Metric system: units of volume

WEBVTT
Kind: captions
Language: en

00:00:00.870 --> 00:00:04.760
Let's think a little bit
about the metric system

00:00:04.760 --> 00:00:09.150
units for volume, or essentially
how much space something

00:00:09.150 --> 00:00:11.460
is taking up in
three dimensions.

00:00:11.460 --> 00:00:18.120
So the base unit in the metric
system for volume is the liter.

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And there's a couple of ways
that you can visualize a liter.

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One way you could
think about a liter

00:00:23.310 --> 00:00:30.910
is if you took a cube that
is 10 centimeters deep, 10

00:00:30.910 --> 00:00:35.470
centimeters wide, and
10 centimeters tall,

00:00:35.470 --> 00:00:38.050
then this amount of space
that you're taking up,

00:00:38.050 --> 00:00:42.150
this volume is 1 liter.

00:00:42.150 --> 00:00:45.870
So this right over
here is 1 liter.

00:00:45.870 --> 00:00:48.160
Another way to connect
it to our everyday lives

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is you've probably
gone and bought,

00:00:49.960 --> 00:00:53.490
or your parents have bought,
a 2-liter bottle of something.

00:00:53.490 --> 00:00:54.780
Oftentimes, it's soda.

00:00:54.780 --> 00:00:58.200
So those 2-liter bottles
are-- as I just mentioned,

00:00:58.200 --> 00:00:59.750
these are 2 liters.

00:00:59.750 --> 00:01:01.550
So let me make my
best attempt to draw

00:01:01.550 --> 00:01:03.480
what those bottles look like.

00:01:03.480 --> 00:01:08.490
They look something like this.

00:01:08.490 --> 00:01:11.490
At least in the US, oftentimes
soda, and other things,

00:01:11.490 --> 00:01:16.100
will be sold in these
2-liter bottles.

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So if you take half of this,
you are looking at a liter.

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So liter would be
about half of this.

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So if it's half full, a liter
would be about that much.

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And hopefully,
that is consistent

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or that makes sense relative
to this 10 centimeter

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by 10 centimeter by
10 centimeter cube.

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Now, if you want
to measure things

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that are a lot smaller than a
liter, the typical unit used--

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and obviously in
the metric system,

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you can always use the
prefixes deci, centi.

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But the one that's
most typically used

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is the milliliter--
milli-- the milliliter.

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And we've already
seen the prefix milli.

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It means 1/1,000.

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So this means
1/1,000 of a liter.

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Or another way of thinking
about it is 1 liter

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is equal to 1,000 milliliters.

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And if you wanted to visualize
what a milliliter looks like,

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imagine taking a cube.

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And instead of making it 10
centimeters on each dimension,

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make it only 1 centimeter
in each dimension.

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So 1 centimeter wide,
1 centimeter deep,

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and 1 centimeter high, and then
you're looking at a milliliter.

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And if you want to think
about the type of things that

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are measured in milliliters,
you might think things

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about dosage of medicine.

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So for example, a
typical teaspoon

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that you might see
in your cabinet

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is going to be a little
bit over 4 milliliters,

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almost 5 milliliters.

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So that might be good for
medicine dosage or maybe

00:03:02.710 --> 00:03:06.750
small ingredients in
some type of a recipe.

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If you want to go larger than
a liter-- and once again,

00:03:09.710 --> 00:03:11.520
you could use all
the metric prefixes.

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You could use deciliter.

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You could use hectoliter.

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But the one that's most
typically used is kiloliter.

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And as the prefix
kilo implies, this

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is equivalent to 1,000 liters.

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And if you want
to visualize this,

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this actually isn't as large
as you might assume it to be.

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If you just take a
cube, and this side,

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instead of taking each
dimension being 10 centimeters,

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if you were to take a cube where
each dimension is exactly 1

00:03:44.690 --> 00:03:55.720
meter, so 1 meter deep, 1
meter wide, and 1 meter tall,

00:03:55.720 --> 00:04:00.360
this volume is equivalent
to 1 kiloliter.

00:04:03.222 --> 00:04:04.680
So you could imagine
something like

00:04:04.680 --> 00:04:07.740
a kilometer would be very
useful for measuring,

00:04:07.740 --> 00:04:12.991
say, the volume of water
inside of a swimming pool.


Metric system: units of distance

WEBVTT
Kind: captions
Language: en

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The base unit for distance in
the metric system is the meter.

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And to get a sense of how long
a meter is, the average human

00:00:10.340 --> 00:00:14.010
being is between 1.5
and 2 meters tall.

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So 1.5 meters would be
a not-so-tall person,

00:00:18.340 --> 00:00:20.220
but 2 meters would
be quite tall.

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In fact, if you're 2 meters
tall or above 2 meters tall,

00:00:23.100 --> 00:00:25.080
you might want to
consider basketball.

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So, for example, in this
drawing right over here

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by Leonardo da Vinci, if this is
an average-sized male, a meter,

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it would be more than half
way across his wingspan.

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So it might be about that much.

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And obviously, I am just
roughly drawing this,

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just to give you a sense of
how far a meter might be.

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And I just wrote
a lowercase m here

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as really just a short
way of writing meter.

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So you could imagine
that the smaller

00:00:53.790 --> 00:00:57.150
things you might want to
measure with the meter

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are things like a human
being-- a human being's

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height or a human
being's wingspan.

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If you wanted to say, well, what
are some of the larger things

00:01:04.700 --> 00:01:06.533
that you would want to
measure with a meter,

00:01:06.533 --> 00:01:09.100
you might imagine something
like the height of a skyscraper.

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So this right over here is
the Empire State Building,

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at one time the tallest
building in the world, now just

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a tall building in the world.

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And this is 443 meters tall.

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So this is starting to be on
the larger scale of things

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that you would want to
measure with a meter.

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Now you're probably
asking, well,

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what happens if I
want to measure things

00:01:30.766 --> 00:01:32.960
that are even larger than that?

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Well the metric
system provides us

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prefixes to essentially
say multiples of meters.

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And the unit of distance that
is larger than the meter that

00:01:43.020 --> 00:01:47.800
is most typically
used is the kilometer.

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I've heard a few people say
"kill-O-meter," but kilometer,

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I'll pronounce is
"kuh-LAW-me-ter,"

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which is equivalent
to 1,000 meters.

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And so when you're
thinking about kilometers,

00:02:01.550 --> 00:02:04.220
this is thinking about the
distance within a city.

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This would be even the distance
from one city to another city.

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Even the radius of the planet
is often measured in kilometers.

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And to once again get a sense
of that, this right over here

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is a map of New York City.

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And right over here
they give us the scale.

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This distance right over
here is 5 kilometers.

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So 5 kilometers just to
give us a sense of things--

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and they wrote km
for short so 5 km.

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This lowercase k, lowercase m is
just shorthand for kilometers,

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this would be equal to-- well
if 1 kilometer is 1,000 meters,

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5 kilometers is going
to be 5 times as many.

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It's going to be 5,000 meters is
this distance right over here.

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If you were to try to
imagine 1 kilometer,

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it would be 1/5 of that.

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So 1 kilometer on this map
might look something like that.

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Now there's other units
in the metric system that

00:03:07.340 --> 00:03:11.259
allow us to describe distances
less than a kilometer but more

00:03:11.259 --> 00:03:11.800
than a meter.

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But they're not
as typically used.

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But I'll list them here, just
so that you see that they exist.

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You have the "hect-O-meter,"
or "heck-TOM-eter"--

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it's so infrequently used that
I really haven't heard a lot

00:03:22.180 --> 00:03:26.430
of people say it-- which
is equal to 100 meters.

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And you have the "DECK-a-meter"
or "deck-AM-eter,"

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and I actually think
it's "DECK-a-meter."

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Dekameter, which is 10 meters.

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And I'm going to
write these in orange

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because they're not
that frequently used.

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For example, it's
not typical to hear

00:03:43.540 --> 00:03:47.140
someone say that the Empire
State Building is 4.43

00:03:47.140 --> 00:03:52.750
hectometers or for them to say
that this is 44.3 dekameters.

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They would typically say
that this is 443 meters.

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Now you're probably saying,
OK, well, this is fine.

00:04:00.830 --> 00:04:02.830
Using these prefixes
on the meter,

00:04:02.830 --> 00:04:04.740
I'm able to describe
distances that

00:04:04.740 --> 00:04:07.020
are larger than a meter,
that are multiples

00:04:07.020 --> 00:04:10.570
of tens of the meter
or a multiple of 100

00:04:10.570 --> 00:04:12.120
or a multiple of
1,000 of the meter.

00:04:12.120 --> 00:04:13.750
But what if I want
to go smaller?

00:04:13.750 --> 00:04:16.680
Well, the metric system
has units for that.

00:04:16.680 --> 00:04:18.730
And if we go just
1/10 of a meter,

00:04:18.730 --> 00:04:20.490
this is not used as
typically, but I'll

00:04:20.490 --> 00:04:23.640
write it here-- the decimeter.

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The decimeter is
1/10 of a meter.

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Or another way of
saying it is 1 meter

00:04:31.090 --> 00:04:36.010
is equal to 10 decimeters,
lowercase dm for short.

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Once again, this is
not so typically used.

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But if we go one
scale even below that,

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we get to the centimeter,
which is a heavily used unit.

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And here, the prefix
centi means 1/100.

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So this is 1/100 of a meter.

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Another way of thinking
about it-- 1 meter

00:04:59.540 --> 00:05:03.100
is equal to 100 centimeters.

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And if you wanted to imagine
the scale of a centimeter,

00:05:05.500 --> 00:05:07.350
you could imagine this
frog right over here

00:05:07.350 --> 00:05:10.790
on this person's hand might
be several centimeters long.

00:05:10.790 --> 00:05:15.730
So a centimeter on this drawing
might be around that distance.

00:05:15.730 --> 00:05:18.130
Now if you want to measure
things even smaller than that,

00:05:18.130 --> 00:05:20.085
we have another
fairly common unit,

00:05:20.085 --> 00:05:21.210
and that is the millimeter.

00:05:25.220 --> 00:05:28.670
And the prefix milli
here refers to 1/1,000.

00:05:28.670 --> 00:05:32.970
So it's 1/1,000 of a meter.

00:05:32.970 --> 00:05:36.980
Or another way of thinking
about it is 1 meter

00:05:36.980 --> 00:05:40.650
is equal to 1,000 millimeter.

00:05:40.650 --> 00:05:42.569
Actually, let me just
write m for short,

00:05:42.569 --> 00:05:44.360
just so we used to also
seeing it that way.

00:05:44.360 --> 00:05:50.640
1 meter is equal to
1,000 millimeters.

00:05:50.640 --> 00:05:52.550
And if you wanted
to imagine how long

00:05:52.550 --> 00:05:54.570
or how far a millimeter
is, you could go down

00:05:54.570 --> 00:05:56.861
the scale of things that are
smaller than a centimeter.

00:05:56.861 --> 00:05:58.330
So these ants,
for example, might

00:05:58.330 --> 00:06:00.990
be 3 or 4 millimeters long.

00:06:00.990 --> 00:06:03.310
So a millimeter in this
drawing right over here

00:06:03.310 --> 00:06:07.370
might be something like that.

00:06:07.370 --> 00:06:09.940
The important thing to realize
or just to conceptualize

00:06:09.940 --> 00:06:12.190
is you might want to use
different units depending

00:06:12.190 --> 00:06:13.840
on the scale that
you're measuring.

00:06:13.840 --> 00:06:16.150
And it's also useful
to just realize

00:06:16.150 --> 00:06:19.300
what these typical prefixes
refer to because we're

00:06:19.300 --> 00:06:21.160
seeing it used in distance here.

00:06:21.160 --> 00:06:23.430
They're all based on the
base unit of distance.

00:06:23.430 --> 00:06:26.970
But when we're measuring volume
or we're measuring other things

00:06:26.970 --> 00:06:30.984
in the metric system, these
same prefixes also show up.

00:06:30.984 --> 00:06:32.900
So you see here when
we're measuring distance,

00:06:32.900 --> 00:06:34.570
kilo refers to 1,000.

00:06:34.570 --> 00:06:37.290
A kilometer is
literally 1,000 meters.

00:06:37.290 --> 00:06:38.820
Hecto refers to 100.

00:06:38.820 --> 00:06:40.880
A hectometer-- 100 meters.

00:06:40.880 --> 00:06:42.650
Deka refers to 10.

00:06:42.650 --> 00:06:45.060
Deci refers to 1/10.

00:06:45.060 --> 00:06:47.810
So decimeter, literally
1/10 of a meter.

00:06:47.810 --> 00:06:51.390
Centimeter-- 1/100,
1/100 of a meter.

00:06:51.390 --> 00:06:54.532
Milli refers to 1/1,000.


Comparing numbers represented in different ways

WEBVTT
Kind: captions
Language: en

00:00:00.201 --> 00:00:02.685
- So we're asked to
compare these two numbers

00:00:02.685 --> 00:00:04.101
right over here and I just took a picture

00:00:04.101 --> 00:00:05.785
from the Khan Academy exercise

00:00:05.785 --> 00:00:08.107
but this isn't it, itself, so
I can't, I can't click on this,

00:00:08.107 --> 00:00:10.534
but if you did click on
this on the exercise,

00:00:10.534 --> 00:00:12.682
you'd get to choose
between one of these three,

00:00:12.682 --> 00:00:13.800
but I'll just write it down.

00:00:13.800 --> 00:00:15.231
So we're gonna compare 2.7 to

00:00:15.231 --> 00:00:16.723
two and 17 hundredths,

00:00:17.518 --> 00:00:18.934
so there's a bunch of
ways you could do this,

00:00:18.934 --> 00:00:21.123
you could convert both
of them to mixed numbers.

00:00:21.291 --> 00:00:26.039
So, for example, 2.7,
2.7, you could rewrite,

00:00:26.039 --> 00:00:29.369
this is the same thing
as two and seven tenths,

00:00:30.009 --> 00:00:31.609
two and seven tenths,

00:00:31.609 --> 00:00:34.047
you could compare two and seven tenths to,

00:00:35.247 --> 00:00:36.622
to this right over here, which is

00:00:36.622 --> 00:00:40.866
two and 17 hundredths,
two and 17 hundredths.

00:00:41.846 --> 00:00:43.263
So, they both have a two,
so you want to compare

00:00:43.263 --> 00:00:45.173
the fraction part, so what's larger?

00:00:45.178 --> 00:00:48.110
Seven tenths or 17 hundredths?

00:00:48.579 --> 00:00:49.822
Well, if it doesn't jump out at you,

00:00:49.822 --> 00:00:52.034
you could convert this to hundredths.

00:00:52.448 --> 00:00:54.573
Seven tenths is the same
thing if you want to convert

00:00:54.573 --> 00:00:56.895
it to hundredths, you can
multiply the denominator

00:00:56.895 --> 00:01:00.133
by 10, which would make the 10 into 100,

00:01:00.133 --> 00:01:02.264
and then you'd also have to
multiply the numerator by 10.

00:01:03.153 --> 00:01:05.533
So two and 7 tenths is the same thing

00:01:05.533 --> 00:01:07.640
as two and 70 hundredths.

00:01:08.354 --> 00:01:12.214
And so 70 hundredths is for
sure bigger than 17 hundredths.

00:01:12.731 --> 00:01:14.919
So, this number,

00:01:15.389 --> 00:01:18.605
two and seven tenths, or two
and 70 hundredths, or 2.7,

00:01:18.605 --> 00:01:21.002
is going to be greater than this number,

00:01:21.089 --> 00:01:22.529
so it's going to be greater than,

00:01:22.529 --> 00:01:25.437
we open the symbol to the larger number.

00:01:25.884 --> 00:01:28.699
Another way that we could
have thought about this,

00:01:29.088 --> 00:01:31.392
is we could have converted
both of them to decimals.

00:01:31.909 --> 00:01:35.432
So we have 2.7, which we
can leave as a decimal.

00:01:35.644 --> 00:01:40.644
2.7 but then two and 17
hundredths, we could write as 2.17.

00:01:42.718 --> 00:01:44.901
This is 17 hundredths over here.

00:01:45.166 --> 00:01:46.432
And there's a bunch of ways that you could

00:01:46.432 --> 00:01:48.150
make this comparison, you could just say,

00:01:48.150 --> 00:01:50.749
oh look, two and seven
tenths is the same thing

00:01:50.749 --> 00:01:55.749
as two and 70 hundredths, over
here I have 70 hundredths,

00:01:55.753 --> 00:01:57.651
over here I only have 17 hundredths,

00:01:57.785 --> 00:01:59.172
so this is going to be larger.

00:01:59.411 --> 00:02:01.378
This one's going to be
larger right over here.

00:02:01.685 --> 00:02:02.683
Another way you could
have thought about it

00:02:02.683 --> 00:02:03.867
is we'll just start in the ones place,

00:02:03.867 --> 00:02:06.469
they both have two ones, so
that doesn't tell you much,

00:02:06.469 --> 00:02:08.430
but as soon as you go to the tenths place,

00:02:08.430 --> 00:02:11.112
this number as seven tenths and this one

00:02:11.112 --> 00:02:13.829
only has one tenth, so
this number right over here

00:02:13.829 --> 00:02:16.597
is going to be greater than that number.

00:02:17.067 --> 00:02:19.013
Let's go to, let's do another example.

00:02:20.086 --> 00:02:24.132
Which of the following are
less than two point zero three?

00:02:24.241 --> 00:02:26.012
Or two and three hundredths?

00:02:26.644 --> 00:02:28.914
Each big square represents one whole.

00:02:29.442 --> 00:02:31.103
So one way we could do it, and this is

00:02:31.103 --> 00:02:32.228
kind of the way that jumps out at me,

00:02:32.228 --> 00:02:35.253
is let's, let's write
all of these as decimals.

00:02:35.978 --> 00:02:39.542
So this one over here, we have one whole,

00:02:39.542 --> 00:02:42.318
another whole, and then over
here I don't have a full whole,

00:02:43.038 --> 00:02:45.774
let's see, I've taken a whole,
I've divided it into tenths,

00:02:45.989 --> 00:02:47.590
and I have two tenths right over here,

00:02:47.590 --> 00:02:51.764
so this number right over here
is equal to two and two tenths,

00:02:52.432 --> 00:02:55.044
you see that, two, one, two, and then two

00:02:55.044 --> 00:02:58.638
of the ten equal sections,
so two and two tenths,

00:02:58.991 --> 00:03:02.456
which is the same thing as 2.2.

00:03:02.868 --> 00:03:06.526
And if we wanted to compare it to 2.03,

00:03:06.526 --> 00:03:08.510
well we just have to think about this,

00:03:08.510 --> 00:03:09.985
well there's a, there's a bunch of ways

00:03:09.985 --> 00:03:11.308
you could think about this,

00:03:11.308 --> 00:03:14.894
you could view this as two point two zero,

00:03:14.894 --> 00:03:17.865
which would mean this is
two and 20 hundredths,

00:03:18.218 --> 00:03:20.679
and two and 20 hundredths
is for sure greater

00:03:20.679 --> 00:03:23.099
than two and three hundredths.

00:03:23.814 --> 00:03:28.411
So, this is not less than
2.03, this one over here

00:03:28.411 --> 00:03:32.619
is greater than 2.03, so
I'm gonna rule that one out.

00:03:33.194 --> 00:03:34.275
Another way you could
have thought about this

00:03:34.275 --> 00:03:36.757
is this is two and two
tenths which is the same

00:03:36.757 --> 00:03:40.193
thing as two and 20
hundredths, which this is

00:03:40.193 --> 00:03:42.376
another way of representing that,

00:03:42.376 --> 00:03:43.933
and you say, well this
one over, the number

00:03:43.933 --> 00:03:48.082
you're comparing against is
two and three hundredths.

00:03:48.668 --> 00:03:51.241
So 20 hundredths is greater
than three hundredths.

00:03:51.595 --> 00:03:54.340
So once again this is not less than 2.03.

00:03:54.799 --> 00:03:57.044
Here we have two and 12 hundredths,

00:03:57.410 --> 00:03:58.688
and actually this is useful
because I already have

00:03:58.688 --> 00:04:00.615
our original number represented as

00:04:00.615 --> 00:04:03.911
two and three hundredths, so the whole

00:04:03.911 --> 00:04:06.599
number part, the two, is the same,

00:04:06.697 --> 00:04:08.167
so when you look at the fraction part,

00:04:08.253 --> 00:04:11.997
12 hundredths is greater
than three hundredths,

00:04:12.189 --> 00:04:14.899
so this one is also not less than 2.03.

00:04:15.671 --> 00:04:17.523
Now what about 23 hundredths?

00:04:18.051 --> 00:04:22.503
23 hundredths, we can write
like this, 23 hundredths,

00:04:23.008 --> 00:04:26.022
or we could write it
like this, 23 hundredths,

00:04:26.491 --> 00:04:27.676
and you might be tempted to say,

00:04:27.676 --> 00:04:29.707
oh well hey, 23 hundredths,
that's bigger than

00:04:29.707 --> 00:04:32.806
three hundredths, but
remember, we have two wholes

00:04:32.806 --> 00:04:34.245
over here, we have two wholes,

00:04:34.245 --> 00:04:36.950
we have no wholes over here, we have,

00:04:36.950 --> 00:04:38.494
over here, one would think, but you have

00:04:38.494 --> 00:04:40.746
nothing in the ones
place, over here you have

00:04:40.746 --> 00:04:42.529
something in the ones place.

00:04:42.616 --> 00:04:43.474
So if you look at the ones place,

00:04:43.474 --> 00:04:45.703
you have two ones, you
have zero ones over here,

00:04:45.703 --> 00:04:47.973
it doesn't matter how
many hundredths you have,

00:04:47.979 --> 00:04:49.924
if you have less than a 100 hundredths,

00:04:50.197 --> 00:04:53.599
and so, this one is for
sure less than 2.03.

00:04:53.599 --> 00:04:56.275
This one is, this is
significantly less than even one.

00:04:56.453 --> 00:04:58.683
So this one is the only, of the three,

00:04:58.683 --> 00:05:00.964
that is less than 2.03.

00:05:01.678 --> 00:05:03.123
Let's do one more of these.

00:05:04.174 --> 00:05:06.874
Order the following values
from least to greatest.

00:05:07.180 --> 00:05:08.481
And once again I took a picture

00:05:08.481 --> 00:05:10.455
from the Khan Academy exercise,

00:05:10.455 --> 00:05:11.964
so I'm not gonna be
able to drag 'em around,

00:05:11.964 --> 00:05:13.462
if you're doing the exercise, you would be

00:05:13.462 --> 00:05:15.075
able to drag them around, but I'm

00:05:15.075 --> 00:05:16.874
just gonna, I'm just gonna
think about the numbers

00:05:16.874 --> 00:05:18.366
and then write them in order.

00:05:19.115 --> 00:05:21.902
So, I want to write them
all, let's write them all

00:05:21.902 --> 00:05:25.983
in, as decimals, let's
write them all as decimals,

00:05:25.983 --> 00:05:27.427
I guess is the easiest thing to do.

00:05:27.812 --> 00:05:30.627
So here, this one's already
written as a decimal, 2.59.

00:05:30.900 --> 00:05:35.491
24 tenths, 24 tenths, so
let's think about this.

00:05:36.054 --> 00:05:38.207
That's 24 over 10.

00:05:38.839 --> 00:05:41.474
Well, 24 over 10 is the same thing,

00:05:41.474 --> 00:05:46.474
this is equal to 20 over
10, plus four over 10,

00:05:47.257 --> 00:05:49.665
20 tenths, this is two
wholes right over here,

00:05:50.379 --> 00:05:52.509
so this is the same thing
as two and four tenths,

00:05:53.561 --> 00:05:58.303
two and four tenths, or,
the same thing as 2.4,

00:05:58.494 --> 00:06:01.628
two and four tenths, now if
we wanna make a comparison

00:06:01.628 --> 00:06:03.916
to two and 59 hundredths, we could throw

00:06:03.916 --> 00:06:05.913
another zero right over here, and say OK,

00:06:05.913 --> 00:06:09.168
we can view this as two and 40 hundredths.

00:06:09.477 --> 00:06:11.113
So these are all different
ways of representing this,

00:06:11.113 --> 00:06:12.437
some of you all might have
been able to go immediately,

00:06:12.437 --> 00:06:14.654
hey look, 10 tenths is one,

00:06:14.654 --> 00:06:16.958
20 tenths is two,

00:06:17.173 --> 00:06:22.173
so 24 tenths is going to be
two and four tenths, or 2.4,

00:06:22.351 --> 00:06:25.334
or 2.40, now let's try this number,

00:06:25.334 --> 00:06:27.244
two and three tenths, represented as

00:06:27.244 --> 00:06:30.691
2.3, if we want to think of it in terms of

00:06:30.691 --> 00:06:32.961
if we want to think of it
in terms of hundredths,

00:06:33.129 --> 00:06:34.568
you could say, well this
is the same thing as

00:06:34.568 --> 00:06:38.061
two and 30 hundredths,
which you could also

00:06:38.061 --> 00:06:41.300
represent as 2.30, and
the reason why I'm adding

00:06:41.300 --> 00:06:42.428
the hundredth there is so we can

00:06:42.428 --> 00:06:44.535
more easily make the comparison.

00:06:44.889 --> 00:06:46.282
So you're comparing, you're comparing

00:06:46.282 --> 00:06:48.824
two and 59 hundredths,
to two and 40 hundredths,

00:06:48.824 --> 00:06:51.059
to two and 30 hundredths.

00:06:51.425 --> 00:06:53.369
Well, they all have two in the ones place,

00:06:53.990 --> 00:06:55.690
they all have two in the ones place.

00:06:55.986 --> 00:06:57.955
So then we just have to
go to the tenths place.

00:06:58.122 --> 00:06:59.860
And you see, this has the most tenths,

00:06:59.860 --> 00:07:01.687
five tenths, this is the second most,

00:07:01.687 --> 00:07:04.176
four tenths, and this
has the least tenths,

00:07:04.296 --> 00:07:08.005
three tenths, so, ordering
from least to greatest:

00:07:08.010 --> 00:07:09.781
the least is two and three tenths,

00:07:10.436 --> 00:07:14.400
the least and three tenths,
which is equal to 2.3.

00:07:14.835 --> 00:07:18.521
The next, the one larger,
next larger than that,

00:07:18.573 --> 00:07:23.573
is going to be 24 tenths, 24
tenths, which is equal to 2.4,

00:07:26.689 --> 00:07:30.306
and then the largest is 2.59.

00:07:30.334 --> 00:07:31.587
And once again, this only, they all have

00:07:31.587 --> 00:07:34.037
two in the ones place and
then you go to the tenths,

00:07:34.037 --> 00:07:37.422
this has three tenths,
four tenths, five tenths.


Comparing decimals visually example

WEBVTT
Kind: captions
Language: en

00:00:00.523 --> 00:00:02.636
- [Voiceover] The goal
of this video is to try

00:00:02.636 --> 00:00:04.826
to compare these two quantities.

00:00:04.826 --> 00:00:07.966
I have 0.17 and I have 0.2,

00:00:07.966 --> 00:00:10.828
and I wanna figure out
which of these two is larger

00:00:10.828 --> 00:00:12.519
or maybe they're equal,
and I encourage you

00:00:12.519 --> 00:00:15.201
to pause the video to
try to figure that out.

00:00:15.201 --> 00:00:17.944
One way to do it is to
try to visualize these.

00:00:17.944 --> 00:00:21.535
Each of these large squares
you can view as a whole.

00:00:21.535 --> 00:00:24.719
And this one on the left, I
have it split into 100 smaller

00:00:24.719 --> 00:00:27.245
sections 'cause you
notice we have 10 rows,

00:00:27.245 --> 00:00:30.846
and each row has 10 squares,
so we have 100 squares here.

00:00:30.846 --> 00:00:35.141
So, each of these squares
represents 1/100 of the whole.

00:00:35.141 --> 00:00:37.630
And so this number up here, 0.17,

00:00:37.630 --> 00:00:41.168
we could view that as 17/100.

00:00:41.168 --> 00:00:44.499
So let's color in 17/100.

00:00:44.499 --> 00:00:47.974
17/100 is going to be,

00:00:47.974 --> 00:00:52.487
so that's 1/100, two, three, four, five,

00:00:52.487 --> 00:00:56.750
six, seven, eight, nine, 10/100.

00:00:56.750 --> 00:01:00.130
And notice 10/100, I filled
in one out of the 10 rows,

00:01:00.130 --> 00:01:02.325
so this is the same thing as 1/10.

00:01:02.325 --> 00:01:06.549
So that's 10/100, 11/100, 12/100,

00:01:06.549 --> 00:01:10.077
13, 14, 15, 16, 17.

00:01:10.077 --> 00:01:14.868
So, one way to visualize
0.17, which is 17/100,

00:01:14.868 --> 00:01:18.739
is the fraction of this whole
that is filled in magenta.

00:01:18.739 --> 00:01:20.800
Now what about 0.2?

00:01:20.800 --> 00:01:23.974
0.2 is the same thing as 2/10.

00:01:23.974 --> 00:01:26.881
So we could take our whole
and divide it into 1/10,

00:01:26.881 --> 00:01:30.781
divide it into 10 equal
sections which we've done here.

00:01:30.781 --> 00:01:34.133
Notice each of these
sections is equal to 10/100.

00:01:34.133 --> 00:01:37.385
And that makes sense,
1/10 is equal to 10/100.

00:01:37.385 --> 00:01:39.497
Let's fill in two of them
now 'cause we're dealing

00:01:39.497 --> 00:01:41.216
with 2/10.

00:01:41.216 --> 00:01:43.316
So let's fill in two of them.

00:01:43.316 --> 00:01:46.981
We have 1/10 and 2/10.

00:01:46.981 --> 00:01:51.295
Which of these is larger?

00:01:51.295 --> 00:01:53.901
We see we're filling in more
of the whole when we're doing

00:01:53.901 --> 00:01:58.286
2/10 than when we're doing 17/100.

00:01:58.286 --> 00:02:02.259
And that makes sense because
2/10 is the same thing.

00:02:02.259 --> 00:02:04.447
2/10 is the same thing.

00:02:04.447 --> 00:02:06.787
Another way of me saying
2/10 is you could write it

00:02:06.787 --> 00:02:09.291
as 20/100.

00:02:09.291 --> 00:02:11.769
20/100 is greater than 17/100.

00:02:11.769 --> 00:02:13.477
To get the 20/100,

00:02:13.477 --> 00:02:15.723
you'd have to fill in these three as well.

00:02:15.723 --> 00:02:17.539
Notice when you fill out those three,

00:02:17.539 --> 00:02:20.807
you're filling out the same
fraction of your whole.

00:02:20.807 --> 00:02:23.376
So, which one's larger?

00:02:23.376 --> 00:02:24.696
2/10 is.

00:02:24.696 --> 00:02:26.516
And how do we write that down?

00:02:26.516 --> 00:02:27.999
When we write it in equality,

00:02:27.999 --> 00:02:30.095
we wanna open to the larger number.

00:02:30.095 --> 00:02:31.559
You want to open to that one.

00:02:31.559 --> 00:02:34.672
So we have 0.17 or 17/100,

00:02:34.672 --> 00:02:38.039
is less than 2/10.

00:02:38.039 --> 00:02:40.221
Now, another way that we
could've tackled this,

00:02:40.221 --> 00:02:43.928
even without having to draw all of this,

00:02:43.928 --> 00:02:47.627
is we could've just gone
to the largest place value.

00:02:47.627 --> 00:02:52.157
So if you went to the one's
place, we have zero ones.

00:02:52.157 --> 00:02:55.182
And we have zero ones here,
so that doesn't help us.

00:02:55.182 --> 00:02:56.670
Then you go to the next largest,

00:02:56.670 --> 00:02:59.129
so you go to the 1/10 place.

00:02:59.129 --> 00:03:02.847
Here you have 1/10, here you have 2/10.

00:03:02.847 --> 00:03:05.123
So immediately, without
even looking at what comes

00:03:05.123 --> 00:03:09.107
after this, this could be
0.17358, it could keep going,

00:03:09.107 --> 00:03:12.274
but the bottom line is
you have more 1/10 here

00:03:12.274 --> 00:03:14.921
than you have 1/10 here,
which tells you that this one

00:03:14.921 --> 00:03:19.608
over here is going to be larger.

00:03:19.608 --> 00:03:23.144
So the general thing is, look
at the largest place value.

00:03:23.144 --> 00:03:25.886
If one of the numbers has a larger digit

00:03:25.886 --> 00:03:28.141
in the largest place value,
it's gonna be larger.

00:03:28.141 --> 00:03:31.310
If they're equal, go to the
next larger place value.

00:03:31.310 --> 00:03:33.472
And you could keep going like
that, but another way to think

00:03:33.472 --> 00:03:35.797
about it is just to visualize it,

00:03:35.797 --> 00:03:38.514
just like we did over here.


Comparing decimals example 1

WEBVTT
Kind: captions
Language: en

00:00:00.504 --> 00:00:05.305
- Let's compare the number
0.7 to the number 0.09.

00:00:05.914 --> 00:00:07.841
And there's a bunch of ways to do this,

00:00:07.841 --> 00:00:10.396
but the way that I'm going to tackle it is

00:00:10.396 --> 00:00:12.160
I'm gonna start looking
at each of the digits,

00:00:12.160 --> 00:00:13.948
starting with the leftmost digit.

00:00:13.948 --> 00:00:15.829
And so we can start right over here

00:00:15.829 --> 00:00:17.606
in the ones place.

00:00:17.616 --> 00:00:18.685
You always want to compare ones place

00:00:18.685 --> 00:00:20.241
to ones place, so for example

00:00:20.241 --> 00:00:21.913
if we compare these two numbers,

00:00:21.913 --> 00:00:23.561
they both have zero ones.

00:00:23.561 --> 00:00:25.744
So the ones place doesn't tell us much.

00:00:25.744 --> 00:00:28.785
So now let's go one
place value to the right.

00:00:28.785 --> 00:00:30.643
Let's go to the tenths place.

00:00:30.643 --> 00:00:32.895
This number has seven tenths,

00:00:32.895 --> 00:00:35.287
while this number has zero tenths.

00:00:35.287 --> 00:00:39.188
That by itself tells us that
this is the larger number.

00:00:39.188 --> 00:00:41.579
We would put an inequality
symbol right over here.

00:00:41.579 --> 00:00:44.272
We wanna open it up to the larger number,

00:00:44.272 --> 00:00:46.455
where it points to the smaller number.

00:00:46.455 --> 00:00:51.419
So this says 0.7 is greater than 0.09.

00:00:51.772 --> 00:00:53.189
Now you might be tempted
to say oh wait, wait.

00:00:53.189 --> 00:00:55.952
Look, but if we went one
more digit to the right

00:00:55.952 --> 00:00:58.459
you have nine hundredths here,

00:00:58.459 --> 00:01:00.294
and you have no hundredths over here.

00:01:00.294 --> 00:01:01.965
We could write a zero over here,

00:01:01.965 --> 00:01:03.196
and you'd say well look,

00:01:03.196 --> 00:01:05.512
you have no hundredths over here.

00:01:05.820 --> 00:01:07.399
But the nine hundredths don't matter.

00:01:07.399 --> 00:01:09.442
Remember, even if you had 10 hundredths,

00:01:09.442 --> 00:01:12.158
that's the same thing as one tenth.

00:01:12.158 --> 00:01:14.759
So it doesn't matter that nine is somehow

00:01:14.759 --> 00:01:15.966
greater than seven.

00:01:15.966 --> 00:01:18.335
What matters is it's in
a place to the right.

00:01:18.335 --> 00:01:21.191
Even if you increased by
another hundredth here

00:01:21.191 --> 00:01:23.188
you'd only get to one tenth.

00:01:23.188 --> 00:01:26.069
This thing over here has seven tenths.

00:01:26.214 --> 00:01:27.654
Let's do another one of these.

00:01:29.454 --> 00:01:31.276
Let's say we wanted to compare,

00:01:31.276 --> 00:01:33.133
let's say we wanted to compare

00:01:34.493 --> 00:01:38.546
0.29,

00:01:40.462 --> 00:01:42.011
let's say I wanna compare that

00:01:42.011 --> 00:01:46.556
to 0.31.

00:01:47.746 --> 00:01:49.441
Now this one you might say is a little bit

00:01:49.441 --> 00:01:50.927
more straightforward, depending on how

00:01:50.927 --> 00:01:51.809
you think about it.

00:01:51.809 --> 00:01:53.899
If you say hey, this is 29 hundredths,

00:01:53.899 --> 00:01:55.733
this is 31 hundredths,

00:01:55.733 --> 00:01:58.310
we have more hundredths
on the right-hand side.

00:01:58.310 --> 00:02:02.026
So let me open my inequality
to the larger value

00:02:02.026 --> 00:02:04.881
and I would say 0.29, or 29 hundredths

00:02:04.881 --> 00:02:07.250
is less than 31 hundredths.

00:02:07.250 --> 00:02:08.922
Another way you could have done this

00:02:08.922 --> 00:02:12.010
is you could have looked
in the ones place,

00:02:12.010 --> 00:02:14.448
say okay, they both have zero ones,

00:02:14.448 --> 00:02:16.491
but then you look in the tenths place,

00:02:16.491 --> 00:02:18.256
say this only has two tenths,

00:02:18.256 --> 00:02:19.927
while this has three tenths.

00:02:19.927 --> 00:02:21.483
I shouldn't have to keep looking

00:02:21.483 --> 00:02:23.085
at the digits to the right of that.

00:02:23.085 --> 00:02:24.455
I can just compare this two tenths

00:02:24.455 --> 00:02:25.662
to the three tenths.

00:02:25.662 --> 00:02:28.472
Three tenths is larger, and so I would say

00:02:28.472 --> 00:02:33.472
that 29 hundredths is
less than 31 hundredths.

00:02:34.509 --> 00:02:36.459
Let's do one more, just for fun.

00:02:37.479 --> 00:02:40.796
Let's compare, let's compare

00:02:43.466 --> 00:02:47.529
0.6 to, I'll do them in the same color.

00:02:48.185 --> 00:02:50.275
0.06.

00:02:50.275 --> 00:02:53.798
Which of these is the larger number?

00:02:54.175 --> 00:02:56.126
Well we do the same thing
that we've been doing.

00:02:56.126 --> 00:02:58.587
You can first go to the ones place.

00:02:58.587 --> 00:03:01.350
Say okay, this has no
ones, this has no ones.

00:03:01.350 --> 00:03:02.883
Okay that doesn't tell us much.

00:03:02.883 --> 00:03:04.020
Then the tenths place.

00:03:04.020 --> 00:03:06.899
This has six tenths, this has zero tenths.

00:03:06.899 --> 00:03:09.500
So this number is going to be larger.

00:03:09.500 --> 00:03:10.568
It has more tenths.

00:03:10.568 --> 00:03:12.193
It doesn't matter who has more hundredths.

00:03:12.193 --> 00:03:13.772
Hundredths are much smaller than tenths.

00:03:13.772 --> 00:03:15.839
They're a tenth of the size of a tenth.

00:03:15.839 --> 00:03:17.928
So this has six tenths,
this has zero tenths.

00:03:17.928 --> 00:03:20.134
So this number is larger.

00:03:20.134 --> 00:03:24.267
0.6 is greater than 0.06.

00:03:24.267 --> 00:03:25.869
It's actually ten times greater

00:03:25.869 --> 00:03:27.629
but we can talk about
that in other videos.


Place value for decimals greater than one (examples)

WEBVTT
Kind: captions
Language: en

00:00:00.000 --> 00:00:03.777
We're told that "Each square below
represents one whole."

00:00:03.777 --> 00:00:07.352
So this big square right over here
is a whole,

00:00:07.352 --> 00:00:10.669
and then this big square over here
is another whole.

00:00:10.669 --> 00:00:15.103
Then they ask us "Which of the following
does the shaded area represent?

00:00:15.103 --> 00:00:19.102
Select all that apply." So let's see--
the shaded area. We're shaded in blue.

00:00:19.102 --> 00:00:23.104
So let's see-- one way to think about it
is we have 1 whole over here.

00:00:23.104 --> 00:00:29.433
and then over here we've divided it
into tenths: there's 1, 2, 3, 4,

00:00:29.433 --> 00:00:35.197
5, 6, 7, 8, 9, 10 equal sections,
and we've shaded in one of them.

00:00:35.197 --> 00:00:40.936
So we've shaded 1 tenth.
So this would be 1 whole and 1 tenth.

00:00:40.936 --> 00:00:44.622
So we could say that this
is 1 and 1 tenth.

00:00:44.622 --> 00:00:48.201
So that's one way to think about it,
but what about these other ones?

00:00:48.201 --> 00:00:51.665
Well even this one has been
divided into tenths,

00:00:51.665 --> 00:00:55.034
and you can view 1 whole
as 10 tenths. You see that here,

00:00:55.034 --> 00:00:58.477
where we've divided it
into 10 equal sections. 10 tenths,

00:00:58.477 --> 00:01:02.296
and we've shaded all 10 tenths in.
So this whole you could view

00:01:02.296 --> 00:01:08.621
as 10 tenths:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10.

00:01:08.621 --> 00:01:10.947
And then we have an 11th tenth.

00:01:13.197 --> 00:01:18.301
So we have-- if you count these
blue rectangles, we have 11 tenths.

00:01:18.301 --> 00:01:21.564
So you could also write this as 11 tenths.

00:01:21.564 --> 00:01:24.970
Now 11 hundredths? No, I don't think--
we haven't even

00:01:24.970 --> 00:01:28.703
divided this into hundredths,
and 11 hundredths would be

00:01:28.703 --> 00:01:33.802
a little more than 1 tenth. And so
this is definitely way more than that.

00:01:33.802 --> 00:01:37.508
So I could check my answer (and
actually you don't see it but it's

00:01:37.508 --> 00:01:41.608
happening off-screen) but this is
what I would go with for that.

00:01:41.608 --> 00:01:44.758
Let's do a couple more of these.

00:01:44.758 --> 00:01:48.088
So it says "Which of the following
describes the location of the point

00:01:48.088 --> 00:01:50.268
on the number line?" Let's see.

00:01:50.268 --> 00:01:55.524
I have 1, and then between 1 and 2
I've divided it into 10 equal spaces.

00:01:55.524 --> 00:02:00.227
1, 2, 3, 4, 5, 6, 7, 8, 9, 10.

00:02:00.227 --> 00:02:04.464
So each of these tick marks,
or hash marks, is going to be a tenth.

00:02:04.464 --> 00:02:08.667
So this is 1 and 0 tenths,
1 and 1 tenth, 1 and 2 tenths,

00:02:08.667 --> 00:02:12.068
1 and 3 tenths, 1 and 4 tenths,
1 and 5 tenths,

00:02:12.068 --> 00:02:16.970
1 and 6 tenths, 1 and 7 tenths,
1 and 8 tenths.

00:02:16.970 --> 00:02:22.851
So 1 and 8 tenths is the same thing
as 1.8. 1 and 8 tenths.

00:02:22.851 --> 00:02:25.750
So it's that. But what about
these other options?

00:02:25.750 --> 00:02:29.252
Well one way we could think about
this is-- let's just count the tenths.

00:02:29.252 --> 00:02:31.391
Each of these hash marks is a tenth.

00:02:31.391 --> 00:02:37.534
So 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.

00:02:37.534 --> 00:02:40.001
It makes sense. A whole is 10 tenths.

00:02:40.001 --> 00:02:45.871
Let's keep going, we were at 10 tenths.
11 tenths, 12 tenths, 13 tenths,

00:02:45.871 --> 00:02:52.699
14 tenths, 15 tenths,
16 tenths, 17 tenths, 18 tenths.

00:02:52.699 --> 00:02:55.492
This one also applies.

00:02:55.492 --> 00:03:00.037
18 hundredths: this would be
between 10 hundredths and 20 hundredths

00:03:00.037 --> 00:03:02.965
which would be the same thing as
between 1 tenth and 2 tenths.

00:03:02.965 --> 00:03:07.201
So 18 hundredths is going to be
someplace around here,

00:03:07.201 --> 00:03:10.164
so I definitely will not select that one.

00:03:10.164 --> 00:03:13.624
Let's try a few more of these.

00:03:13.624 --> 00:03:19.871
So they say "Write a decimal
that is equal to 24 tenths."

00:03:19.871 --> 00:03:24.167
Alright, 24 tenths. So remember
we could view this as--

00:03:24.167 --> 00:03:32.992
I'll just write it down-- we could view
this as 20 tenths plus 4 tenths.

00:03:32.992 --> 00:03:37.732
But what is 20 tenths equal to?

00:03:37.732 --> 00:03:40.867
10 tenths is equal to a whole,

00:03:40.867 --> 00:03:44.139
so 20 tenths is going to be
equal to 2 wholes.

00:03:44.139 --> 00:03:47.526
So this could be viewed
as 2 plus 4 tenths,

00:03:47.526 --> 00:03:51.468
or another way to write this--
we could just write 4 in the tenths place.

00:03:51.468 --> 00:03:54.241
So we could just write this as 2.4.

00:03:54.241 --> 00:04:00.494
24 tenths: 20 tenths are 2 wholes
and then you have another 4 tenths.

00:04:00.494 --> 00:04:03.007
Let's do one other one.

00:04:03.007 --> 00:04:06.200
"102 hundredths."

00:04:06.200 --> 00:04:13.633
So we could rewrite this as
100 hundredths plus 2 hundredths.

00:04:16.433 --> 00:04:20.614
Now, what is 100 hundredths?

00:04:20.614 --> 00:04:24.422
Well 100 hundredths
is equal to 1, is equal to a whole.

00:04:24.422 --> 00:04:27.000
So 100 hundredths is just equal to 1.

00:04:27.000 --> 00:04:29.338
So you could view this as
1 plus 2 hundredths.

00:04:29.338 --> 00:04:33.684
Another way to write
two hundredths is 0.02.

00:04:33.684 --> 00:04:39.340
So what's 1 plus 0.02?
Well it's just going to be 1.02.

00:04:39.340 --> 00:04:43.167
And you see that here.
You have 1 and 2 hundredths.

00:04:43.167 --> 00:04:46.649
1 is the same thing as 100 hundredths.

00:04:46.649 --> 00:04:50.603
So this is 100 hundredths
and you have 2 hundredths

00:04:50.603 --> 00:04:54.963
gives you 102 hundredths.

00:04:54.963 --> 00:04:57.372
Alright, let's do another one.

00:04:57.372 --> 00:05:01.242
"What is 32 tenths written as a decimal?"

00:05:01.242 --> 00:05:04.974
So we just have to remind ourselves:
10 tenths is equal to a whole.

00:05:04.974 --> 00:05:10.652
20 tenths is equal to 2 ones.
30 tenths is equal to 3 ones.

00:05:10.652 --> 00:05:14.404
So this is going to be equal to 3 ones
and then another 2 tenths.

00:05:14.404 --> 00:05:17.875
3 ones and another 2 tenths.

00:05:17.875 --> 00:05:19.615
Let's keep going.

00:05:19.615 --> 00:05:22.506
"What is 203 hundredths
written as a decimal?"

00:05:22.506 --> 00:05:26.616
Well we have to remind ourselves
that 200 hundredths is equal to 2 ones.

00:05:26.616 --> 00:05:30.385
So here this is the same thing as
2 ones and 3 hundredths.

00:05:30.385 --> 00:05:36.274
2 ones-- this case right here--
2 ones and 3 hundredths.

00:05:36.274 --> 00:05:38.121
Let's do a couple more of these.

00:05:38.121 --> 00:05:42.071
"1.05 is equal to how many hundredths?"

00:05:42.078 --> 00:05:46.700
Well, one whole, or 1,
is equal to 100 hundredths.

00:05:46.700 --> 00:05:50.045
So this is 100 hundredths
plus 5 hundredths,

00:05:50.045 --> 00:05:53.021
or 105 hundredths.

00:05:53.021 --> 00:05:55.788
Alright. Let's do another one.

00:05:55.788 --> 00:05:59.951
"How can 2.60 be written in words?"

00:05:59.951 --> 00:06:06.393
So I could write this as 2 and 6 tenths.
2 ones and 6 tenths.

00:06:06.393 --> 00:06:11.240
I could also think of this as
2 ones and 60 hundredths.

00:06:11.240 --> 00:06:15.062
Or I could view this as 260 hundredths.

00:06:15.062 --> 00:06:16.831
So let's see which of these choices--

00:06:16.831 --> 00:06:19.075
So "2 ones and 6 hundredths"...

00:06:19.075 --> 00:06:23.102
No, no, it's 2 ones and 60 hundredths,
not 6 hundredths.

00:06:23.102 --> 00:06:27.028
It's 6 tenths right over here.
6 tenths or 60 hundredths.

00:06:27.028 --> 00:06:28.477
I won't select that.

00:06:28.477 --> 00:06:30.516
"260 hundredths."

00:06:30.516 --> 00:06:34.025
Yeah, that's right because 2 ones
is that same thing as 200 hundredths

00:06:34.025 --> 00:06:36.766
and then we have another
60 hundredths right over there.

00:06:36.766 --> 00:06:37.883
So that's right.

00:06:37.883 --> 00:06:43.383
"260 tenths." No, 260 tenths--
remember 10 tenths is equal to a whole,

00:06:43.383 --> 00:06:47.029
so 260 tenths would be 26,
would be 26 ones.

00:06:47.029 --> 00:06:49.000
So it's not that choice either.

00:06:49.000 --> 00:06:51.538
So anyway, I think we've done
plenty of examples.

00:06:51.538 --> 00:06:53.528
Hopefully you have enjoyed that.


Fraction-decimal intuition problems (examples)

WEBVTT
Kind: captions
Language: en

00:00:00.376 --> 00:00:02.257
- [Voiceover] We are told the square below

00:00:02.257 --> 00:00:04.138
represents one whole.

00:00:04.138 --> 00:00:06.831
So this big square here
represents a whole.

00:00:06.831 --> 00:00:11.831
Express the shaded area as
both a fraction and a decimal.

00:00:11.939 --> 00:00:13.495
So let's see, we've taken the whole

00:00:13.495 --> 00:00:17.233
and we've divided it into
one, two, three, four,

00:00:17.233 --> 00:00:22.156
five, six, seven, eight,
nine, ten, equal sections.

00:00:22.156 --> 00:00:24.872
Each of these columns or
each of these tall rectangles

00:00:24.872 --> 00:00:28.355
represent one tenth of the whole because

00:00:28.355 --> 00:00:31.838
they are ten equal sections
that it has been split into.

00:00:31.838 --> 00:00:34.485
So each of these is a tenth and let's see

00:00:34.485 --> 00:00:38.479
we have filled in one,
two, three, four, five,

00:00:38.479 --> 00:00:40.777
six, of those tenths.

00:00:40.777 --> 00:00:43.030
So if I wanted to
represent it as a fraction

00:00:43.030 --> 00:00:46.652
I would say this is 6/10 and
if I were to represent it

00:00:46.652 --> 00:00:49.577
as a decimal I would say, okay, well,

00:00:49.577 --> 00:00:53.525
I have zero ones and I have six tenths,

00:00:53.525 --> 00:00:56.938
so as a decimal it is 0.6.

00:00:56.938 --> 00:00:59.329
Let's do a couple more of these examples.

00:00:59.329 --> 00:01:03.393
So let's say, so okay, look at that.

00:01:03.393 --> 00:01:06.388
Now I have, let's see, the big
square represents one whole.

00:01:06.388 --> 00:01:07.746
Express the shaded area as both a fraction

00:01:07.746 --> 00:01:09.037
and a decimal.

00:01:09.037 --> 00:01:10.732
So what's going on over here?

00:01:10.732 --> 00:01:15.732
So I have ten rows and in
each row I have ten squares.

00:01:16.075 --> 00:01:17.953
So ten times ten.

00:01:17.953 --> 00:01:20.553
This has a hundred squares in it.

00:01:20.553 --> 00:01:23.990
So I've divided my whole into
a hundred equal sections.

00:01:23.990 --> 00:01:27.774
So each of these little
squares is one hundredth.

00:01:27.774 --> 00:01:30.468
So here I have shaded in one, two,

00:01:30.468 --> 00:01:34.972
three, four, five out of
the hundred hundredths,

00:01:34.972 --> 00:01:38.223
or I could say I have five
hundredths right over here.

00:01:38.223 --> 00:01:42.356
So as a fraction, I
could write this as 5/100

00:01:42.356 --> 00:01:45.166
and as a decimal I could
say, oh, I have no ones.

00:01:45.166 --> 00:01:50.065
I have no tenths and I
have five hundredths.

00:01:50.065 --> 00:01:54.848
Let's do a couple more examples of this.

00:01:54.848 --> 00:01:58.472
So let's say that I wanted to...

00:01:58.472 --> 00:02:01.303
Let's see, it says, express
the location of the point

00:02:01.303 --> 00:02:05.714
on the number line as both
a fraction and a decimal.

00:02:05.714 --> 00:02:07.502
All right. So let's think about it.

00:02:07.502 --> 00:02:11.055
So this is 2/10, this is 3/10.

00:02:11.055 --> 00:02:13.446
And you see it is 0/10, 1/10,

00:02:13.446 --> 00:02:15.954
or this is 0, 1/10, 2/10, 3/10,

00:02:15.954 --> 00:02:19.367
and before each, or between each tenth

00:02:19.367 --> 00:02:21.294
they've split it into ten equal sections.

00:02:21.294 --> 00:02:26.294
One, two, three, four, five,
six, seven, eight, nine, ten.

00:02:26.565 --> 00:02:29.142
So each of these, each
of these little hashmarks

00:02:29.142 --> 00:02:31.905
represent one hundredth.

00:02:31.905 --> 00:02:33.182
So one way you could view this is

00:02:33.182 --> 00:02:36.572
we're at two tenths,
so we have two tenths,

00:02:36.572 --> 00:02:39.800
and then we're going to
have one, two, three,

00:02:39.800 --> 00:02:44.629
four, five, six, seven hundredths.

00:02:44.629 --> 00:02:46.742
So we could view this point as two tenths

00:02:46.742 --> 00:02:48.716
and seven hundredths.

00:02:48.716 --> 00:02:50.806
So actually let me write
it as a decimal first.

00:02:50.806 --> 00:02:55.806
So we have two tenths and
we have seven hundredths.

00:02:56.100 --> 00:02:57.562
Now another way to think about this

00:02:57.562 --> 00:02:59.536
is we have 27 hundredth.

00:02:59.536 --> 00:03:00.372
You can count them.

00:03:00.372 --> 00:03:02.485
Remember each of these is one hundredth.

00:03:02.485 --> 00:03:06.269
So zero, one, two, three, four, five, six,

00:03:06.269 --> 00:03:11.269
seven, eight, nine, ten,
11, 12, 13, 14, 15, 16,

00:03:11.494 --> 00:03:16.494
17, 18, 19, 20, 21, 22, 23,
24, 25, 26, 27, 27 hundredths.

00:03:19.899 --> 00:03:21.571
And most people when they see this number

00:03:21.571 --> 00:03:23.869
they won't say two tenths
and seven hundredths.

00:03:23.869 --> 00:03:26.331
They'll just say 27 hundredths.

00:03:26.331 --> 00:03:30.464
Well how do you write 27
hundredths as a fraction?

00:03:30.464 --> 00:03:33.691
Well, it's 27/100.

00:03:33.691 --> 00:03:38.637
27 over, over 100.

00:03:38.637 --> 00:03:40.703
Let's do, I don't know,
I'm kind of in the mood.

00:03:40.703 --> 00:03:42.863
Let's do one more of these.

00:03:42.863 --> 00:03:44.279
The big square represents one whole.

00:03:44.279 --> 00:03:45.928
Express the shaded area as both a fraction

00:03:45.928 --> 00:03:47.599
and a decimal.

00:03:47.599 --> 00:03:49.666
So we've already seen,
there's a hundred of these.

00:03:49.666 --> 00:03:53.752
The whole is split into a
hundred equal, smaller sections.

00:03:53.752 --> 00:03:56.283
So each of these small
squares is a hundredth

00:03:56.283 --> 00:03:58.837
and so how many hundredths
do we have shaded in?

00:03:58.837 --> 00:04:02.227
So this is going to be ten
hundredths, 20 hundredths,

00:04:02.227 --> 00:04:04.062
21 hundredths.

00:04:04.062 --> 00:04:07.962
So as a fraction I'd write that as 21/100.

00:04:07.962 --> 00:04:10.772
Now, you could, there's a couple
of ways to think about it.

00:04:10.772 --> 00:04:12.676
If we're familiar with it
already we would say okay,

00:04:12.676 --> 00:04:16.484
look, two tenths is the
same thing as 20 hundredths,

00:04:16.484 --> 00:04:18.991
so it's going to be two
tenths and one hundredth,

00:04:18.991 --> 00:04:20.338
or 21 hundredth.

00:04:20.338 --> 00:04:21.522
Another way to think about it is

00:04:21.522 --> 00:04:24.866
this first row right over
here, that's a tenth,

00:04:24.866 --> 00:04:28.465
then this next one is a
tenth, so you have two tenths,

00:04:28.465 --> 00:04:30.020
and then you have a hundredth over here.

00:04:30.020 --> 00:04:31.088
So any way you want to think about it.

00:04:31.088 --> 00:04:35.448
This is 21 hundredths or two
tenths and one hundredth.


Plotting decimal numbers on a number line (examples)

WEBVTT
Kind: captions
Language: en

00:00:00.380 --> 00:00:01.327
- [Voiceover] We're asked to move

00:00:01.327 --> 00:00:05.503
the orange dot to 5.90 on the number line,

00:00:05.503 --> 00:00:08.382
or you could view this as 5 90/100,

00:00:08.382 --> 00:00:11.075
or 5 9/10.

00:00:11.075 --> 00:00:14.071
All right, so let's see, this is 5.8,

00:00:14.071 --> 00:00:17.228
and then this is 6.0.

00:00:17.228 --> 00:00:18.622
One way to think about it is

00:00:18.622 --> 00:00:21.348
5.9 is exactly halfway

00:00:21.348 --> 00:00:23.948
between 5.8 and 6.0,

00:00:23.948 --> 00:00:26.085
and this is written as 5.90,

00:00:26.085 --> 00:00:28.267
but we could view this as 5.9,

00:00:28.267 --> 00:00:32.052
so it's going to be exactly halfway.

00:00:32.052 --> 00:00:35.528
Now, one interesting
thing to think about is

00:00:35.528 --> 00:00:38.364
what do each of these
tick marks represent?

00:00:38.364 --> 00:00:40.848
Well, if this is 5.8, and if 1/10

00:00:40.848 --> 00:00:43.913
higher than 5.8 is 5.9 over here,

00:00:43.913 --> 00:00:46.741
and then 1/10 higher than that is 6.0,

00:00:46.741 --> 00:00:49.565
so from here to here is 1/10,

00:00:49.565 --> 00:00:52.448
and then from here to
here is another 1/10.

00:00:53.982 --> 00:00:55.346
Then they've divided each 1/10

00:00:55.346 --> 00:00:58.746
into one, two, three, four, five,

00:00:58.746 --> 00:01:02.437
six, seven, eight, nine, 10 sections,

00:01:02.437 --> 00:01:05.149
so each of these represent 1/10 of 1/10,

00:01:05.149 --> 00:01:07.304
or 1/100, so for example,

00:01:07.304 --> 00:01:09.728
this would be 5.81, 5.82,

00:01:09.728 --> 00:01:13.155
5.83, 5.84, 5.85,

00:01:13.155 --> 00:01:16.336
5.86, 5.87, 5.88,

00:01:16.336 --> 00:01:20.557
5.89, 5.90.

00:01:20.557 --> 00:01:23.320
So either way, I think we got it.

00:01:23.320 --> 00:01:25.307
All right, let's keep
doing some more of these.

00:01:26.195 --> 00:01:28.438
Move the orange dot to 2.87

00:01:28.438 --> 00:01:29.622
on the number line.

00:01:29.622 --> 00:01:30.899
All right, this is interesting.

00:01:30.899 --> 00:01:32.084
So, this is 2.8.

00:01:32.084 --> 00:01:33.105
That's 3.0.

00:01:33.105 --> 00:01:34.698
Halfway in between would be

00:01:34.698 --> 00:01:36.213
this longer hash mark,

00:01:36.213 --> 00:01:37.811
or this longer tick mark, right over here.

00:01:37.811 --> 00:01:39.993
This would be 2.9.

00:01:39.993 --> 00:01:42.496
So 2.87, this is just like we saw

00:01:42.496 --> 00:01:43.889
in the last example.

00:01:43.889 --> 00:01:45.278
Each of these is 1/100,

00:01:45.278 --> 00:01:48.784
so this is 2.8, this would be 2.81,

00:01:48.784 --> 00:01:52.661
2.82, 2.83, 2.84,

00:01:52.661 --> 00:01:56.395
2.85, 2.86,

00:01:56.395 --> 00:02:00.040
2.87, and we could just check.

00:02:00.040 --> 00:02:04.949
This would be 2.88, 2.89, 2.9,

00:02:04.949 --> 00:02:07.410
or 2.90, which is exactly halfway

00:02:07.410 --> 00:02:09.337
between 2.8 and 3.0,

00:02:09.337 --> 00:02:10.939
so I'm feeling good about that.

00:02:10.939 --> 00:02:11.961
Let's check our answer.

00:02:11.961 --> 00:02:12.936
We got it right.

00:02:12.936 --> 00:02:14.538
You know, after you get a question right,

00:02:14.538 --> 00:02:15.629
it doesn't hurt to look at the hints

00:02:15.629 --> 00:02:16.860
at that point, so let's just see

00:02:16.860 --> 00:02:18.392
how they tackled it.

00:02:18.392 --> 00:02:20.157
So, they say, "Above we've drawn

00:02:20.157 --> 00:02:23.129
"the number line from 2.8 to 3.0,"

00:02:23.129 --> 00:02:25.103
and they divided into 20 equal pieces.

00:02:25.103 --> 00:02:27.099
Yup, that looks right.

00:02:27.099 --> 00:02:28.446
Let's see their next hint.

00:02:28.446 --> 00:02:30.623
So, they say that piece of the line

00:02:30.623 --> 00:02:32.899
is 3.0 minus 2.8.

00:02:32.899 --> 00:02:34.371
That's gonna be 2/10,

00:02:34.371 --> 00:02:37.459
and then you divide by 20, is 0.1.

00:02:37.459 --> 00:02:39.038
So, that's another way that
they're just saying that,

00:02:39.038 --> 00:02:40.854
"Hey, each of these is 1/100,"

00:02:40.854 --> 00:02:41.663
but we already saw that.

00:02:41.663 --> 00:02:44.124
2.81, 2.82, 2.83, 2.84,

00:02:44.124 --> 00:02:46.864
2.85, 2.86, 2.87.

00:02:46.864 --> 00:02:48.234
Let's just do another one.

00:02:48.234 --> 00:02:50.887
The hints actually, I think,
keep going after that.

00:02:50.887 --> 00:02:54.480
So (mumbles) I encourage
you to look at the hints.

00:02:54.480 --> 00:02:55.873
See if you can make sense of them

00:02:55.873 --> 00:02:57.986
after you try the exercise.

00:02:57.986 --> 00:03:01.317
So, let's try another one.

00:03:01.317 --> 00:03:03.270
Let's do one more.

00:03:03.270 --> 00:03:06.846
Move the orange dot to
0.27 on the number line.

00:03:06.846 --> 00:03:09.925
Well, this is 0.2, this is 0.3,

00:03:09.925 --> 00:03:12.386
so going from here to here is 1/10,

00:03:12.386 --> 00:03:13.919
and then they've divided that 1/10

00:03:13.919 --> 00:03:16.124
into 10 sections, so each of these

00:03:16.124 --> 00:03:19.212
is 1/10 of 1/10, which is 1/100.

00:03:19.212 --> 00:03:22.254
So, this is 2/10 and 0/100,

00:03:22.254 --> 00:03:26.689
2/10 and 1/100, 2/10 and 2/100,

00:03:26.689 --> 00:03:29.986
2/10 and 3/100, 2/10 and 4/100,

00:03:29.986 --> 00:03:32.819
2/10 and 5/100, 2/10 and 6/100,

00:03:32.819 --> 00:03:34.932
2/10 and 7/100.

00:03:34.932 --> 00:03:36.836
This is 2/10 and 7/100.

00:03:36.836 --> 00:03:40.319
Another way you could view
it is, this is 20/100.

00:03:40.319 --> 00:03:42.571
2/10 is the same thing as 20/100.

00:03:42.571 --> 00:03:45.938
21/100, 22/100, 23/100,

00:03:45.938 --> 00:03:50.507
24/100, 25/100, 26/100,

00:03:50.507 --> 00:03:52.667
27/100.

00:03:52.667 --> 00:03:53.735
All right.

00:03:53.735 --> 00:03:56.121
Check our answer, and
let's just see the hints.

00:03:56.121 --> 00:03:58.165
They say "10 equal pieces."

00:03:58.165 --> 00:03:59.460
They show us that right over here.

00:03:59.460 --> 00:04:00.900
They actually labeled it.

00:04:00.900 --> 00:04:02.989
Anyway, hopefully this helps.

00:04:02.989 --> 00:04:05.924
I encourage you to go try
this exercise out now.


Decimal intuition with grids (examples)

WEBVTT
Kind: captions
Language: en

00:00:00.329 --> 00:00:02.023
- [Voiceover] We're told
that each square below

00:00:02.023 --> 00:00:03.533
represents one whole.

00:00:03.533 --> 00:00:05.622
So this square is a whole,
this is another whole,

00:00:05.622 --> 00:00:07.179
so together that's two.

00:00:07.179 --> 00:00:09.663
And then we have
something less than whole.

00:00:09.663 --> 00:00:13.146
And they say what decimal is
represented by the shaded area?

00:00:13.146 --> 00:00:15.677
So it's going to be
two and then something.

00:00:15.677 --> 00:00:18.626
So it's going to be two point something.

00:00:18.626 --> 00:00:20.042
And let's think about
what we have over here.

00:00:20.042 --> 00:00:21.946
This is one whole, two wholes.

00:00:21.946 --> 00:00:24.059
And then over here, we've taken a whole

00:00:24.059 --> 00:00:26.032
and we've divided it into one, two,

00:00:26.032 --> 00:00:29.330
three, four, five, six, seven, eight,

00:00:29.330 --> 00:00:31.791
nine, ten equal sections.

00:00:31.791 --> 00:00:33.927
So we've divided it into tenths.

00:00:33.927 --> 00:00:36.689
Each of these bars is equal to a tenth

00:00:36.689 --> 00:00:38.571
and we have seven of them shaded in.

00:00:38.571 --> 00:00:40.474
One, two, three, four,

00:00:40.474 --> 00:00:43.029
five, six, seven.

00:00:43.029 --> 00:00:45.699
So this right over here is seven tenths.

00:00:45.699 --> 00:00:47.650
So this is going to be one, two,

00:00:47.650 --> 00:00:49.786
and seven tenths.

00:00:49.786 --> 00:00:52.108
So, if we wanted to
write it as mixed number

00:00:52.108 --> 00:00:54.057
we'd write it as two and seven tenths,

00:00:54.057 --> 00:00:56.026
but they say what decimal is represented

00:00:56.026 --> 00:00:57.418
by the shaded area?

00:00:57.418 --> 00:00:59.671
So instead of writing
two and seven tenths,

00:00:59.671 --> 00:01:02.109
we could write 2.7.

00:01:02.109 --> 00:01:04.384
Because the space immediately to the right

00:01:04.384 --> 00:01:07.216
of the decimal points,
that's the tenths place.

00:01:07.216 --> 00:01:10.538
So we have two ones, two
wholes right over here.

00:01:10.538 --> 00:01:14.322
And then we have seven tenths,
this is the tenths place.

00:01:14.322 --> 00:01:15.623
And we could check out answer.

00:01:15.623 --> 00:01:16.714
We got it right.

00:01:16.714 --> 00:01:18.804
Let's do another one of these.

00:01:18.804 --> 00:01:19.709
So the same thing.

00:01:19.709 --> 00:01:22.008
What decimal is represented
by the shaded area?

00:01:22.008 --> 00:01:23.726
So we have three wholes,

00:01:23.726 --> 00:01:26.489
and then this whole is
divided into tenths,

00:01:26.489 --> 00:01:28.440
now it's divided into these vertical bars.

00:01:28.440 --> 00:01:30.739
We have one, two, three, four,

00:01:30.739 --> 00:01:33.780
five, six, seven, eight, nine, ten

00:01:33.780 --> 00:01:34.709
vertical bars.

00:01:34.709 --> 00:01:36.985
They're equal, so they're
divided into tenths,

00:01:36.985 --> 00:01:38.587
and we've shaded in five of them.

00:01:38.587 --> 00:01:40.652
So this one over here is five tenths.

00:01:40.652 --> 00:01:43.556
So it is three wholes and five tenths.

00:01:43.556 --> 00:01:45.715
So it's going to be three wholes

00:01:45.715 --> 00:01:48.756
and in the tenths place we would put five.

00:01:48.756 --> 00:01:53.075
3.5, three wholes and five tenths.

00:01:53.075 --> 00:01:54.445
We can check our answer.

00:01:54.445 --> 00:01:55.467
Got it right.

00:01:55.467 --> 00:01:57.008
Let's do a few more of these.

00:01:57.989 --> 00:02:01.936
What decimal is being
represented by the shaded area?

00:02:01.936 --> 00:02:03.770
So over here, let's see,

00:02:03.770 --> 00:02:06.139
I have a hundred squares.

00:02:06.139 --> 00:02:09.691
You see I have 10 columns

00:02:09.691 --> 00:02:11.874
and each of them has 10 squares in it,

00:02:11.874 --> 00:02:13.963
so 10 times 10 is 100.

00:02:13.963 --> 00:02:16.262
So I have 100 squares here, equal squares,

00:02:16.262 --> 00:02:18.096
so I've divided it into hundredths,

00:02:18.096 --> 00:02:20.722
and I've shaded in one, two, three, four,

00:02:20.722 --> 00:02:25.134
five, six, seven, eight,
nine of the hundredths.

00:02:25.134 --> 00:02:26.387
Hundredths.

00:02:26.387 --> 00:02:28.152
So how do I represent that?

00:02:28.152 --> 00:02:30.404
So zero, that's the ones place.

00:02:30.404 --> 00:02:32.841
That's the tenths place.

00:02:32.841 --> 00:02:35.025
And now I'm in the hundredths place.

00:02:35.025 --> 00:02:38.787
And so we have nine of
the hundredths shaded in.

00:02:38.787 --> 00:02:42.060
So this right over here
would be nine hundredths,

00:02:42.060 --> 00:02:44.150
which is exactly what we have there.

00:02:44.150 --> 00:02:45.590
Alright, let's do,

00:02:45.590 --> 00:02:47.641
let's do one more of these.

00:02:48.645 --> 00:02:50.642
Alright, well it's the same thing.

00:02:50.642 --> 00:02:53.358
We have two of the hundredths filled in.

00:02:53.358 --> 00:02:54.984
So I'll write zero point,

00:02:54.984 --> 00:02:56.725
if I did that that would be two tenths.

00:02:56.725 --> 00:02:57.793
That's not what we have filled in.

00:02:57.793 --> 00:02:59.535
We have two hundredths.

00:02:59.535 --> 00:03:01.624
Hundredths filled in.

00:03:01.624 --> 00:03:04.756
So this is 0.02 and we're done.


Decimals as words

WEBVTT
Kind: captions
Language: en

00:00:00.562 --> 00:00:02.431
- [Voiceover] Let's say
that I had the number

00:00:02.431 --> 00:00:06.761
zero point one seven.

00:00:06.761 --> 00:00:09.640
How could I say this number?

00:00:09.640 --> 00:00:12.351
I said it one way, I said
zero point one seven,

00:00:12.351 --> 00:00:14.051
but what are other ways
that I could say it,

00:00:14.051 --> 00:00:15.131
especially if I wanted to express it

00:00:15.131 --> 00:00:17.233
in terms of tenths or hundredths

00:00:17.233 --> 00:00:18.707
or other places?

00:00:18.707 --> 00:00:20.786
And like always, try to pause the video

00:00:20.786 --> 00:00:23.165
and try think about it on your own.

00:00:23.165 --> 00:00:25.010
Alright, so there's
actually a couple of ways

00:00:25.010 --> 00:00:28.191
that we could say this number.

00:00:28.191 --> 00:00:30.722
One is just to say zero point one seven.

00:00:30.722 --> 00:00:32.568
Other ways are to say look,

00:00:32.568 --> 00:00:36.329
I have a one in the tenths place,

00:00:36.329 --> 00:00:40.450
so that's going to be one tenth,

00:00:40.450 --> 00:00:43.059
one tenth and

00:00:43.059 --> 00:00:47.838
one tenth and I have a seven
in the hundredths place,

00:00:47.838 --> 00:00:50.659
so this is a seven right over here

00:00:50.659 --> 00:00:52.470
in the hundredths place, so I can say

00:00:52.470 --> 00:00:56.777
one tenth and seven hundredths.

00:00:56.777 --> 00:00:58.158
Hun-

00:00:58.158 --> 00:01:00.352
Hundredths.

00:01:00.352 --> 00:01:01.490
And there you go.

00:01:01.490 --> 00:01:04.148
That's one way to say this number.

00:01:04.148 --> 00:01:05.611
Now another to think about it

00:01:05.611 --> 00:01:09.326
is just say the whole thing
in terms of hundredths.

00:01:09.326 --> 00:01:12.310
So a tenth is how many hundredths?

00:01:12.310 --> 00:01:15.827
Well a tenth is the same
thing as 10 hundredths,

00:01:15.827 --> 00:01:18.022
so you could say, you could say

00:01:18.022 --> 00:01:20.620
instead of a tenth, you could
say this is 10 hundredths,

00:01:20.620 --> 00:01:21.699
and the way I'm writing it right now,

00:01:21.699 --> 00:01:24.242
very few people would
actually do it this way.

00:01:24.242 --> 00:01:27.803
10 hundredths and

00:01:27.803 --> 00:01:30.288
and seven hundredths.

00:01:30.288 --> 00:01:34.660
And seven hundredths.

00:01:34.660 --> 00:01:36.681
Well not I could just
add these hundredths,

00:01:36.681 --> 00:01:38.330
if I have 10 hundredths and I have another

00:01:38.330 --> 00:01:42.195
seven hundredths, that's
going to be 17 hundredths.

00:01:42.195 --> 00:01:44.714
So I could just write this down as

00:01:44.714 --> 00:01:48.034
17 hundredths.

00:01:48.034 --> 00:01:49.427
Hundredths.

00:01:49.427 --> 00:01:50.914
And to make that intuition of how we could

00:01:50.914 --> 00:01:53.130
just call this 17
hundredths instead of just

00:01:53.130 --> 00:01:55.522
calling it one tenth and seven hundredths,

00:01:55.522 --> 00:01:58.076
let's actually count by hundredths.

00:01:58.076 --> 00:02:02.000
So that is one hundredth,

00:02:02.000 --> 00:02:03.660
that is two hundredth,

00:02:03.660 --> 00:02:04.903
and actually, let me just go straight to

00:02:04.903 --> 00:02:07.038
nine hundredths.

00:02:07.038 --> 00:02:09.303
So I skipped a bunch right over here.

00:02:09.303 --> 00:02:10.962
And what would be the
next, how would I say

00:02:10.962 --> 00:02:12.634
10 hundredths?

00:02:12.634 --> 00:02:14.491
Well 10 hundredths, let
me write it this way,

00:02:14.491 --> 00:02:19.262
10 hundredths is the
same thing as one tenth.

00:02:19.262 --> 00:02:21.980
So if we go from nine
hundredths, the next,

00:02:21.980 --> 00:02:24.638
if I'm counting by hundredths,
the next one's going to be

00:02:24.638 --> 00:02:27.017
10 hundredths.

00:02:27.017 --> 00:02:29.769
Now once again, 10
hundredths is the same thing

00:02:29.769 --> 00:02:32.891
as one tenth, just the
same way that 10 ones

00:02:32.891 --> 00:02:35.097
is the same thing as one 10.

00:02:35.097 --> 00:02:36.258
I hope that doesn't confuse you,

00:02:36.258 --> 00:02:37.082
but we could keep counting.

00:02:37.082 --> 00:02:39.973
10 hundredths, 11 hundredths,

00:02:39.973 --> 00:02:43.467
12 hundredths, 13 hundredths,

00:02:43.467 --> 00:02:47.554
14 hundredths, 15 hundredths,

00:02:47.554 --> 00:02:52.244
16 hundredths, and then
finally 17 hundredths.

00:02:52.244 --> 00:02:53.451
So hopefully that gives
you a little intuition

00:02:53.451 --> 00:02:55.169
for why we can call this number,

00:02:55.169 --> 00:02:56.888
instead of just calling
it zero point one seven,

00:02:56.888 --> 00:02:59.232
or one tenth and seven hundredths,

00:02:59.232 --> 00:03:02.670
we could call this 17 hundredths.

00:03:02.670 --> 00:03:04.364
So with that out of the way,
let's do a couple of examples

00:03:04.364 --> 00:03:06.523
going the other way.

00:03:06.523 --> 00:03:10.191
Let's say we're given a name of a number

00:03:10.191 --> 00:03:12.735
or the words, and we wanna
write it down as a decimal.

00:03:12.735 --> 00:03:17.529
So this is four tens and three hundredths.

00:03:17.529 --> 00:03:20.083
Alright, so four tens.

00:03:20.083 --> 00:03:22.578
So the four tens right over here.

00:03:22.578 --> 00:03:24.529
So actually let me just
put some places over here,

00:03:24.529 --> 00:03:27.489
so this would be, if
this is our tens place,

00:03:27.489 --> 00:03:32.064
and then this is our ones place,

00:03:32.064 --> 00:03:33.886
and then you're gonna have your decimal,

00:03:33.886 --> 00:03:37.148
and then you're gonna
have your tenths place,

00:03:37.148 --> 00:03:39.911
tenths place, and then
you're going to have,

00:03:39.911 --> 00:03:41.373
and I'll do this in a different color,

00:03:41.373 --> 00:03:43.405
your hundredths place.

00:03:43.405 --> 00:03:44.902
Hun-

00:03:44.902 --> 00:03:47.109
Hundredths place.

00:03:47.109 --> 00:03:49.733
So we're going to have four tens.

00:03:49.733 --> 00:03:52.564
Not tenths, four tens.

00:03:52.564 --> 00:03:56.048
So four tens, zero ones,

00:03:56.048 --> 00:03:58.009
zero ones, we got our decimal,

00:03:58.009 --> 00:04:00.981
they don't have any tenths
over here so zero tenths,

00:04:00.981 --> 00:04:03.803
and then we have three hundredths.

00:04:03.803 --> 00:04:08.191
Three hundredths, so three hundredths.

00:04:08.191 --> 00:04:11.127
So four tens, which is
the same thing as 40,

00:04:11.127 --> 00:04:12.951
and three hundredths right over here,

00:04:12.951 --> 00:04:16.027
so 40 point zero three.

00:04:16.027 --> 00:04:18.918
Let's do another one of
these, this is kinda fun.

00:04:18.918 --> 00:04:22.075
So we have 24 hundredths.

00:04:22.075 --> 00:04:23.816
24 hundredths.

00:04:23.816 --> 00:04:26.707
So by the logic that we
saw in the first one,

00:04:26.707 --> 00:04:29.226
in the first one, we
could just write this as,

00:04:29.226 --> 00:04:31.176
remember, this would be nine hundredths,

00:04:31.176 --> 00:04:32.825
and if we want one more hundredth,

00:04:32.825 --> 00:04:34.718
this would be 10 hundredths.

00:04:34.718 --> 00:04:36.516
So if we want to do 24 hundredths,

00:04:36.516 --> 00:04:38.919
it would just be zero point two four.

00:04:38.919 --> 00:04:40.858
And if you're saying well wait a minute,

00:04:40.858 --> 00:04:44.236
this looks like two tenths
and four hundredths,

00:04:44.236 --> 00:04:45.467
you'd be right!

00:04:45.467 --> 00:04:49.019
But remember, so actually let
me, I could re-write this as,

00:04:49.019 --> 00:04:53.843
I could re-write this as two tenths,

00:04:54.545 --> 00:04:58.562
two tenths and four hundredths.

00:04:58.562 --> 00:05:00.699
Let me say and

00:05:00.699 --> 00:05:03.265
four hundredths.

00:05:03.265 --> 00:05:05.481
Hundredths.

00:05:05.481 --> 00:05:08.895
But remember, a tenth is
equal to 10 hundredths,

00:05:08.895 --> 00:05:13.527
so two tenths is the same
thing as 20 hundredths.

00:05:13.527 --> 00:05:15.234
Hundredths.

00:05:15.234 --> 00:05:16.393
I have trouble saying-

00:05:16.393 --> 00:05:18.553
So this is the same thing as 20 hundredths

00:05:18.553 --> 00:05:20.875
and four hundredths.

00:05:20.875 --> 00:05:24.682
And four, let me write it neatly.

00:05:24.682 --> 00:05:28.294
Four hundredths.

00:05:28.294 --> 00:05:29.964
And of course 20 hundredths
and four hundredths

00:05:29.964 --> 00:05:32.762
is the same thing as 24 hundredths.

00:05:32.762 --> 00:05:36.193
So hopefully that makes sense.


Decompose hundredths on number line

WEBVTT
Kind: captions
Language: en

00:00:00.063 --> 00:00:02.361
- [Voiceover] So we
have an example exercise

00:00:02.361 --> 00:00:04.183
from our Khan Academy exercises.

00:00:04.183 --> 00:00:05.867
This is the decomposed fractions.

00:00:05.867 --> 00:00:07.725
with denominators of 100.

00:00:07.725 --> 00:00:10.719
Use the following number line
to complete the equation.

00:00:10.719 --> 00:00:13.030
The equation says 26-hundredths

00:00:13.030 --> 00:00:15.478
is equal to star-tenths

00:00:15.478 --> 00:00:17.777
plus six-hundredths.

00:00:17.777 --> 00:00:19.240
And they give us this number line

00:00:19.240 --> 00:00:20.633
and on this number line--

00:00:20.633 --> 00:00:22.491
Let's see, this is zero right over here,

00:00:22.491 --> 00:00:24.558
zero-tenths, which is
the same thing as zero,

00:00:24.558 --> 00:00:27.715
and it goes all the way to 26-hundredths.

00:00:27.715 --> 00:00:29.492
Let's see if that makes sense.

00:00:29.492 --> 00:00:32.139
Well, you see between
zero-tenth and one-tenth,

00:00:32.139 --> 00:00:34.019
they split into 10 equal sections.

00:00:34.019 --> 00:00:36.271
One, two, three, four, five, six,

00:00:36.271 --> 00:00:38.558
seven, eight, nine, 10.

00:00:38.558 --> 00:00:41.670
So if you divide a tenth into tenths,

00:00:41.670 --> 00:00:43.457
each of these is going to be 100.

00:00:43.457 --> 00:00:45.861
A hundredth is one-tenth of a tenth.

00:00:45.861 --> 00:00:48.135
So that's 100, 200, 300, 400,

00:00:48.135 --> 00:00:51.644
five, six, seven, eight,
nine, 10-hundredths,

00:00:52.214 --> 00:00:57.133
11, 12, 13, 14, 15, 16, 17, 18, 19

00:00:57.133 --> 00:00:59.133
20-hundredths.

00:00:59.133 --> 00:01:02.604
21, 22, 23, 24, 25, 26-hundredths.

00:01:02.604 --> 00:01:04.541
So that's exactly what they wrote there.

00:01:04.541 --> 00:01:06.364
So they say 26-hundredths,

00:01:06.364 --> 00:01:07.908
which is this thing right over here,

00:01:07.908 --> 00:01:10.367
is equal to star-tenths,

00:01:10.367 --> 00:01:12.980
which is really what's
being depicted in magenta,

00:01:12.980 --> 00:01:14.466
plus six-hundredths.

00:01:14.466 --> 00:01:16.324
The six-hundredths is this
green right over here.

00:01:16.324 --> 00:01:17.148
Adding the six-hundredths.

00:01:17.148 --> 00:01:21.106
Adding one, two, three,
four, five, six-hundredths.

00:01:21.106 --> 00:01:23.312
So what is this right over here?

00:01:23.312 --> 00:01:26.667
This magenta or this pink arrow?

00:01:26.667 --> 00:01:28.804
Well we could say that's 20-hundredths.

00:01:28.804 --> 00:01:31.462
If you count it that's 10, 20-hundredths.

00:01:31.462 --> 00:01:33.830
Or, you could see, well
that's just two-tenths.

00:01:33.830 --> 00:01:36.823
So 26-hundredths is the same thing

00:01:36.823 --> 00:01:39.679
as two-tenths plus six-hundredths.

00:01:39.679 --> 00:01:41.280
And it gets you right over there.

00:01:41.280 --> 00:01:44.689
So this right over here
is going to be two-tenths.


Decomposing hundredths into tenths and hundredths

WEBVTT
Kind: captions
Language: en

00:00:00.611 --> 00:00:03.251
- So this, this picture right over here,

00:00:03.251 --> 00:00:04.811
we've taken this square,

00:00:04.811 --> 00:00:09.411
we've divided it into 100
equal, smaller squares,

00:00:09.411 --> 00:00:10.432
and then we've colored in,

00:00:10.432 --> 00:00:11.711
let's see how many we've colored in.

00:00:11.711 --> 00:00:13.891
Each of these rows has
10 squares, so this is,

00:00:13.891 --> 00:00:17.251
10, 20, 30, 40,

00:00:17.251 --> 00:00:20.311
41, 42, 43, 44, 45,

00:00:20.311 --> 00:00:22.091
46, 47.

00:00:22.091 --> 00:00:23.652
So over here, we have colored in

00:00:23.652 --> 00:00:27.851
47 out of 100 equal, smaller squares.

00:00:27.851 --> 00:00:29.302
Or you could say that this,

00:00:29.302 --> 00:00:32.044
what's shaded in in blue
and green right over here,

00:00:32.044 --> 00:00:35.324
this represents 47 hundredths.

00:00:35.324 --> 00:00:38.515
This is represents 47
hundredths of the entire,

00:00:38.515 --> 00:00:40.588
of the entire whole.

00:00:40.588 --> 00:00:42.708
Now what I'm curious about is,

00:00:42.708 --> 00:00:44.588
I wanna break up this fraction.

00:00:44.588 --> 00:00:48.748
I wanna write it as 40 over,

00:00:48.748 --> 00:00:49.688
actually lemme write it this way.

00:00:49.688 --> 00:00:53.050
I wanna write it as four over 10,

00:00:53.050 --> 00:00:54.810
plus,

00:00:54.810 --> 00:00:57.630
plus something over 100.

00:00:57.630 --> 00:00:59.030
And I'll just write star.

00:00:59.030 --> 00:01:01.571
Plus star over 100.

00:01:01.571 --> 00:01:03.130
And my question to you is,

00:01:03.130 --> 00:01:06.490
what is the star going to be equal to?

00:01:06.490 --> 00:01:07.990
The star is equal to what?

00:01:07.990 --> 00:01:10.801
And pause the video to
try to figure it out.

00:01:10.801 --> 00:01:14.550
Alright, so let's, let's
work this together.

00:01:14.550 --> 00:01:17.090
So one thing that we
could say immediately,

00:01:17.090 --> 00:01:19.030
is we could say that

00:01:19.030 --> 00:01:22.870
47 over 100

00:01:22.870 --> 00:01:25.280
is equal to 40 hundredths,

00:01:25.280 --> 00:01:27.198
40 hundredths.

00:01:27.198 --> 00:01:30.798
You see that over here,
10, 20, 30, 40 hundredths.

00:01:30.798 --> 00:01:33.718
This is 10, 20,

00:01:33.718 --> 00:01:36.738
30, 40 hundredths,

00:01:36.738 --> 00:01:38.298
plus,

00:01:38.298 --> 00:01:42.678
one, two, three, four,
five, six, seven hundredths.

00:01:42.678 --> 00:01:46.088
Plus seven hundredths.

00:01:46.958 --> 00:01:49.019
Now, 40 hundredths is the

00:01:49.019 --> 00:01:51.949
same thing as four tenths.

00:01:51.949 --> 00:01:55.364
40 hundredths is the same
thing as four tenths.

00:01:55.364 --> 00:01:57.264
There's a bunch of ways
we could think about it.

00:01:57.264 --> 00:01:58.964
One is, you could think about dividing

00:01:58.964 --> 00:02:01.524
this larger, larger square into tenths,

00:02:01.524 --> 00:02:04.064
so this would be a tenth right over here,

00:02:04.064 --> 00:02:05.544
that would be a tenth,

00:02:05.544 --> 00:02:07.004
this would be another tenth,

00:02:07.004 --> 00:02:08.664
that's two tenths.

00:02:08.664 --> 00:02:11.584
This would be three tenths.

00:02:11.584 --> 00:02:12.684
And all I'm doing here, is I'm dividing

00:02:12.684 --> 00:02:15.124
the larger thing into tents,

00:02:15.124 --> 00:02:16.415
into tenths, I should say.

00:02:16.415 --> 00:02:17.975
If I'm taking the larger,

00:02:17.975 --> 00:02:19.375
if I'm taking the larger square,

00:02:19.375 --> 00:02:21.015
instead of dividing it into hundredths,

00:02:21.015 --> 00:02:22.715
I divide it into tenths.

00:02:22.715 --> 00:02:25.295
So this would be four tenths,

00:02:25.295 --> 00:02:26.816
(mumbles) doing five tenths,

00:02:27.746 --> 00:02:29.056
six tenths,

00:02:29.946 --> 00:02:31.286
six tenths,

00:02:31.286 --> 00:02:33.646
seven tenths,

00:02:33.646 --> 00:02:35.606
eight tenths,

00:02:35.606 --> 00:02:36.986
and nine tenths,

00:02:36.986 --> 00:02:38.346
and then 10 tenths.

00:02:38.346 --> 00:02:40.146
Notice, if you look at the orange lines,

00:02:40.146 --> 00:02:42.646
I've divided my square not
into a hundred equal sections,

00:02:42.646 --> 00:02:44.546
but into ten equal sections.

00:02:44.546 --> 00:02:46.486
And so you see, these 40 hundredths

00:02:46.486 --> 00:02:48.126
that are in blue right over there,

00:02:48.126 --> 00:02:50.496
that's the same thing as one tenth,

00:02:51.646 --> 00:02:52.879
two tenths,

00:02:54.199 --> 00:02:55.452
three tenths,

00:02:56.682 --> 00:02:58.943
and four tenths.

00:02:58.943 --> 00:03:02.614
So that is the four
tenths, right over there.

00:03:02.614 --> 00:03:04.285
Another way you could think about it,

00:03:04.285 --> 00:03:05.826
when you go from hundredths to tenths,

00:03:05.826 --> 00:03:09.066
each 10 hundredths, each 10 hundredths,

00:03:09.066 --> 00:03:11.697
is are equal to one tenth.

00:03:11.697 --> 00:03:15.217
So you're dividing both
the denominator by 10,

00:03:15.217 --> 00:03:16.877
when you go from hundredths to tenths.

00:03:16.877 --> 00:03:19.697
And you'd also divide the numerator by 10,

00:03:19.697 --> 00:03:22.397
going from hundredths to tenths.

00:03:22.397 --> 00:03:24.657
So 40 divided by 10 is four,

00:03:24.657 --> 00:03:26.937
100 divided by 10 is 10.

00:03:26.937 --> 00:03:27.917
So hopefully you're convinced that

00:03:27.917 --> 00:03:30.357
40 hundredths is the same
thing as four tenths.

00:03:30.357 --> 00:03:31.797
But what's left over?

00:03:31.797 --> 00:03:34.897
Well, we still have the
seven hundredths over here.

00:03:34.897 --> 00:03:37.178
So 40 hundredths plus seven hundredths

00:03:37.178 --> 00:03:41.877
is the same thing as four
tenths, plus seven hundredths.

00:03:41.877 --> 00:03:43.639
So the star right over here,

00:03:43.639 --> 00:03:45.759
this is going to, let me actually,

00:03:45.759 --> 00:03:47.051
let me erase this.

00:03:47.051 --> 00:03:48.571
The star right over here,

00:03:48.571 --> 00:03:52.011
I could write that as seven hundredths.

00:03:52.011 --> 00:03:53.311
So you see, 47 hundredths,

00:03:53.311 --> 00:03:54.532
which is all the stuff shaded,

00:03:54.532 --> 00:03:56.552
that's the same thing as the four tenths.

00:03:56.552 --> 00:03:58.392
Which is the same thing as 40 hundredths,

00:03:58.392 --> 00:03:59.652
shaded in blue.

00:03:59.652 --> 00:04:01.632
Plus these one, two, three, four,

00:04:01.632 --> 00:04:04.752
five, six, seven
hundredths, right over here.

00:04:04.752 --> 00:04:06.952
47 on 100, or 47 hundredths,

00:04:06.952 --> 00:04:09.412
4 tenths, plus seven hundredths.


Visually converting from tenths to hundredths

WEBVTT
Kind: captions
Language: en

00:00:00.249 --> 00:00:01.851
- [Voiceover] What I hope
to do in this fraction is

00:00:01.851 --> 00:00:04.824
be able to rewrite the fraction 8/10

00:00:04.824 --> 00:00:08.225
as being something over 100.

00:00:08.225 --> 00:00:10.222
So I could put a question mark here.

00:00:10.222 --> 00:00:12.347
I could put a star over here.

00:00:12.347 --> 00:00:14.321
Star over 100.

00:00:14.321 --> 00:00:15.749
And what I care about is figure out

00:00:15.749 --> 00:00:17.595
what is this star equal to.

00:00:17.595 --> 00:00:22.552
Eight over 10 is equal to what over 100?

00:00:22.552 --> 00:00:25.756
And I encourage you to pause
the video to think about it.

00:00:25.756 --> 00:00:27.544
Now to help us work through this

00:00:27.544 --> 00:00:32.420
I have set up a little diagram,
or actually two diagrams

00:00:32.420 --> 00:00:35.323
to think about what 8/10 looks like.

00:00:35.323 --> 00:00:36.914
And then I have the same whole,

00:00:36.914 --> 00:00:38.992
instead of being split into /10,

00:00:38.992 --> 00:00:40.989
I have it split up in /200.

00:00:40.989 --> 00:00:43.485
I have it spit up to 100 equal sections.

00:00:43.485 --> 00:00:44.820
And we just have to figure out

00:00:44.820 --> 00:00:47.154
how many of these 100 equal sections

00:00:47.154 --> 00:00:51.519
are equivalent to the eight
out of the 10 equal sections

00:00:51.519 --> 00:00:53.017
right over here.

00:00:53.017 --> 00:00:55.025
So lets think about that a little bit.

00:00:55.025 --> 00:00:57.556
So once again, we have
10 equal sections here.

00:00:57.556 --> 00:01:00.784
And we have colored in
one, let me mark'em all.

00:01:00.784 --> 00:01:04.139
If we've colored in one, two, three, four,

00:01:04.139 --> 00:01:07.390
five, six, seven, eight of them.

00:01:07.390 --> 00:01:11.685
This diagram, this
picture, represents 8/10.

00:01:11.685 --> 00:01:14.356
10 equal sections I have
colored in eight of them.

00:01:14.356 --> 00:01:17.601
Now how do I do that if
I'm talking about /100.

00:01:17.601 --> 00:01:20.056
Well it's the same whole right over here.

00:01:20.056 --> 00:01:23.652
Now if I want to fill up the
same amount of that whole,

00:01:23.652 --> 00:01:26.533
so let me get a little paint brush here.

00:01:26.953 --> 00:01:31.229
So it would the the equivalent of 1/10

00:01:31.229 --> 00:01:33.709
would be filling in 10/100.

00:01:33.709 --> 00:01:35.823
So that's 10/100 right over there.

00:01:35.823 --> 00:01:38.516
Then 2/10 or that second /10,

00:01:38.516 --> 00:01:40.606
every time I fill in a
/10, that's the same thing

00:01:40.606 --> 00:01:43.218
as filling in 10/100.

00:01:43.218 --> 00:01:45.726
Let me write that down,
cause that's interesting.

00:01:45.726 --> 00:01:48.222
So we see here that 1/10

00:01:48.222 --> 00:01:51.949
is equal to 10 over 100.

00:01:51.949 --> 00:01:53.621
Every time I fill in a /10,

00:01:56.141 --> 00:01:57.823
that's 1/10 right over there.

00:01:57.823 --> 00:01:58.984
If you look at this diagram,

00:01:58.984 --> 00:02:01.817
that's the equivalent to 10/100.

00:02:01.817 --> 00:02:05.451
It's equivalent to 10 of
those 100 equal sections.

00:02:05.451 --> 00:02:08.528
So if I wanna fill out 8/10,

00:02:08.528 --> 00:02:12.487
that's gonna be eight
time 10/100 or 80/100.

00:02:12.487 --> 00:02:14.252
And lets just see that right over here.

00:02:14.252 --> 00:02:17.920
So we already did 10/100, 20/100.

00:02:19.780 --> 00:02:22.158
This is gonna be 30/100.

00:02:22.158 --> 00:02:24.387
40/100.

00:02:24.387 --> 00:02:26.883
50/100.

00:02:26.883 --> 00:02:28.990
60/100.

00:02:29.970 --> 00:02:31.817
70/100.

00:02:32.137 --> 00:02:33.687
And 80/100.

00:02:33.687 --> 00:02:36.090
Notice I've filled in the same amount,

00:02:36.090 --> 00:02:38.284
and I can fill it in just to
make it a little bit clearer.

00:02:38.284 --> 00:02:40.583
But I filled in the same amount

00:02:40.583 --> 00:02:43.346
of both of these equal wholes.

00:02:43.346 --> 00:02:46.748
But over here, how many of
these squares have I filled in?

00:02:46.748 --> 00:02:50.823
I have filled in 80, now
let me get my pen going.

00:02:50.823 --> 00:02:54.585
I have over here, I have filled in 80

00:02:54.585 --> 00:02:57.174
out of my 100 squares.

00:02:57.174 --> 00:02:59.287
While over here, I filled in eight

00:02:59.287 --> 00:03:02.304
out of my 10 equal rectangles.

00:03:02.874 --> 00:03:04.453
But they're the same amount of area.

00:03:04.453 --> 00:03:06.694
They're the same fraction of the whole.

00:03:06.694 --> 00:03:09.492
So eight over 10 is going
to be the same thing

00:03:09.492 --> 00:03:13.521
as 80 over 100. You see
it's the exact same thing.

00:03:13.521 --> 00:03:15.784
We've just divided the
one on the right here

00:03:15.784 --> 00:03:18.315
into 10 times as many sections.

00:03:18.315 --> 00:03:20.417
And you can even see it mathematically.

00:03:20.417 --> 00:03:23.726
Then look, if we divided into
10 times as many sections.

00:03:23.726 --> 00:03:26.593
So, if we multiply a denominator by 10

00:03:26.593 --> 00:03:28.254
to go from 10 to 100.

00:03:28.254 --> 00:03:31.121
Well that means that each of
this eight sections in this one

00:03:31.121 --> 00:03:34.488
are going to represent 10
times as many in this one.

00:03:34.488 --> 00:03:36.915
So we would say, well,
eight is going to represent

00:03:36.915 --> 00:03:40.177
10 times as many of the /100.

00:03:40.177 --> 00:03:42.116
So eight times 10 is 80.

00:03:42.116 --> 00:03:44.391
10 times 10 is 100.

00:03:44.391 --> 00:03:47.120
8/10 is the same thing as 80/100.

00:03:47.120 --> 00:03:50.949
And in general, if you're
trying to rewrite a fraction

00:03:50.949 --> 00:03:53.087
and not change its value,

00:03:53.087 --> 00:03:54.748
so you want an equivalent fraction,

00:03:54.748 --> 00:03:57.325
as long as you multiply the denominator,

00:03:57.325 --> 00:03:59.217
as long as you multiply the numerator

00:03:59.217 --> 00:04:01.748
and the denominator by the same thing,

00:04:01.748 --> 00:04:05.092
you will not be changing
the value of the fraction.

00:04:05.092 --> 00:04:07.739
It's also true if you divide the numerator

00:04:07.739 --> 00:04:09.388
and the denominator by the same thing.

00:04:09.388 --> 00:04:12.546
You also will not be changing
the value of the fraction.

00:04:12.546 --> 00:04:14.693
In this case we have
multiply both the numerator

00:04:14.693 --> 00:04:16.551
and the denominator by 10.

00:04:16.551 --> 00:04:18.566
And you see why we did it.


Whole number and fraction multiplication concept

WEBVTT
Kind: captions
Language: en

00:00:00.940 --> 00:00:07.360
So we have here, it says 2 times
4/3 is equal to 8 times blank.

00:00:07.360 --> 00:00:10.090
And what I encourage you to do
is pause the video right now

00:00:10.090 --> 00:00:13.940
and try to think about what
should go in this blank.

00:00:13.940 --> 00:00:16.360
So I'm assuming
you've given your try.

00:00:16.360 --> 00:00:18.180
Now, let's think through this.

00:00:18.180 --> 00:00:23.300
So 2 times 4/3, we can literally
view that as the same thing

00:00:23.300 --> 00:00:31.410
as-- if we rewrite the 4/3, this
is the same thing as 2 times--

00:00:31.410 --> 00:00:33.060
instead of writing
4/3 like this,

00:00:33.060 --> 00:00:36.440
I'm literally going to
write it as four 1/3's.

00:00:36.440 --> 00:00:39.180
And I know it sounds like I just
said the same thing over again.

00:00:39.180 --> 00:00:43.820
But I'm literally going to write
1/3 four times-- 1/3 plus 1/3

00:00:43.820 --> 00:00:47.730
plus 1/3 plus 1/3.

00:00:47.730 --> 00:00:50.270
If you call each of
these 1/3, you literally

00:00:50.270 --> 00:00:51.260
have four of them.

00:00:51.260 --> 00:00:52.700
This is four 1/3's.

00:00:52.700 --> 00:00:59.090
2 times 4/3 is the same thing as
2 times, literally, four 1/3's.

00:00:59.090 --> 00:01:00.710
Now, what would this be?

00:01:00.710 --> 00:01:06.810
Well, this is going to be equal
to-- let me just copy and paste

00:01:06.810 --> 00:01:10.460
this-- is going to
be this two times.

00:01:10.460 --> 00:01:12.920
So copy, and then
let me paste it.

00:01:12.920 --> 00:01:16.470
So that's one group of
those 1/3's, of those four

00:01:16.470 --> 00:01:21.000
1/3's, or one group of
one of these four 1/3's.

00:01:21.000 --> 00:01:23.055
And then, we'll
have another one.

00:01:23.055 --> 00:01:24.430
And then, we'll
have another one.

00:01:24.430 --> 00:01:25.971
And we're going to
add them together.

00:01:25.971 --> 00:01:29.090
That's literally 2 times 4/3.

00:01:29.090 --> 00:01:31.010
So let's add these together.

00:01:31.010 --> 00:01:32.220
Now what do we have?

00:01:32.220 --> 00:01:33.812
Well, we have a bunch of 1/3's.

00:01:33.812 --> 00:01:35.020
And we need to count them up.

00:01:35.020 --> 00:01:40.540
We have one, two, three, four,
five, six , seven, eight 1/3's.

00:01:40.540 --> 00:01:42.110
This is literally
equal to-- and we

00:01:42.110 --> 00:01:44.210
could, just to make it
clear what I've just done,

00:01:44.210 --> 00:01:47.490
we could ignore the
parentheses and just add up

00:01:47.490 --> 00:01:49.059
all of these things together.

00:01:49.059 --> 00:01:50.850
So that might make it
a little bit clearer.

00:01:50.850 --> 00:01:54.190
So let me do that just to
make it clear that I literally

00:01:54.190 --> 00:01:57.540
take-- I've taken eight 1/3's
and I'm adding them together,

00:01:57.540 --> 00:02:00.150
which is the exact
same thing as 8/3.

00:02:00.150 --> 00:02:06.590
So let me clear that, and let me
clear that, let me clear that.

00:02:06.590 --> 00:02:09.710
And so this is literally, or
this is clearly, or hopefully

00:02:09.710 --> 00:02:16.080
clearly, equal to 8 times 1/3.

00:02:16.080 --> 00:02:18.860
I have 8 1/3's there.

00:02:18.860 --> 00:02:20.560
So going back to the
original question,

00:02:20.560 --> 00:02:21.476
what is this equal to?

00:02:21.476 --> 00:02:25.810
2 times 4/3 is the same
thing as 8 times 1/3.

00:02:25.810 --> 00:02:29.210
And we've already seen
that 8 times 1/3, well,

00:02:29.210 --> 00:02:31.240
that's literally 8/3.

00:02:31.240 --> 00:02:36.325
So we could also write
it like this-- 8 over 3.

00:02:36.325 --> 00:02:42.874
Let me do that 3 in that
other color-- 8 over 3.


Conceptual understanding of multiplying fractions and whole numbers

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Kind: captions
Language: en

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We've already seen that the
fraction 2/5, or fractions

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like the fraction 2/5, can
be literally represented

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as 2 times 1/5, which
is the same thing, which

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is equal to literally
having two 1/5s.

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So 1/5 plus 1/5.

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And if we wanted
to visualize it,

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let me make a hole
here and divide it

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into five equal sections.

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And so this represents
two of those fifths.

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This is the first of the
fifths, and then this

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is the second of the fifths,
Literally 2/5, 2/5, 2/5.

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Now let's think about something
a little bit more interesting.

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What would 3 times
2/5 represent?

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3 times 2/5.

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And I encourage you
to pause this video

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and, based on what
we just did here,

00:00:57.079 --> 00:01:01.260
think about what you think
this would be equivalent to.

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Well, we just saw that 2/5
would be the same thing

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as-- so let me just
rewrite this as instead

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of 3 times 2/5
written like this,

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let me write 2/5
like that-- so this

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is the same thing as
3 times 2 times 1/5.

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And multiplication, we can
multiply the 2 times the 1/5

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first and then
multiply by the 3,

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or we can multiply the 3
times the 2 first and then

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multiply by the 1/5.

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So you could view this literally
as being equal to 3 times 2

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is, of course, 6, so this is
the same thing as 6 times 1/5.

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And if we were to try
to visualize that again,

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so that's a whole.

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That's another whole.

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Each of those wholes
have been divided

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into five equal sections.

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And so we're going to
color in six of them.

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So that's the first 1/5, second
1/5, third 1/5, fourth 1/5,

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fifth 1/5-- and that
gets us to a whole--

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and then we have
6/5 just like that.

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So literally 3 times 2/5
can be viewed as 6/5.

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And of course, 6
times 1/5, or 6/5,

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can be written as--
so this is equal to,

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literally-- let me do the
same color-- 6/5, 6 over 5.

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Now you might have said, well,
what if we, instead of viewing

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2/5 as this, as we just
did in this example,

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we view 2/5 as 1/5 plus
1/5, what would happen then?

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Well, let's try it out.

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So 3 times 2/5-- I'll rewrite
it-- 3 times 2/5, 2 over 5,

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is the same thing as
3 times 1/5 plus 1/5.

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2/5 is the same thing
as 1/5 plus 1/5.

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So 3 times 1/5 plus
1/5 which would

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be equal to-- well, I just
have to have literally

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three of these added together.

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So it's going to be
1/5 plus 1/5 plus 1/5

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plus 1/5 plus-- I think
you get the idea here--

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plus 1/5 plus 1/5.

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Well, what's this going to be?

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Well, we literally
have 6/5 here.

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We can ignore the parentheses
and just add all of these

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together.

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We, once again, have
1, 2, 3, 4, 5, 6/5.

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So once again, this
is equal to 6/5.

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So hopefully this
shows that when

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you multiply-- The 2/5 we saw
already represents two 1/5s.

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We already saw that,
or 2 times 1/5.

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And 3 times 2/5 is literally
the same thing as 3 times

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2 times 1/5.

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In this case, that would be 6/5.