820
So 13 and 1/2 is the
same thing as 2 times 13

00:02:39.820 --> 00:02:42.860
is 26 plus 1 is 27.

00:02:42.860 --> 00:02:44.980
So that's 27/2.

00:02:44.980 --> 00:02:51.150
And then we could say minus--
let's see, 4 times 13 is 52,

00:02:51.150 --> 00:02:57.410
plus 1 is 53, so minus 53/4.

00:02:57.410 --> 00:03:00.480
And then in order to
do the subtraction,

00:03:00.480 --> 00:03:02.590
you have to have the
same denominator.

00:03:02.590 --> 00:03:04.720
And so 4 is a multiple
of 2, so we just

00:03:04.720 --> 00:03:07.780
have to multiply the numerator
and denominator here by 2.

00:03:07.780 --> 00:03:18.330
So we have 54/4 minus 53/4,
which is equal to-- well,

00:03:18.330 --> 00:03:22.920
54 minus 53 is 1, over
4-- 1/4 of a centimeter.

00:03:22.920 --> 00:03:25.272
For this problem, this would
clearly be a little bit

00:03:25.272 --> 00:03:26.730
too much that you
would have to do.

00:03:26.730 --> 00:03:28.920
But this is useful
to know just in case

00:03:28.920 --> 00:03:30.730
it wasn't as obvious
that these weren't

00:03:30.730 --> 00:03:33.050
just next to each other.


Currency conversion word problem

WEBVTT
Kind: captions
Language: en

00:00:00.670 --> 00:00:02.840
Dennis is vacationing
in China and wants

00:00:02.840 --> 00:00:05.530
to spend $30 on a new sweater.

00:00:05.530 --> 00:00:10.220
The sweater he likes
costs 197 Chinese yuan .

00:00:10.220 --> 00:00:14.540
One US dollar can be
converted into 6 Chinese yuan.

00:00:14.540 --> 00:00:19.262
Dennis will have blank Chinese
yuan if he converts his $30.

00:00:19.262 --> 00:00:20.470
Well, let's think about this.

00:00:20.470 --> 00:00:23.660
He's going to take $30,
and the conversion rate

00:00:23.660 --> 00:00:27.010
is 6 yuan per dollar.

00:00:27.010 --> 00:00:29.970
So he's going to have $30
times 6 yuan per dollar.

00:00:29.970 --> 00:00:32.439
So he's going to
have 30 times 6 yuan.

00:00:32.439 --> 00:00:36.970
And 30 times 6, well, that's the
same thing as 3 times 6 times

00:00:36.970 --> 00:00:39.470
10, or 180.

00:00:39.470 --> 00:00:43.570
So he's going to have
a 180 Chinese yuan.

00:00:43.570 --> 00:00:45.910
Now does he have enough
money to buy the sweater?

00:00:45.910 --> 00:00:48.360
Well, the sweater cost 197 yuan.

00:00:48.360 --> 00:00:52.460
So no, he does not have enough
money to buy the sweater.


Word problem: making change

WEBVTT
Kind: captions
Language: en

00:00:00.650 --> 00:00:05.830
Charles bought 5 apples
that cost $0.47 each.

00:00:05.830 --> 00:00:10.340
He paid with a five-dollar bill.

00:00:10.340 --> 00:00:13.930
How much change did
Charles receive?

00:00:13.930 --> 00:00:15.660
So let's think about
everything in cents

00:00:15.660 --> 00:00:18.230
since they gave us the
cost in terms of cents.

00:00:18.230 --> 00:00:21.940
So first of all, how much
would the 5 apples cost?

00:00:21.940 --> 00:00:23.820
Well, we got 5 apples.

00:00:23.820 --> 00:00:26.810
5 apples-- let me do
that same green color.

00:00:26.810 --> 00:00:30.060
We have 5 apples, and
each of those apples

00:00:30.060 --> 00:00:31.770
are going to cost $0.47.

00:00:31.770 --> 00:00:37.450
So 5 apples times
$0.47 per apple, this

00:00:37.450 --> 00:00:41.130
will give us the total cost
of the 5 apples in cents.

00:00:41.130 --> 00:00:44.034
So what's 5 times 47?

00:00:44.034 --> 00:00:44.700
Well, let's see.

00:00:44.700 --> 00:00:47.866
5 times 40 is 200.

00:00:47.866 --> 00:00:50.120
5 times 7 is 35.

00:00:50.120 --> 00:00:53.180
So it's going to be 235 cents.

00:00:53.180 --> 00:00:57.290
So it's 235.

00:00:57.290 --> 00:01:02.210
And just to remind
ourselves, this is 235 cents.

00:01:02.210 --> 00:01:04.319
Now, how much did he pay?

00:01:04.319 --> 00:01:07.520
He paid with a five-dollar bill.

00:01:07.520 --> 00:01:10.940
Well, a five-dollar bill is
going to be how many cents?

00:01:10.940 --> 00:01:12.240
Well, let's think about it.

00:01:12.240 --> 00:01:18.300
A five-dollar bill times
100 cents per dollar,

00:01:18.300 --> 00:01:22.810
he's essentially
paying with 500 cents.

00:01:22.810 --> 00:01:26.220
So this right over
here is the cost,

00:01:26.220 --> 00:01:28.650
and then this is what he paid.

00:01:28.650 --> 00:01:30.310
So we could figure
out how much change

00:01:30.310 --> 00:01:32.830
he needs to get back
in terms of cents.

00:01:32.830 --> 00:01:36.120
So he paid 500.

00:01:36.120 --> 00:01:39.150
The cost was 235.

00:01:39.150 --> 00:01:42.610
235, so we just
need to subtract.

00:01:42.610 --> 00:01:44.670
And you might be able
to do this in your head.

00:01:44.670 --> 00:01:46.560
But in case you can't,
we can solve this.

00:01:46.560 --> 00:01:48.400
We can do this by regrouping.

00:01:48.400 --> 00:01:50.020
We have a 0 in the ones place.

00:01:50.020 --> 00:01:52.210
We have a 0 in the tens place.

00:01:52.210 --> 00:01:54.940
But let's try to regroup
from the hundreds place.

00:01:54.940 --> 00:01:56.520
We could take one
of the hundreds,

00:01:56.520 --> 00:01:58.900
so now we have only 400 left.

00:01:58.900 --> 00:02:01.010
And a hundred is
equal to 10 tens.

00:02:01.010 --> 00:02:03.730
So we could put a 10
in the tens place.

00:02:03.730 --> 00:02:05.660
But then we could take
one of those tens away,

00:02:05.660 --> 00:02:07.260
so we only have 9 tens.

00:02:07.260 --> 00:02:10.160
And if you took a 10 away, then
you put that in the ones place,

00:02:10.160 --> 00:02:12.310
it's going to become a 10.

00:02:12.310 --> 00:02:14.630
And now we're ready to subtract.

00:02:14.630 --> 00:02:18.570
So we are left with
10 minus 5 is 5.

00:02:18.570 --> 00:02:20.630
9 minus 3 is 6.

00:02:20.630 --> 00:02:23.600
4 minus 2 is 2.

00:02:23.600 --> 00:02:27.160
So how much change
does Charles receive?

00:02:27.160 --> 00:02:31.570
Well, it would be 265 cents.

00:02:31.570 --> 00:02:34.340
If we wanted to write
this in terms of dollars,

00:02:34.340 --> 00:02:36.810
we already know that there
are 100 cents per dollar.

00:02:40.200 --> 00:02:46.630
So you could view this as
200 cents plus 65 cents.

00:02:46.630 --> 00:02:51.840
And 200 cents-- well, this is
two groups of 100 cents, or $2.

00:02:51.840 --> 00:02:56.540
So this right over here
is $2 and 65 cents.

00:02:56.540 --> 00:02:59.360
Or you could view this--
because 65 cents is really

00:02:59.360 --> 00:03:01.420
65 hundredths of a dollar.

00:03:01.420 --> 00:03:10.150
You could view this as $2 and
65/100 of a dollar, or $2.65.

00:03:10.150 --> 00:03:13.750
So that's how much change
Charles should receive.


Time word problem: When to leave to get home on time

WEBVTT
Kind: captions
Language: en

00:00:00.590 --> 00:00:04.630
If the trip home takes
39 minutes, at what time

00:00:04.630 --> 00:00:06.600
does Chris have
to leave in order

00:00:06.600 --> 00:00:09.465
to be home by a
quarter after 6:00?

00:00:12.680 --> 00:00:14.740
So let's draw a time
line and then think

00:00:14.740 --> 00:00:16.779
about what has to happen here.

00:00:16.779 --> 00:00:18.570
This is at least how
I need to visualize it

00:00:18.570 --> 00:00:20.420
in order to solve this problem.

00:00:20.420 --> 00:00:23.060
And I'm going to do the hours
before 6:00 and after 6:00.

00:00:23.060 --> 00:00:25.170
So I'll start at 5:00 and
I'll go up to 7:00 just

00:00:25.170 --> 00:00:27.516
to make sure that we
capture everything.

00:00:27.516 --> 00:00:29.140
I can draw a straighter
line than that,

00:00:29.140 --> 00:00:31.810
so let me draw it a
little bit straighter.

00:00:31.810 --> 00:00:34.420
Still not perfect,
but it'll do the job.

00:00:34.420 --> 00:00:37.280
So let's say that
this is 5 o'clock.

00:00:37.280 --> 00:00:40.780
This is 6 o'clock.

00:00:40.780 --> 00:00:43.510
And they don't specify
whether it's AM or PM.

00:00:43.510 --> 00:00:44.805
And this is 7 o'clock.

00:00:47.680 --> 00:00:51.020
They tell us he has to be
home by a quarter after 6:00.

00:00:51.020 --> 00:00:53.310
So what is a quarter after 6:00?

00:00:53.310 --> 00:00:56.060
Well, it's going to be a
quarter of the way between 6

00:00:56.060 --> 00:00:57.320
and 7 o'clock.

00:00:57.320 --> 00:01:01.010
So this would be half of the
way between 6 and 7 o'clock.

00:01:01.010 --> 00:01:03.220
And then a quarter
would be half of that.

00:01:03.220 --> 00:01:05.640
So this would be a
quarter after 6:00.

00:01:05.640 --> 00:01:09.460
And if we wanted to specify
what time a quarter after 6:00

00:01:09.460 --> 00:01:12.690
is, a quarter of the way
between 6:00 and 7:00,

00:01:12.690 --> 00:01:15.300
we know there are 60
minutes in an hour.

00:01:15.300 --> 00:01:16.990
So this distance is 60 minutes.

00:01:16.990 --> 00:01:19.890
A quarter of 60 is 15 minutes.

00:01:19.890 --> 00:01:23.240
So this time right
over here is 6:15.

00:01:23.240 --> 00:01:25.600
And that's when
Chris has to be home.

00:01:25.600 --> 00:01:29.180
Now, they tell us that the
trip home takes 39 minutes.

00:01:29.180 --> 00:01:34.890
So he would have to have left
39 minutes before this in order

00:01:34.890 --> 00:01:37.610
to get home at 6:15.

00:01:37.610 --> 00:01:41.660
So let's go 39 minutes
before this to figure out

00:01:41.660 --> 00:01:43.620
the time that he would
have to leave in order

00:01:43.620 --> 00:01:45.600
to be home by 6:15.

00:01:45.600 --> 00:01:52.780
So what is 39
minutes before 6:15?

00:01:52.780 --> 00:01:54.930
Now, the way my
brain processes it,

00:01:54.930 --> 00:01:57.990
I like to think about,
well, how much time

00:01:57.990 --> 00:02:00.050
does it take to get to the hour?

00:02:00.050 --> 00:02:01.600
And then how much
time do you have

00:02:01.600 --> 00:02:04.430
left to go before the hour?

00:02:04.430 --> 00:02:08.880
So this part right over
here is 15 minutes.

00:02:08.880 --> 00:02:13.370
If you go back 15 minutes
from 6:15 and go to 6 o'clock,

00:02:13.370 --> 00:02:15.460
that was 15 minutes.

00:02:15.460 --> 00:02:19.440
So we've already gone 15 minutes
back if we go to 6 o'clock.

00:02:19.440 --> 00:02:22.350
And then how many minutes
do we have left to go back?

00:02:22.350 --> 00:02:24.860
Well, we went 15 of the 39.

00:02:24.860 --> 00:02:30.080
39 minus 15 is 24.

00:02:30.080 --> 00:02:33.980
So we have to go another
24 minutes before the hour.

00:02:33.980 --> 00:02:47.890
So this time right over here
is 24 minutes before 6 o'clock.

00:02:47.890 --> 00:02:50.140
And once again, the way we
figured it out, well, look.

00:02:50.140 --> 00:02:52.620
Going from 6:15, if
you go 15 minutes back,

00:02:52.620 --> 00:02:54.050
you get to 6 o'clock.

00:02:54.050 --> 00:02:56.390
We have to go 39,
so we have 24 left.

00:02:56.390 --> 00:02:59.260
So then we have to go 24
minutes before 6 o'clock.

00:02:59.260 --> 00:03:01.230
But 24 minutes before
6 o'clock would

00:03:01.230 --> 00:03:04.011
be how many minutes
after 5 o'clock?

00:03:04.011 --> 00:03:05.510
Well, once again,
we know that there

00:03:05.510 --> 00:03:07.610
are 60 minutes in an hour.

00:03:07.610 --> 00:03:10.000
So what's 60 minus 24?

00:03:10.000 --> 00:03:11.440
Let me do it right over here.

00:03:11.440 --> 00:03:18.760
So 60 minus 24 is equal to 36.

00:03:18.760 --> 00:03:20.690
And you could either
do that in your head.

00:03:20.690 --> 00:03:23.530
Or you could say, hey, look,
I could maybe borrow here.

00:03:23.530 --> 00:03:24.830
This is a 10.

00:03:24.830 --> 00:03:26.070
This is a 5 for a regroup.

00:03:26.070 --> 00:03:27.270
10 minus 4 is 6.

00:03:27.270 --> 00:03:29.230
5 minus 2 is 3.

00:03:29.230 --> 00:03:37.560
The way my brain does it is
I say, oh, well, 60 minus 20

00:03:37.560 --> 00:03:39.120
would get me to 40.

00:03:39.120 --> 00:03:42.110
And then I need to subtract
another 4 more to get to 36.

00:03:42.110 --> 00:03:45.610
But either way, if we're talking
about 24 minutes before 6

00:03:45.610 --> 00:03:54.800
o'clock, that's the equivalent
to 36 minutes after 5 o'clock.

00:03:54.800 --> 00:03:57.820
So this time right
over here is 5:36.

00:04:00.660 --> 00:04:02.290
So when they say,
what time does Chris

00:04:02.290 --> 00:04:05.560
have to leave in order to be
home by a quarter after 6:00?

00:04:05.560 --> 00:04:07.110
5:36.


How to convert kilograms to milligrams and tons to ounces

WEBVTT
Kind: captions
Language: en

00:00:00.630 --> 00:00:03.080
So I have two conversion
scenarios right over here.

00:00:03.080 --> 00:00:06.040
I want to convert 3
kilograms into milligrams.

00:00:06.040 --> 00:00:08.280
And I want to convert
4 tons into ounces.

00:00:08.280 --> 00:00:10.570
So this is clearly
in the metric system.

00:00:10.570 --> 00:00:13.062
And this right over here is
in the US customary system.

00:00:13.062 --> 00:00:14.520
So I encourage you
pause this video

00:00:14.520 --> 00:00:16.977
and try to do these
conversions on your own.

00:00:16.977 --> 00:00:18.560
Well, to think about
this one, we just

00:00:18.560 --> 00:00:22.320
have to think about what
these prefixes mean.

00:00:22.320 --> 00:00:29.040
So I could rewrite
this is 3 kilograms,

00:00:29.040 --> 00:00:32.716
and we're going to convert it
into some amount of milligrams.

00:00:35.580 --> 00:00:39.110
And we've already seen that the
prefix "kilo," this literally

00:00:39.110 --> 00:00:42.470
means 1,000.

00:00:42.470 --> 00:00:50.530
And the prefix "milli," means 1
over 1,000 or 1,000 of a gram.

00:00:50.530 --> 00:00:52.450
So let's just convert
to grams first.

00:00:52.450 --> 00:00:54.670
Let's go from
kilograms to grams.

00:00:54.670 --> 00:00:57.710
And then we can go from
grams to milligrams.

00:00:57.710 --> 00:01:02.560
So we could say
that 3 kilograms is

00:01:02.560 --> 00:01:15.250
going to be equal to
3 times 1,000 grams.

00:01:15.250 --> 00:01:20.600
So this is equal to 3,000.

00:01:20.600 --> 00:01:22.720
This is literally 3,000 grams.

00:01:22.720 --> 00:01:24.230
That's one way to
interpret "kilo,"

00:01:24.230 --> 00:01:26.650
so this gets us to 3,000 grams.

00:01:26.650 --> 00:01:30.180
Now, how to go from the
grams to the milligrams?

00:01:30.180 --> 00:01:32.790
Well, we already
said right over here

00:01:32.790 --> 00:01:34.560
that 1 milligram--
Let me write it here,

00:01:34.560 --> 00:01:41.660
1 milligram is equal to 1
over 1,000 or 1,000 of a gram.

00:01:41.660 --> 00:01:44.330
But another way of thinking
about this statement

00:01:44.330 --> 00:01:50.280
is that 1 gram is equal
to 1,000 milligrams.

00:01:50.280 --> 00:01:53.530
So if we keep this in
mind, we have 3,000 grams.

00:01:53.530 --> 00:01:58.690
Each of those are going to
be equal to 1,000 milligrams.

00:01:58.690 --> 00:02:03.850
So this is equal to 3,000 grams.

00:02:03.850 --> 00:02:06.760
Each of those are equivalent
to 1,000 milligrams,

00:02:06.760 --> 00:02:11.250
so times 1,000.

00:02:11.250 --> 00:02:14.180
And this is going to give
us the number of milligrams.

00:02:14.180 --> 00:02:15.430
And what is this going to be?

00:02:18.220 --> 00:02:23.500
1,000 thousands is a million,
so 3,000 thousands is 3 million.

00:02:23.500 --> 00:02:31.320
This is going to get us
3 million milligrams.

00:02:31.320 --> 00:02:34.070
Another way to think
about this multiplication,

00:02:34.070 --> 00:02:36.170
I've got 3 zeroes,
here 3 zeroes here,

00:02:36.170 --> 00:02:39.950
so my final product
should-- so 3 times 1 is 3,

00:02:39.950 --> 00:02:43.210
and then I should follow
that with the 6 zeroes

00:02:43.210 --> 00:02:45.967
so I get 3 million milligrams.

00:02:45.967 --> 00:02:47.550
Now let's do the
same thing over here.

00:02:47.550 --> 00:02:52.970
Let's convert this US customary
ton right over here to ounces.

00:02:52.970 --> 00:02:56.630
What we'll do first is we'll go
to pounds, and then from pounds

00:02:56.630 --> 00:02:58.110
we can go to ounces.

00:02:58.110 --> 00:03:07.620
And we know that 1 ton
is equal to 2,000 pounds.

00:03:07.620 --> 00:03:12.602
So 4 tons are going to be
equal to, well each of those

00:03:12.602 --> 00:03:13.810
are going to be 2,000 pounds.

00:03:13.810 --> 00:03:18.150
So it's going to be
4 times 2,000 pounds.

00:03:18.150 --> 00:03:22.235
Which is equal to 8,000 pounds.

00:03:22.235 --> 00:03:23.610
Make sure I have
some space here.

00:03:29.030 --> 00:03:33.630
Now how many ounces are
in each of those pounds?

00:03:33.630 --> 00:03:37.220
Well, we know that
1 pound, we know

00:03:37.220 --> 00:03:43.660
that 1 pound is
equal to 16 ounces.

00:03:43.660 --> 00:03:46.370
So 8,000 pounds,
so this over here--

00:03:46.370 --> 00:03:51.900
so let me write
this, 8,000 pounds.

00:03:51.900 --> 00:03:55.010
If each of those 8,000 have
16 ounces, or equivalent to 16

00:03:55.010 --> 00:04:01.570
ounces, this is going to
be 8,000 times 16 ounces.

00:04:01.570 --> 00:04:04.530
So what is 8,000 times 16?

00:04:04.530 --> 00:04:12.380
So this is going to be 8
times 16 is 80 plus 48 is 128.

00:04:12.380 --> 00:04:20.100
But we want to do 8,000 times,
so it's going to be 128,000.

00:04:20.100 --> 00:04:23.850
So 4 tons are a lot of ounces.


How to convert gallons to quarts, quarts to pints, pints to cups, and cups to ounces

WEBVTT
Kind: captions
Language: en

00:00:00.800 --> 00:00:05.060
So right here we've listed two
quantities or two fluid volumes

00:00:05.060 --> 00:00:07.800
right over here in terms
of gallons, 1 gallon and 2

00:00:07.800 --> 00:00:08.320
gallons.

00:00:08.320 --> 00:00:09.903
And what I want to
do in this video is

00:00:09.903 --> 00:00:13.830
try to convert this quantity
of fluid, this volume of fluid,

00:00:13.830 --> 00:00:17.210
I want to convert it into
these other units within the US

00:00:17.210 --> 00:00:18.749
customary system.

00:00:18.749 --> 00:00:20.290
So I encourage you
to pause the video

00:00:20.290 --> 00:00:21.664
and first try to
do the 1 gallon.

00:00:21.664 --> 00:00:26.010
Try to convert it into quarts,
pints, cups, and fluid ounces.

00:00:26.010 --> 00:00:31.400
Well, 1 gallon is
equal to 4 quarts.

00:00:31.400 --> 00:00:34.720
So we can just multiply by 4.

00:00:34.720 --> 00:00:40.770
1 quart is equal to 2 pints,
so we can multiply this by 2.

00:00:40.770 --> 00:00:43.420
So 4 quarts, each
of them are 2 pints.

00:00:43.420 --> 00:00:46.960
4 times 2 gets us to 8 pints.

00:00:46.960 --> 00:00:50.660
Each pint is equal to 2
cups, so we have 8 pints.

00:00:50.660 --> 00:00:52.450
Each of them are
equal to 2 cups.

00:00:52.450 --> 00:00:55.990
We're going to have 16 cups.

00:00:55.990 --> 00:00:58.170
And then finally, if we're
converting from a cup

00:00:58.170 --> 00:01:02.680
to a fluid ounce, each
cup is 8 fluid ounces.

00:01:02.680 --> 00:01:06.850
So if we have 16 cups, it's
going to be 16 times 8.

00:01:06.850 --> 00:01:09.190
8 times 8 is 64, and it's
going to be twice that.

00:01:09.190 --> 00:01:14.117
That's going to be
128 fluid ounces.

00:01:14.117 --> 00:01:15.950
Now, let's do the same
thing with 2 gallons.

00:01:15.950 --> 00:01:19.397
Try to convert that into quarts,
pints, cups, and fluid ounces.

00:01:19.397 --> 00:01:20.980
And I encourage you
to pause the video

00:01:20.980 --> 00:01:23.370
and try it on your own first.

00:01:23.370 --> 00:01:24.840
Well, same idea.

00:01:24.840 --> 00:01:29.860
1 gallon is equivalent
to 4 quarts.

00:01:29.860 --> 00:01:34.810
So 2 gallons are going to be
2 times 4 quarts, or 8 quarts.

00:01:34.810 --> 00:01:36.640
quart is 2 pints.

00:01:36.640 --> 00:01:38.400
So if we want to go
from quarts to pints,

00:01:38.400 --> 00:01:40.050
we'd want to multiply by 2.

00:01:40.050 --> 00:01:42.330
So this is going to be 16 pints.

00:01:42.330 --> 00:01:45.860
And then each pint is 2 cups.

00:01:45.860 --> 00:01:50.210
So multiplying 16 of them, then
that's going to be 32 cups.

00:01:50.210 --> 00:01:55.610
And then finally,
each cup is 8 ounces.

00:01:55.610 --> 00:01:57.850
32 times 8 is going to be?

00:01:57.850 --> 00:02:02.370
Let's see, it's going to be 256.

00:02:02.370 --> 00:02:03.960
And notice something here.

00:02:03.960 --> 00:02:06.260
When we went from 1
gallon to 2 gallons,

00:02:06.260 --> 00:02:10.009
we essentially increased the
quantity of gallons by 2,

00:02:10.009 --> 00:02:11.085
or we multiplied by 2.

00:02:11.085 --> 00:02:12.460
And you see that
across the board

00:02:12.460 --> 00:02:15.640
here as it's going from
4 quarts to 8 quarts.

00:02:15.640 --> 00:02:18.170
This is going from
8 pints to 16 pints.

00:02:18.170 --> 00:02:21.040
This is going from
16 cups to 32 cups,

00:02:21.040 --> 00:02:25.890
going from 128
fluid ounces to 256.

00:02:25.890 --> 00:02:29.202
When you increase the volume
in gallons by a factor of 2,

00:02:29.202 --> 00:02:31.160
you're, of course, going
to increase the volume

00:02:31.160 --> 00:02:35.792
in any unit you measure
it in by a factor of 2.


How to convert kilometers to meters and meters centimeters

WEBVTT
Kind: captions
Language: en

00:00:00.554 --> 00:00:01.970
What I want to do
in this video is

00:00:01.970 --> 00:00:04.240
convert this amount
of kilometers

00:00:04.240 --> 00:00:05.830
into meters and centimeters.

00:00:05.830 --> 00:00:07.790
So we'll first start
with the 2 kilometers.

00:00:07.790 --> 00:00:09.780
And I encourage you to
now pause this video

00:00:09.780 --> 00:00:11.890
and try to do this on your own.

00:00:11.890 --> 00:00:14.650
Well, the one thing that we know
is that a kilometer literally

00:00:14.650 --> 00:00:17.110
means 1,000 meters.

00:00:17.110 --> 00:00:22.200
So you could literally view
this is as 2 times 1,000 meters.

00:00:22.200 --> 00:00:23.260
Let me write that down.

00:00:23.260 --> 00:00:28.420
So this is going to be equal
to 2 times 1,000 meters, which

00:00:28.420 --> 00:00:31.780
is equal to 2,000 meters.

00:00:31.780 --> 00:00:34.910
If we wanted to convert the
11 kilometers into meters,

00:00:34.910 --> 00:00:35.880
it's the same thing.

00:00:35.880 --> 00:00:40.450
11 kilometers-- this right
over here-- means 1,000 meters.

00:00:40.450 --> 00:00:44.110
So you could think of it
as 11 times 1,000 meters.

00:00:44.110 --> 00:00:50.430
So 11 times 1,000 is
going to be 11,000 meters.

00:00:50.430 --> 00:00:54.740
Now let's convert these
distances into centimeters.

00:00:54.740 --> 00:00:56.120
And here we just
have to remember

00:00:56.120 --> 00:01:00.360
that 1 meter is equal
to 100 centimeters.

00:01:00.360 --> 00:01:01.840
Let me write that down.

00:01:01.840 --> 00:01:06.880
1 meter is equal
to 100 centimeters.

00:01:06.880 --> 00:01:10.140
And that's because the prefix
centi means one hundredth.

00:01:10.140 --> 00:01:12.850
Another way you can write
it is that one centimeter

00:01:12.850 --> 00:01:17.640
is equal to one
hundredth of a meter.

00:01:17.640 --> 00:01:19.530
But here we have a
certain number of meters,

00:01:19.530 --> 00:01:21.270
and each of those
meters are going

00:01:21.270 --> 00:01:24.030
to be equivalent
to 100 centimeters.

00:01:24.030 --> 00:01:28.110
So if we wanted to write
2,000 meters as centimeters,

00:01:28.110 --> 00:01:30.830
we could say, well,
we have 2,000 meters.

00:01:30.830 --> 00:01:35.260
Each of those are going to be
equivalent to 100 centimeters.

00:01:35.260 --> 00:01:39.400
And so this is going to be
equal to 2,000 times 100.

00:01:39.400 --> 00:01:42.310
Well, that's going to
be 2, and since where

00:01:42.310 --> 00:01:44.900
we have the three
zeroes from the 2,000.

00:01:44.900 --> 00:01:47.070
And then every time
you multiply by 10,

00:01:47.070 --> 00:01:48.460
you're going to
add another zero.

00:01:48.460 --> 00:01:51.141
Or you're going to have
another zero at the end of it.

00:01:51.141 --> 00:01:52.640
And we're going to
be at multiplying

00:01:52.640 --> 00:01:56.590
by 100 is equivalent to
multiplying by 10 twice.

00:01:56.590 --> 00:01:59.640
So we're going to
have two more zeroes.

00:01:59.640 --> 00:02:04.695
So this is going to be
200,000 centimeters.

00:02:04.695 --> 00:02:07.200
Now let's do the same
thing right over here

00:02:07.200 --> 00:02:09.740
with the kilometers,
the 11 kilometers,

00:02:09.740 --> 00:02:11.039
which are 11,000 meters.

00:02:11.039 --> 00:02:13.122
And once again, I encourage
you to pause the video

00:02:13.122 --> 00:02:14.790
and try to convert
it into centimeters.

00:02:14.790 --> 00:02:16.180
Well, same idea.

00:02:16.180 --> 00:02:20.550
You have 11,000 meters,
and each of them

00:02:20.550 --> 00:02:23.530
are equivalent to
100 centimeters.

00:02:23.530 --> 00:02:25.550
So this is going to
be 11, and let's see,

00:02:25.550 --> 00:02:28.190
we have one, two, three,
four, five zeroes.

00:02:31.360 --> 00:02:36.140
So this gets us to
1,100,000 centimeters.


How to convert feet to inches

WEBVTT
Kind: captions
Language: en

00:00:00.500 --> 00:00:03.250
Complete the table to show
equivalent measurements

00:00:03.250 --> 00:00:04.510
in feet and inches.

00:00:04.510 --> 00:00:06.430
So they gave us the
measurements in feet,

00:00:06.430 --> 00:00:08.790
and they want us to
figure out how many inches

00:00:08.790 --> 00:00:10.330
this number of feet are.

00:00:10.330 --> 00:00:13.927
So we know that 1 foot is
equivalent to 12 inches,

00:00:13.927 --> 00:00:16.010
so we can fill out this
first one right over here.

00:00:16.010 --> 00:00:17.450
12 inches make up 1 foot.

00:00:17.450 --> 00:00:19.400
1 foot is 12 inches.

00:00:19.400 --> 00:00:20.890
Now, what about 2 feet?

00:00:20.890 --> 00:00:23.890
Well, that's just going
to be 2 times 12 inches.

00:00:23.890 --> 00:00:29.800
12 inches per foot times
2 feet gives us 24 inches.

00:00:29.800 --> 00:00:31.130
Well, here I have 5 feet.

00:00:31.130 --> 00:00:33.590
I have 12 feet--
here I have 5 feet.

00:00:33.590 --> 00:00:40.350
I have 12 inches per foot,
so 5 times 12 is 60 inches.

00:00:40.350 --> 00:00:42.230
And then finally, 10 feet.

00:00:42.230 --> 00:00:47.965
10 feet times 12 inches per
foot gets us to 120 inches.


Finding reasonable unit of measurement example

WEBVTT
Kind: captions
Language: en

00:00:00.620 --> 00:00:02.770
Identify the most
reasonable units

00:00:02.770 --> 00:00:05.660
to measure each of
the following choices.

00:00:05.660 --> 00:00:08.970
So the time it takes to
bake one pan of cookies.

00:00:08.970 --> 00:00:11.930
Let's see, that's
usually in the minutes,

00:00:11.930 --> 00:00:14.660
so I'll go with
minutes unless you're

00:00:14.660 --> 00:00:16.670
doing some type of slow baking.

00:00:16.670 --> 00:00:20.300
But I'll say minutes is
a reasonable unit here.

00:00:20.300 --> 00:00:22.790
The time it takes to
pour a cup of coffee.

00:00:22.790 --> 00:00:25.617
Well, that might take you,
at most, 1 or 2 seconds.

00:00:25.617 --> 00:00:27.950
So you definitely don't want
to do it in hours or years.

00:00:27.950 --> 00:00:29.250
And we already used up
minutes, and you definitely

00:00:29.250 --> 00:00:30.625
don't want to use
minutes either.

00:00:30.625 --> 00:00:31.990
It's only a few seconds.

00:00:31.990 --> 00:00:36.410
The time it takes to drive
from Chicago to Saint Louis.

00:00:36.410 --> 00:00:38.550
Well, that hopefully
won't take you years.

00:00:38.550 --> 00:00:41.390
That'll take you-- I don't
know the exact distance,

00:00:41.390 --> 00:00:43.880
but it's going to take you
several hours to do that.

00:00:43.880 --> 00:00:47.390
So I will go with hours.

00:00:47.390 --> 00:00:49.540
Let's do a few more of these.

00:00:49.540 --> 00:00:51.270
Identify the most
reasonable units

00:00:51.270 --> 00:00:54.372
to measure each of the
following choices below.

00:00:54.372 --> 00:00:56.330
So we have kilometers,
meters, and millimeters.

00:00:56.330 --> 00:00:58.150
And a kilometer, of
course, kilo tells

00:00:58.150 --> 00:01:00.770
us that's equivalent
to 1,000 meters.

00:01:00.770 --> 00:01:03.519
And milli means
one-thousandth of a meter.

00:01:03.519 --> 00:01:05.019
Or another way of
thinking about it,

00:01:05.019 --> 00:01:09.840
a meter is 1,000 millimeters
and a kilometer is 1,000 meters.

00:01:09.840 --> 00:01:12.220
The length of a ladybug.

00:01:12.220 --> 00:01:16.730
Well, the length, unless it's
some kind of monster ladybug,

00:01:16.730 --> 00:01:20.420
we're probably thinking
in millimeters.

00:01:20.420 --> 00:01:22.760
The height of an average person.

00:01:22.760 --> 00:01:26.170
So an average person
is multiple meters.

00:01:26.170 --> 00:01:30.900
It's going to be at least 1
meter tall and more likely

00:01:30.900 --> 00:01:31.950
closer to 2 meters.

00:01:31.950 --> 00:01:34.250
Especially your average
male, adult male,

00:01:34.250 --> 00:01:36.780
would be right
around 2 meters tall.

00:01:36.780 --> 00:01:39.570
So I would go with meters.

00:01:39.570 --> 00:01:41.370
The length of a marathon.

00:01:41.370 --> 00:01:44.290
So this is a long-distance
race we're talking about here.

00:01:44.290 --> 00:01:50.280
If you're used to thinking
in US customary units,

00:01:50.280 --> 00:01:52.550
a marathon is 26 miles.

00:01:52.550 --> 00:01:55.580
A kilometer isn't
quite equal to a mile.

00:01:55.580 --> 00:01:58.280
1.6 kilometers is
equal to a mile,

00:01:58.280 --> 00:02:00.645
but it also makes sense to
measure this in kilometers.

00:02:00.645 --> 00:02:02.395
You would measure the
length of a marathon

00:02:02.395 --> 00:02:03.900
in miles or kilometers.

00:02:03.900 --> 00:02:06.020
You'd measure the height
of an average person,

00:02:06.020 --> 00:02:08.690
if you're using US customary
units, you would do it in feet.

00:02:08.690 --> 00:02:11.610
If you're using metric units,
you would do it in meters.

00:02:11.610 --> 00:02:13.770
The distance between San
Francisco and Los Angeles.

00:02:13.770 --> 00:02:16.400
So once again, this is
several thousand kilometers.

00:02:16.400 --> 00:02:17.682
We'll go with kilometers.

00:02:17.682 --> 00:02:19.390
Or actually, San
Francisco to Los Angeles

00:02:19.390 --> 00:02:21.115
is several hundred kilometers.

00:02:21.115 --> 00:02:22.949
I thought that said New
York to Los Angeles.

00:02:22.949 --> 00:02:25.323
San Francisco to Los Angeles,
several hundred kilometers,

00:02:25.323 --> 00:02:26.850
but still you want
to do kilometers.

00:02:26.850 --> 00:02:29.570
The length of an
average-sized swimming pool.

00:02:29.570 --> 00:02:33.240
Well, meters seems like a
reasonable measure there.

00:02:33.240 --> 00:02:36.250
Your average pool might
be 25 meters or 50 meters

00:02:36.250 --> 00:02:37.670
or something like that.

00:02:37.670 --> 00:02:40.240
The thickness of
a slice of bread.

00:02:40.240 --> 00:02:44.500
So a slice of bread, it's
definitely a lot thinner

00:02:44.500 --> 00:02:46.750
than a meter, so I'm going
to go with the millimeters.

00:02:50.120 --> 00:02:51.990
Let me check our answer.

00:02:51.990 --> 00:02:52.490
That right.

00:02:52.490 --> 00:02:54.564
Let's do one more.

00:02:54.564 --> 00:02:55.980
Identify the most
reasonable units

00:02:55.980 --> 00:03:00.000
to measure the weight of each
of the following choices below.

00:03:00.000 --> 00:03:01.650
So see, we have
ounces and pounds.

00:03:01.650 --> 00:03:05.170
And just as a reminder, 1
pound is equal to 16 ounces

00:03:05.170 --> 00:03:09.000
or an ounce is equal to
a sixteenth of a pound.

00:03:09.000 --> 00:03:11.940
So a couch-- well, that's going
to be many, many, many pounds,

00:03:11.940 --> 00:03:13.570
probably over 100 pounds.

00:03:13.570 --> 00:03:16.560
So we definitely want to put
this in the pounds category.

00:03:16.560 --> 00:03:19.520
A cookie-- unless it's
a really large cookie,

00:03:19.520 --> 00:03:21.430
it's going to weigh
less than a pound.

00:03:21.430 --> 00:03:23.320
So I'm comfortable
going-- it seems

00:03:23.320 --> 00:03:25.510
reasonable to go with ounces.

00:03:25.510 --> 00:03:27.910
A television-- well, they're
getting lighter every day,

00:03:27.910 --> 00:03:29.243
but they still weigh a good bit.

00:03:29.243 --> 00:03:31.130
They still weigh
multiple pounds, usually

00:03:31.130 --> 00:03:32.950
multiple tens of pounds.

00:03:32.950 --> 00:03:34.960
So we'll go with pounds.

00:03:34.960 --> 00:03:36.890
A cracker-- and once
again, unless we're

00:03:36.890 --> 00:03:39.110
talking about a
really huge cracker,

00:03:39.110 --> 00:03:40.940
most crackers are
very, very light,

00:03:40.940 --> 00:03:45.750
lighter than even a cookie,
so we will go with ounces.


U.S. customary units: fluid volume

WEBVTT
Kind: captions
Language: en

00:00:00.680 --> 00:00:02.660
Let's do a survey about
how we would measure

00:00:02.660 --> 00:00:07.510
the volume of fluids
under US customary units.

00:00:07.510 --> 00:00:09.941
So the smallest volume of
fluid that you'll hear people

00:00:09.941 --> 00:00:12.190
talk about-- and this will
often be in cooking recipes

00:00:12.190 --> 00:00:18.310
or something like this--
you'll talk about a teaspoon.

00:00:18.310 --> 00:00:21.130
And most of us have
teaspoons that are roughly

00:00:21.130 --> 00:00:24.490
the size of a teaspoon in
our cupboards someplace.

00:00:24.490 --> 00:00:27.370
So this recipe might call
for a teaspoon of sugar,

00:00:27.370 --> 00:00:30.152
or a teaspoon of salt,
or a teaspoon of oil.

00:00:30.152 --> 00:00:31.610
And you've seen
what it looks like.

00:00:31.610 --> 00:00:33.318
But those are the
smaller spoons that you

00:00:33.318 --> 00:00:36.980
might have in your cabinets
in your kitchen at home.

00:00:36.980 --> 00:00:39.780
So this might be a
teaspoon right over here.

00:00:39.780 --> 00:00:42.322
Now, if you were to take
3 teaspoons together,

00:00:42.322 --> 00:00:44.280
you have something else
that you would probably

00:00:44.280 --> 00:00:45.310
have in your cabinets.

00:00:45.310 --> 00:00:47.850
So if we multiply
this volume, so

00:00:47.850 --> 00:00:50.042
let's say this right
over here is a teaspoon.

00:00:50.042 --> 00:00:52.250
This right over here is a
teaspoon of some substance.

00:00:52.250 --> 00:00:55.530
If you multiply that by 3,
then you get to the tablespoon.

00:00:59.980 --> 00:01:03.300
So 3 teaspoons
equal 1 tablespoon.

00:01:03.300 --> 00:01:05.910
So a tablespoon's going
to be a little bit bigger.

00:01:05.910 --> 00:01:08.594
So a tablespoon
might look like this.

00:01:08.594 --> 00:01:10.760
These tend to be about the
size of the larger spoons

00:01:10.760 --> 00:01:14.500
that you have in your
cupboard, so a tablespoon,

00:01:14.500 --> 00:01:15.320
just like that.

00:01:15.320 --> 00:01:19.180
So if you have 3 times the
fluid, you get to a tablespoon.

00:01:19.180 --> 00:01:25.100
Now, if you take 2
tablespoons, put them together,

00:01:25.100 --> 00:01:27.030
then you get to the ounce.

00:01:27.030 --> 00:01:28.280
And I have to be careful here.

00:01:28.280 --> 00:01:29.675
You get to the fluid ounce.

00:01:32.260 --> 00:01:36.340
And the US customary units, they
aren't designed to be super,

00:01:36.340 --> 00:01:37.440
super clear.

00:01:37.440 --> 00:01:41.740
Because you also have the
ounce as a measure of weight.

00:01:41.740 --> 00:01:44.110
You have the ounce that
is a measure of weight,

00:01:44.110 --> 00:01:47.570
which is equal to
1/16 of a pound.

00:01:47.570 --> 00:01:49.920
And now you have a fluid
ounce, which you could either

00:01:49.920 --> 00:01:54.804
view as 2 tablespoons or,
as we'll see, 1/8 of a cup.

00:01:54.804 --> 00:01:57.220
Now, you might say, well, why
are they both called ounces?

00:01:57.220 --> 00:01:59.210
What's the relationship
between the two?

00:01:59.210 --> 00:02:03.670
Well, there is somewhat of a
relationship between the two.

00:02:03.670 --> 00:02:08.020
If you took a little bit
over an ounce of water,

00:02:08.020 --> 00:02:10.820
so a weight of ounce
of water, slightly

00:02:10.820 --> 00:02:13.600
over an ounce of
water, that volume

00:02:13.600 --> 00:02:15.830
is going to be
about a fluid ounce.

00:02:20.630 --> 00:02:23.740
An ounce of water in
weight and a fluid ounce

00:02:23.740 --> 00:02:27.040
of water in volume are
very, very, very close,

00:02:27.040 --> 00:02:29.990
although they aren't
exactly the same thing.

00:02:29.990 --> 00:02:32.970
Now, if you think about,
what would you measure here?

00:02:32.970 --> 00:02:35.970
We already talked about recipes,
and teaspoon, tablespoon,

00:02:35.970 --> 00:02:36.780
fluid ounce.

00:02:36.780 --> 00:02:38.940
You might be thinking
about how much medicine

00:02:38.940 --> 00:02:40.080
maybe someone might take.

00:02:40.080 --> 00:02:41.913
Maybe they need to take
2 tablespoons, which

00:02:41.913 --> 00:02:43.680
would be equivalent
to a fluid ounce.

00:02:43.680 --> 00:02:46.980
Now, if you take 8 fluid ounces
and put them together-- so let

00:02:46.980 --> 00:02:51.704
me draw a fluid ounce here
just so we still have drawings.

00:02:51.704 --> 00:02:53.370
So you could imagine
some medicines have

00:02:53.370 --> 00:02:56.170
a little cap on the top that
you could put the medicine in.

00:02:56.170 --> 00:02:59.590
So if you do 2
tablespoons in it,

00:02:59.590 --> 00:03:02.140
maybe that will
be a fluid ounce.

00:03:02.140 --> 00:03:08.165
Now, if you take 8 fluid
ounces then you get to a cup.

00:03:11.190 --> 00:03:13.640
And many of us have
this in our kitchens.

00:03:13.640 --> 00:03:17.160
We have a measuring cup that
will measure exactly a cup.

00:03:17.160 --> 00:03:19.470
And you might have a
recipe for pancakes

00:03:19.470 --> 00:03:24.110
that say, hey, put a
cup of flour in there.

00:03:24.110 --> 00:03:26.580
And also a lot of the cups
that you have in your house

00:03:26.580 --> 00:03:30.660
might be around might be
around the size of a cup.

00:03:30.660 --> 00:03:33.690
If you look at,
say, a can of soda

00:03:33.690 --> 00:03:36.760
that you're probably
familiar with, a can of soda,

00:03:36.760 --> 00:03:41.130
the typical can of soda,
is 12 ounces, not 8 ounces.

00:03:41.130 --> 00:03:43.930
So a typical can of soda
is a cup and a half.

00:03:43.930 --> 00:03:46.240
We see that a cup
is 8 fluid ounces.

00:03:46.240 --> 00:03:49.010
A typical can of soda
is 12 fluid ounces.

00:03:49.010 --> 00:03:52.630
So it is equivalent
to a cup and a half.

00:03:52.630 --> 00:03:56.180
Let me make sure this looks
like a can of some kind.

00:03:56.180 --> 00:04:02.170
So if this was 12 ounces,
this is 1 and 1/2 cups.

00:04:02.170 --> 00:04:05.820
But it gets you a sense of
how much fluid volume a cup

00:04:05.820 --> 00:04:07.350
actually is.

00:04:07.350 --> 00:04:16.589
Now, if we were to take 2 cups,
now you're dealing with a pint.

00:04:16.589 --> 00:04:20.550
And so you might
have seen pints.

00:04:20.550 --> 00:04:23.720
Sometimes they're in
these small cartons.

00:04:23.720 --> 00:04:28.202
So a pint might look something
like this in a carton.

00:04:28.202 --> 00:04:29.410
That looks more like a house.

00:04:29.410 --> 00:04:31.270
But I think, hopefully,
you get the picture

00:04:31.270 --> 00:04:34.460
that this is intended to
be a carton of some kind.

00:04:34.460 --> 00:04:36.110
So you have something like that.

00:04:36.110 --> 00:04:38.150
And so the pint, it's 2 cups.

00:04:38.150 --> 00:04:40.160
And so let's say this is
the fluid inside of it.

00:04:40.160 --> 00:04:42.618
Let's say this was transparent,
and you might see it there.

00:04:42.618 --> 00:04:44.830
Or if you have a
very large mug, that

00:04:44.830 --> 00:04:47.180
might be the size
of a pint, so if you

00:04:47.180 --> 00:04:52.000
have a very large mug like this.

00:04:52.000 --> 00:04:55.310
So my best attempt at
drawing a large mug,

00:04:55.310 --> 00:05:00.510
this might be roughly
equal to a pint.

00:05:00.510 --> 00:05:03.170
So let me put some
fluid in here.

00:05:03.170 --> 00:05:03.990
So there you go.

00:05:03.990 --> 00:05:05.250
There's my large mug.

00:05:05.250 --> 00:05:06.550
It's got a pint.

00:05:06.550 --> 00:05:13.960
Now, if you take 2 pints, now
you are dealing with a quart.

00:05:13.960 --> 00:05:15.520
And you might have
found yourself

00:05:15.520 --> 00:05:17.150
going to your local
convenience store

00:05:17.150 --> 00:05:19.340
and buying a quart of milk.

00:05:19.340 --> 00:05:26.370
A quart of milk, those are kind
of those longer but still kind

00:05:26.370 --> 00:05:31.560
of skinny looking-- so it
might look something like this.

00:05:31.560 --> 00:05:36.300
I'm trying to draw a
carton of a quart of milk.

00:05:36.300 --> 00:05:41.960
And then finally, if you were
to take 4 quarts together,

00:05:41.960 --> 00:05:44.330
you get to a gallon.

00:05:44.330 --> 00:05:49.490
So you take 4 quarts
together-- so times 4--

00:05:49.490 --> 00:05:50.940
you get to a gallon.

00:05:53.640 --> 00:05:56.747
So we're most familiar
with a gallon of milk.

00:05:56.747 --> 00:05:58.580
So let me see if I can
draw a gallon of milk

00:05:58.580 --> 00:06:01.180
here, my best attempt.

00:06:01.180 --> 00:06:04.320
Well, I'm sure someone could
draw a better gallon of milk

00:06:04.320 --> 00:06:04.820
here.

00:06:04.820 --> 00:06:07.780
But at least in the
US, it tends to be

00:06:07.780 --> 00:06:11.490
one of the most typical
ways that they sell milk.

00:06:11.490 --> 00:06:13.710
And it has, oftentimes, a
little red or orange thing

00:06:13.710 --> 00:06:16.940
right on top there,
so a gallon of milk.

00:06:16.940 --> 00:06:19.480
So just to review things,
right here, I just

00:06:19.480 --> 00:06:22.400
multiplied from the smaller
unit to the larger one.

00:06:22.400 --> 00:06:25.330
But if you want to think about
everything in terms of ounces,

00:06:25.330 --> 00:06:26.980
that's one way to
think about it.

00:06:26.980 --> 00:06:34.120
A cup right over here
is equal to 8 ounces.

00:06:34.120 --> 00:06:35.870
8 ounces is equal to a cup.

00:06:35.870 --> 00:06:39.990
If you multiply that by 2,
then you get to 16 ounces

00:06:39.990 --> 00:06:42.470
is equal to a pint.

00:06:42.470 --> 00:06:46.270
If you multiply that by
2, you get 32 ounces.

00:06:46.270 --> 00:06:50.000
32 ounces is equal to a quart.

00:06:50.000 --> 00:06:53.770
And if you multiply
that times 4,

00:06:53.770 --> 00:06:58.760
you get 30 times
4 is 120, plus 8.

00:06:58.760 --> 00:07:04.590
You get 128 ounces per gallon.

00:07:04.590 --> 00:07:07.040
And so next time you go buy
something in the supermarket,

00:07:07.040 --> 00:07:09.580
I encourage you to look at
how it's being measured.

00:07:09.580 --> 00:07:12.650
And you'll see that oftentimes
you might buy a quart of milk,

00:07:12.650 --> 00:07:15.620
but they'll also say that
this is a 32-ounce container.

00:07:15.620 --> 00:07:20.191
And in this context, they're
talking about fluid ounces.


U.S. customary units: weight

WEBVTT
Kind: captions
Language: en

00:00:00.660 --> 00:00:03.350
Let's talk a little bit
about the US customary units

00:00:03.350 --> 00:00:04.570
of weight.

00:00:04.570 --> 00:00:06.850
So the one that's
most typically used

00:00:06.850 --> 00:00:08.850
is the pound,
especially for things

00:00:08.850 --> 00:00:10.470
of kind of a human scale.

00:00:10.470 --> 00:00:12.700
And to understand
what a pound is,

00:00:12.700 --> 00:00:16.200
most playing balls are
roughly about a pound.

00:00:16.200 --> 00:00:19.510
So, for example, a soccer
ball-- my best attempt

00:00:19.510 --> 00:00:21.420
to draw a soccer ball.

00:00:21.420 --> 00:00:24.320
So let's say that this is a
soccer ball right over here.

00:00:24.320 --> 00:00:26.860
And then of course it has
some type of pattern on it.

00:00:26.860 --> 00:00:32.009
So you could imagine a
soccer ball is about a pound.

00:00:32.009 --> 00:00:34.060
So it's roughly one pound.

00:00:34.060 --> 00:00:36.300
And a pound will
often be shorthanded

00:00:36.300 --> 00:00:39.060
with this "lb." right over here.

00:00:39.060 --> 00:00:40.810
So it's about a pound.

00:00:40.810 --> 00:00:43.630
A football, an
American football,

00:00:43.630 --> 00:00:46.859
is also a little under a pound.

00:00:46.859 --> 00:00:48.400
But we could say it
is about a pound,

00:00:48.400 --> 00:00:54.750
just so we get a sense of what
a pound actually represents.

00:00:54.750 --> 00:00:57.650
Now, if you want to go to
scales smaller than a pound,

00:00:57.650 --> 00:00:59.730
you would think about
using the ounce.

00:01:04.780 --> 00:01:07.670
And the relation between the
ounce and the pound when we're

00:01:07.670 --> 00:01:13.030
thinking about weight
is that one pound--

00:01:13.030 --> 00:01:21.680
let me write this--
is equal to 16 ounces.

00:01:21.680 --> 00:01:24.050
Or another way of
thinking about it

00:01:24.050 --> 00:01:29.190
is that 1 ounce is equal
to 1/16 of a pound.

00:01:29.190 --> 00:01:30.700
And if you want to
visualize things

00:01:30.700 --> 00:01:34.960
that weigh about an ounce,
you could imagine a small box

00:01:34.960 --> 00:01:38.210
of matches weigh about an ounce.

00:01:38.210 --> 00:01:43.640
So a small box of matches
might weigh about an ounce.

00:01:43.640 --> 00:01:50.355
Maybe a small AA battery
would weigh about an ounce.

00:01:50.355 --> 00:01:51.730
But that gives
you a sense of it.

00:01:51.730 --> 00:01:53.970
So if you were to take
16 of these together,

00:01:53.970 --> 00:01:57.010
they would be about the
weight of a soccer ball.

00:01:57.010 --> 00:01:59.530
16 of these things together,
they would be about--

00:01:59.530 --> 00:02:03.717
they would be about the weight
of a soccer ball or a football.

00:02:03.717 --> 00:02:05.300
Now, if we want to
think about weights

00:02:05.300 --> 00:02:09.495
that are larger than a pound,
then we would go to the ton.

00:02:13.640 --> 00:02:22.042
And a ton is equal to-- 1
ton is equal to 2,000 pounds.

00:02:22.042 --> 00:02:24.250
And you have to be a little
bit careful with the ton.

00:02:24.250 --> 00:02:26.420
We're talking about
the US customary units,

00:02:26.420 --> 00:02:28.990
and this is where we're
talking about 2,000 pounds.

00:02:28.990 --> 00:02:31.265
But when we're talking on
a more international level,

00:02:31.265 --> 00:02:32.890
this is sometimes
called the short ton.

00:02:32.890 --> 00:02:34.200
There's also a long ton.

00:02:34.200 --> 00:02:35.730
There's also the metric ton.

00:02:35.730 --> 00:02:37.730
But here we're talking
about US customary units,

00:02:37.730 --> 00:02:38.720
which is the short ton.

00:02:38.720 --> 00:02:41.430
So one ton is 2,000 pounds.

00:02:41.430 --> 00:02:45.700
And to get a sense of something
that weighs 2,000 pounds,

00:02:45.700 --> 00:02:49.720
or to get a sense of what
2,000 pounds is like, or what

00:02:49.720 --> 00:02:53.510
might be measured in tons,
a car is a good example.

00:02:53.510 --> 00:02:59.990
Your average midsize sedan
would weigh about a little

00:02:59.990 --> 00:03:02.920
under to a little over
2 tons, so a little

00:03:02.920 --> 00:03:07.230
under to a little
over 4,000 pounds.

00:03:07.230 --> 00:03:10.120
If we're talking about a
small van or minivans or vans

00:03:10.120 --> 00:03:13.911
or trucks, it's going to
be larger than two tons.

00:03:13.911 --> 00:03:15.410
And if you think
about smaller cars,

00:03:15.410 --> 00:03:18.730
you think it's going to be
probably around 3,000 pounds.

00:03:18.730 --> 00:03:20.550
It's going to be
less than 2 tons.

00:03:20.550 --> 00:03:28.891
So a car is going to be
approximately 2 tons.

00:03:28.891 --> 00:03:30.390
So hopefully, that
gives you a sense

00:03:30.390 --> 00:03:35.130
of what units you'd use
in the US customary system

00:03:35.130 --> 00:03:38.741
for different scales of weights.


U.S. customary units: distance

WEBVTT
Kind: captions
Language: en

00:00:00.620 --> 00:00:03.590
Let's talk a little bit
about the US customary units

00:00:03.590 --> 00:00:05.220
for distance.

00:00:05.220 --> 00:00:09.540
If we go to a human scale,
the most typical used unit

00:00:09.540 --> 00:00:13.620
in the US customary
system would be the foot.

00:00:13.620 --> 00:00:15.930
And as you could
imagine, the term foot,

00:00:15.930 --> 00:00:18.710
and if you have many of them,
you are now talking about feet,

00:00:18.710 --> 00:00:21.390
comes from the same
word on the human body.

00:00:21.390 --> 00:00:25.580
We have a foot or
we have two feet.

00:00:25.580 --> 00:00:28.560
Now, not everyone's feet
are the same length.

00:00:28.560 --> 00:00:33.230
But the length of a foot is
roughly a little bit larger

00:00:33.230 --> 00:00:34.620
than most people's feet.

00:00:34.620 --> 00:00:38.630
And there are definitely
people whose feet

00:00:38.630 --> 00:00:41.720
are the size of a foot.

00:00:41.720 --> 00:00:44.350
And if you're in the
US, you've probably

00:00:44.350 --> 00:00:47.420
heard of people measuring
their height in terms of feet.

00:00:47.420 --> 00:00:53.120
So for example, a
slightly above average man

00:00:53.120 --> 00:00:56.760
of slightly above average height
would have a height of 6 feet.

00:00:56.760 --> 00:00:59.700
So for example, right over here,
this gentleman right over here

00:00:59.700 --> 00:01:01.470
was slightly above
average height.

00:01:01.470 --> 00:01:03.770
His height might be 6 feet.

00:01:03.770 --> 00:01:05.680
And that might also
be his wing-span.

00:01:05.680 --> 00:01:08.720
So it would be a distance
something like that.

00:01:08.720 --> 00:01:11.856
If you wanted to measure things
that are a little bit smaller,

00:01:11.856 --> 00:01:14.230
say smaller than a foot, or
if we wanted to measure parts

00:01:14.230 --> 00:01:16.720
of a foot, then you
would go to the inch.

00:01:20.130 --> 00:01:23.190
And the relationship between
the foot and the inch

00:01:23.190 --> 00:01:31.940
is that 12 inches are
equal to one foot.

00:01:31.940 --> 00:01:34.180
So for example, this little
mouse right over here,

00:01:34.180 --> 00:01:36.760
it might be reasonable
to measure it in inches.

00:01:36.760 --> 00:01:43.016
On this scale, an inch
might be, depending

00:01:43.016 --> 00:01:44.390
on the size of
the mouse, an inch

00:01:44.390 --> 00:01:46.820
might be something like that.

00:01:46.820 --> 00:01:48.590
And it's also useful
for measuring things

00:01:48.590 --> 00:01:50.690
like human height,
because very few people

00:01:50.690 --> 00:01:52.510
are a whole number of feet.

00:01:52.510 --> 00:01:54.360
They're usually some
fraction of feet.

00:01:54.360 --> 00:02:02.070
So for example, I am
5 feet and 9 inches.

00:02:04.900 --> 00:02:07.500
And sometimes this
is denoted as 5,

00:02:07.500 --> 00:02:11.360
and you have this apostrophe
here, one apostrophe, and then

00:02:11.360 --> 00:02:14.440
5 foot 9 inches, and this
is two apostrophes, kind

00:02:14.440 --> 00:02:16.922
of saying hey, you're going
to the next unit down.

00:02:16.922 --> 00:02:19.810
These are the inches
right over here.

00:02:19.810 --> 00:02:21.310
Now if you want to
go to things that

00:02:21.310 --> 00:02:25.610
are larger than maybe human
scale, we have units for that

00:02:25.610 --> 00:02:28.590
as well, including the yard.

00:02:28.590 --> 00:02:33.150
The yard is equal to 3 feet.

00:02:33.150 --> 00:02:35.860
And 3 feet, well, each
foot is 12 inches,

00:02:35.860 --> 00:02:41.580
so this is the same
thing as 36 inches.

00:02:41.580 --> 00:02:45.630
And this is most typically
used for measuring

00:02:45.630 --> 00:02:48.380
distances of a lot of some kind.

00:02:48.380 --> 00:02:51.870
And in the United States,
most famously for in football.

00:02:51.870 --> 00:02:55.320
So your regulation-size football
field, the playing field,

00:02:55.320 --> 00:02:57.460
the distance between
the end zones,

00:02:57.460 --> 00:03:01.740
is exactly 100--
I know you can't

00:03:01.740 --> 00:03:06.850
see my writing there--
is exactly 100 yards.

00:03:11.380 --> 00:03:13.200
This distance right over here.

00:03:13.200 --> 00:03:15.340
Right between the end zone.

00:03:15.340 --> 00:03:17.980
Now, if you want to measure
even longer distances,

00:03:17.980 --> 00:03:19.885
that's where we go to the mile.

00:03:23.670 --> 00:03:26.360
And all of these units
are ancient units,

00:03:26.360 --> 00:03:28.750
going back, actually,
thousands of years.

00:03:28.750 --> 00:03:31.620
And the mile, based on
the reading I've found,

00:03:31.620 --> 00:03:33.260
was even used in Roman times.

00:03:33.260 --> 00:03:37.380
And actually, that's some
of the first examples

00:03:37.380 --> 00:03:38.860
of this term being used.

00:03:38.860 --> 00:03:42.480
And it really comes from
the same root word as 1,000,

00:03:42.480 --> 00:03:46.240
of mil, of 1,000 footsteps
of a Roman soldier.

00:03:46.240 --> 00:04:00.080
And now, a standard mile
is exactly 5,280 feet.

00:04:00.080 --> 00:04:03.030
And if you wanted to
figure out this in inches,

00:04:03.030 --> 00:04:05.434
you could just multiply by 12.

00:04:05.434 --> 00:04:06.850
But just to get a
sense of a mile,

00:04:06.850 --> 00:04:12.384
here is a mile on
this map of New York.

00:04:12.384 --> 00:04:14.300
So if you wanted to put
it right on Manhattan,

00:04:14.300 --> 00:04:21.620
this distance right over
here is about a mile.

00:04:21.620 --> 00:04:24.370
So you want to measure really
far distances, either from one

00:04:24.370 --> 00:04:26.490
point in a city to
another, or maybe

00:04:26.490 --> 00:04:28.350
even the distance
between cities,

00:04:28.350 --> 00:04:31.400
or maybe even the
size of the planet,

00:04:31.400 --> 00:04:33.500
or even the distance from
the Earth to the moon,

00:04:33.500 --> 00:04:36.510
or something like that, you
will hear that referenced

00:04:36.510 --> 00:04:39.390
in miles, even the distance
between the Earth and the sun.

00:04:39.390 --> 00:04:41.680
People say it's
93 million miles.

00:04:41.680 --> 00:04:44.017
If you're talking about
maybe, a plot of land,

00:04:44.017 --> 00:04:45.475
you want to measure
its dimensions,

00:04:45.475 --> 00:04:47.183
or you're talking
about a football field,

00:04:47.183 --> 00:04:48.900
then yards feel appropriate.

00:04:48.900 --> 00:04:50.620
If you're kind of
getting to human scale,

00:04:50.620 --> 00:04:52.210
well, human scale on
one level, but you

00:04:52.210 --> 00:04:53.570
could get a little bit
larger if you're maybe

00:04:53.570 --> 00:04:55.170
talking about the
height of a building

00:04:55.170 --> 00:04:56.890
or something like
that, or you're still

00:04:56.890 --> 00:04:59.820
talking about measurement
of say, a plot of land,

00:04:59.820 --> 00:05:03.120
you will still hear people
talk in terms of feet.

00:05:03.120 --> 00:05:05.170
And if you're measuring
either parts of a foot,

00:05:05.170 --> 00:05:07.050
or things that are
smaller than a foot,

00:05:07.050 --> 00:05:10.440
that's when inches
come into play.


Metric system: units of weight

WEBVTT
Kind: captions
Language: en

00:00:00.680 --> 00:00:02.580
Let's think about the
units typically used

00:00:02.580 --> 00:00:08.530
in the metric system to
measure an object's weight.

00:00:08.530 --> 00:00:10.460
And I'm putting the
weight in quotation marks

00:00:10.460 --> 00:00:12.330
right over here because the
units I'm going to talk about

00:00:12.330 --> 00:00:14.270
are-- actually, if we
wanted to be technical,

00:00:14.270 --> 00:00:16.560
they're units of mass.

00:00:16.560 --> 00:00:21.090
And as we'll see later on
in our scientific careers,

00:00:21.090 --> 00:00:23.450
that weight and mass
are not the same thing.

00:00:23.450 --> 00:00:24.460
They are related.

00:00:24.460 --> 00:00:27.486
Mass you could view as
how much stuff there is.

00:00:27.486 --> 00:00:29.110
How much substance
does an object have?

00:00:29.110 --> 00:00:34.610
How hard is it to change
the velocity of an object?

00:00:34.610 --> 00:00:36.480
While weight is,
what's the force

00:00:36.480 --> 00:00:38.510
that gravity is pulling
down on that object?

00:00:38.510 --> 00:00:40.250
Now, in everyday
life, if we're just

00:00:40.250 --> 00:00:42.610
on the same planet or the
same part of the planet,

00:00:42.610 --> 00:00:45.210
if something has more mass,
it's going to have more weight.

00:00:45.210 --> 00:00:46.440
And if something
has more weight,

00:00:46.440 --> 00:00:47.540
it's going to have more mass.

00:00:47.540 --> 00:00:48.998
And that's why in
everyday language

00:00:48.998 --> 00:00:51.490
these words are
often interchanged.

00:00:51.490 --> 00:00:54.080
Later on, we'll see that
these mean different things.

00:00:54.080 --> 00:00:56.080
For the sake of this
video, because we're really

00:00:56.080 --> 00:00:59.190
just getting ourselves warmed
up with some of these units,

00:00:59.190 --> 00:01:00.810
I will use these
interchangeably.

00:01:00.810 --> 00:01:03.420
I'll use them in kind of
the everyday language sense,

00:01:03.420 --> 00:01:06.750
not in the technical
physics sense of the word.

00:01:06.750 --> 00:01:08.970
So in the metric
system when people

00:01:08.970 --> 00:01:12.320
talk about measuring
relatively light things,

00:01:12.320 --> 00:01:16.060
they will often use the gram.

00:01:16.060 --> 00:01:19.060
And to get a sense of
things that weight a gram,

00:01:19.060 --> 00:01:20.580
one example is a paper clip.

00:01:20.580 --> 00:01:23.920
Your average size paper clip
would weigh about a gram.

00:01:23.920 --> 00:01:27.630
A stick of chewing gum, not even
the whole pack of chewing gum,

00:01:27.630 --> 00:01:34.050
just a stick of chewing gum,
would weigh about a gram.

00:01:34.050 --> 00:01:40.100
A dollar bill would
weigh about a gram.

00:01:40.100 --> 00:01:43.694
So this really isn't
a lot of weight.

00:01:43.694 --> 00:01:46.110
Now, if you wanted to measure
things more on, I would say,

00:01:46.110 --> 00:01:48.770
a human scale, you
could then increase

00:01:48.770 --> 00:01:53.800
by a factor of thousand
and go to the kilogram.

00:01:53.800 --> 00:01:54.630
Kilogram.

00:01:54.630 --> 00:01:57.850
And as the unit implies, as the
prefix implies I should say,

00:01:57.850 --> 00:01:59.110
kilo, a thousand.

00:01:59.110 --> 00:02:01.650
This means 1,000 grams.

00:02:01.650 --> 00:02:04.390
And if you want to think about
how much that represents,

00:02:04.390 --> 00:02:06.240
well, many people will
measure their weight

00:02:06.240 --> 00:02:07.530
in terms of kilograms.

00:02:07.530 --> 00:02:14.770
So I, for example, weigh
about 70 kilograms.

00:02:14.770 --> 00:02:15.730
And I'm 5' 9''.

00:02:15.730 --> 00:02:20.180
And I'm about average build
and I weigh about 70 kilograms.

00:02:20.180 --> 00:02:23.600
If you want to imagine
what a kilogram is like,

00:02:23.600 --> 00:02:28.660
imagine taking a liter of
fluid or a liter of water.

00:02:28.660 --> 00:02:31.730
So if you took a liter of water.

00:02:31.730 --> 00:02:36.430
And a liter, you could
imagine as a 10 centimeter

00:02:36.430 --> 00:02:41.810
deep cube, 10 centimeters
wide, and 10 centimeters high.

00:02:41.810 --> 00:02:45.460
If you filled this up with
water, the weight of that thing

00:02:45.460 --> 00:02:48.694
is going to be 1 kilogram.

00:02:48.694 --> 00:02:50.360
I know you're not
used to walking around

00:02:50.360 --> 00:02:53.396
with 1 liter cubes of water.

00:02:53.396 --> 00:02:54.770
Another way of
thinking about it,

00:02:54.770 --> 00:02:56.269
if you go to the
supermarket and you

00:02:56.269 --> 00:02:59.974
were to buy a 2 liter of soda.

00:02:59.974 --> 00:03:01.890
And sometimes you buy 2
liters of other things

00:03:01.890 --> 00:03:03.640
as well-- water, whatever.

00:03:03.640 --> 00:03:09.450
If you buy a 2 liter of soda
is going to weigh-- well,

00:03:09.450 --> 00:03:11.860
actually, 2 liters of
water, in particular,

00:03:11.860 --> 00:03:13.860
is going to weigh-- soda
has other things in it,

00:03:13.860 --> 00:03:17.280
so you can't be as
precise with the weight.

00:03:17.280 --> 00:03:21.340
But 2 liters of
water, I should say,

00:03:21.340 --> 00:03:26.890
are going to weigh
exactly 2 kilograms.

00:03:26.890 --> 00:03:29.230
We're just talking
about the water itself.

00:03:29.230 --> 00:03:30.987
We're not talking
about the container.

00:03:30.987 --> 00:03:33.320
But if you want to get a rough
sense for how much weight

00:03:33.320 --> 00:03:37.470
that is, that's going
to be 2 kilograms.

00:03:37.470 --> 00:03:39.540
So if you're measuring
human scale size

00:03:39.540 --> 00:03:43.230
things, reasonable size
quantities of fluid,

00:03:43.230 --> 00:03:45.830
objects around this
scale, kilogram

00:03:45.830 --> 00:03:47.150
makes a lot more sense.

00:03:47.150 --> 00:03:50.080
If you measure these
very light things,

00:03:50.080 --> 00:03:51.970
you're talking about a gram.

00:03:51.970 --> 00:03:53.450
If you want to get
really precise,

00:03:53.450 --> 00:03:56.990
this might be more in things
if you're doing a drug dosage

00:03:56.990 --> 00:03:59.210
and you need to be very,
very, very precise,

00:03:59.210 --> 00:04:04.370
then you will sometimes see
people go to the milligram.

00:04:04.370 --> 00:04:11.390
But you could imagine a
milligram is 1/1,000 of a gram.

00:04:11.390 --> 00:04:14.480
And so 1/1,000 the weight
of a dollar bill or 1/1,000

00:04:14.480 --> 00:04:17.620
the weight of a paper clip,
this is very, very, very,

00:04:17.620 --> 00:04:18.700
very small.

00:04:18.700 --> 00:04:25.520
So this usually doesn't come
into play in our everyday life.