Components of GDP

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Language: en

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What I want to do in this video
is take an expenditure view

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of GDP, so that we can think
about how GDP can be accounted

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for, how it can be
measured, and how

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we can see how active the
different parts of an economy

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actually are.

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So GDP, market value of all
final goods and services

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produced, not just
changed hands,

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produced within a country
in a given period.

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And the symbol we use for
GDP, and I don't know why,

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but the symbol is Y. Y is GDP.

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And so let's think about it from
an expenditure point of view,

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to think about what
are all the pieces.

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Well, if we're thinking
about expenditure,

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who are all of the players
that might have spent money

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on the goods and services,
on final goods and services,

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produced in our country?

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Who are all the people
that might have done it?

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Well, you could have your firms.

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The firms might have spent money
on these goods and services

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produced in a country.

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You also have your households.

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They obviously could've
spent some money

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on goods and services
produced in this country.

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Then you also have
in most countries,

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in fact in all countries,
you have the government.

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The government could have
spent some of the money

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on the goods and services
produced in this country.

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And if we assume that we're
trading with other countries,

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there are other countries
that might have spent money

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on goods and services.

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Other, outside, so let's
just write foreign.

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People outside of the country
might have spent money

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on goods and services,
so foreign purchases.

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And another way to
think about this

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would have been this is exports.

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Our country is exporting it to
people outside of the country

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and they are purchasing it.

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Now, this is almost complete.

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But if we looked
at all of the money

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that firms are spending and all
the money that households are

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spending and all the money
that governments are spending,

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some of what they're
spending might not

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be on goods and services that
are produced in this country.

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They might be spending
some of their stuff

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on things that are produced
outside of this country.

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So we would have
to subtract it out

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if we really want to have the
goods and services produced

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within the country.

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So what we're
going to want to do

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is subtract out
foreign products.

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Or another way, the more typical
way of thinking about it,

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we would subtract out imports.

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So if we think about all of
the goods and services that

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meet this classification,
the final goods and services

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produced in a country
in a given time,

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that firms spent
money on, and add that

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to all the goods and services
that households spent money on,

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and add that to all the goods
and services that government

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spent on, and all the goods and
services that were purchased

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by foreigners, the
exports, and then

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make sure we're not counting
the goods and services

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that other countries produce--
so we subtract those out-- this

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would give you a
pretty good measure

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of all of the goods and services
produced within a country.

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And this is pretty close to
the way the economists actually

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do measure it.

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So what they do is they say
Y is equal to investment.

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And we saw in a previous
video, investment

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in the macroeconomics
term isn't quite

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what it means in
the everyday term.

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It really essentially means
the spending by firms.

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So pretty much everything
that a firm spends in theory,

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you're spending that money to
make future goods and services,

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or to make the
goods and services--

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so that's all
considered investment.

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And then a little bit of
the household spending

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is considered investment.

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And that is just new houses.

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But the bulk of
household spending

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is considered to be consumption.

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And then everything that
the government spends on,

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whether it's the military and
all the salaries for police

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people and whatever
they do, you know,

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the groundskeeping
at the White House,

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whatever else, if we
thinking about the US, that

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goes straight to G,
government spending.

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And this thing
right over here, you

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have foreign purchases,
exports, minus foreign imports.

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So you have exports
minus imports.

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So you could view
this as net exports.

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If this number is positive,
the net exports are positive.

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We're exporting more
than we're importing.

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If this number is negative,
net exports is negative.

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That means we are importing
more than we are exporting.

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But in traditional
expenditure view of GDP,

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this whole part
right over here will

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be referred to as net exports.

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And so you sum up these things,
which are very closely related

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to maybe the slightly
more intuitive versions

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that we started off
with, and you essentially

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have broken down the
expenditure view of GDP

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in the traditional sense.

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Then in the next few
videos, I'm going

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to start thinking of a
bunch of different examples.

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And we'll think about which
bucket it would fall into

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or how it would affect
one of these buckets.


Income and expenditure views of GDP

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Language: en

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You'll hear people talking about different ways of looking at GDP and in general they will talk about the expenditure view of GDP.

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The expenditure view of GDP vs. the income view of GDP and to realize why these get you to the same number for GDP

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But why you're kind of conceptually looking at 2 different things, we're gonna revisit a very very simple economy- maybe slightly more complicated than that one island economy.

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So in this economy, we have some households, and that's why it's slightly more complicated, because I am talking about households, not just one house on an island.

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You have some households and you have some firms. And for the sake of simplicity, we're going to assume that households own all the factors of production.

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And they essentially rent them out to firms to produce all the goods and services. The firms, and this is another assumption, produce all the goods and services.

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These are two very strong assumptions and these really are not true in the real world. This just helps me draw the diagram.

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Obviously in the real world, households do not own all the factors of production.

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Many, if not most of the factors of production the factories and the ships and whatever else are actually owned by firms in the real world

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but this is not that crazy an assumption because those firms, at the end of the day are owned by people, they are owned by households.

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So in theory, that they could have been transferred to the households and then the households just rent the factors of production to the firms.

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And this is also a hugely simplifying assumption because we know that in the real world, we know that firms don't produce all the goods and services, households also produce goods and services,

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some of which, never get measured. The service for me taking the trash out at night, or doing the lawn, or making dinner

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or the service of parents taking care of their children. None of that gets accounted for.

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But for this, just for simplicity, we're going to make these two assumptions. All the factors of production and the system. The labor, the land, the capital, and if we wanna throw it in, the entrepreneurship, it's all loaned by households

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and all goods and services are produced by firms.

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So just like we saw with that first example of the island, the households do all of the expenditures, and these ends up being all of the revenue for the firms.

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And then the firms spend a lot take that revenue and then spend it to rent many of these factors of production or some or all of these factors of production

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so they hire the people, which is essentially they're renting labor, they might rent the land, they might rent the capital, so all of that ends up becoming income for the households.

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And whatever else is left over, so this is expenses. So if we take this revenue, what it turns into is expenses and profit. Whatever's leftover after expenses is profit.

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We're assuming all the firms are also owned by all the households so the expenses plus the profit end up all going to the households and becoming income, which then becomes expenditures for the households, which then become revenue for the firms.

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So when people say the expenditure vs. the income view of GDP, they're saying "look, I can measure GDP at any one of these points." I could measure the expenditures at a time period by households, in this very simple model which would be the same as the revenue of firms

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in this very simple model, which is the same as expenses plus profit of the firms in this simple model, which is same as the income of the household.

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and so, the expenditure view of GDP would be looking in this very simple model, you see, it gets very complicated very fast, especially when we start thinking about expenditures, not just coming from households, but this is simplifying,

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hugely simplified model to show you that these are the same thing, and say "hey, look at GDP at this point, maybe at that point".

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If you wanna look at the income model, you can look at GDP at that point.

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What we'll see as we go into future videos, as we break things between consumption and investment and government spending and net exports,

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that it isn't quite this simple to diagram out, but when we do think about that, we are thinking when we are thinking about consumption and investment and government,

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we are thinking about it from the expenditure point of view. There's another way of thinking about it, where you could have looked at the aggregate income in that country's point of view

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making some adjustments for things like exports and imports and things like that.

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But hopefully at least this clarifies why these come up with the same number from what you can see in this very simple model

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and that there are two slightly different lenses on the same thing.


Investment and consumption

WEBVTT
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Language: en

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What I want to do in this
video is compare investment

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to consumption.

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And we're going to think
about it in two contexts.

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One I would call the everyday
conventional context.

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And then the other
one would be how

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we would think about it
in an economics context.

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Because these words
mean something

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very particular to an economist.

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And that's important that it
means something particular,

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because we're going
to start using

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these words, or
this terminology,

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or these classifications,
to understand

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where GDP is coming from.

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So in everyday-- let me
draw a line over here.

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This is going to be
everyday or, conversational,

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versions of this term.

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And down here, we'll
put the economics,

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the economic versions
of this term,

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especially when we think of it
in the context of accounting

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for GDP.

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And they're not necessarily
all that different.

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But they are different
in important ways.

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So in investment,
really in both cases,

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you can generally
view it as something

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that you do to get
some future gain.

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So for example, if I today build
a house-- so I build a house.

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So that is the house.

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I built it today.

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And this will be the timeline.

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The house will keep lasting.

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And it's an investment,
because it's

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going to be giving
me future gain.

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A year from now, I'll still
be able to live in that house.

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So I will have the saved rent.

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That's a future gain, a future
gain two years from now.

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It'll keep giving
some type of gain.

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You could have a financial
instrument, maybe

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some type of debt instrument.

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You're lending money
to someone else.

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So maybe you buy a bond,
which is essentially you

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lending money to someone else.

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That is an investment in
the everyday sense of it.

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Because when have that asset,
when you've bought that asset,

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it's going to pay off
something in the future.

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It's going to pay off some
interest or some profits.

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And in the everyday sense,
I would consider something

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like-- hopefully
it would be-- going

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to college would
be an investment.

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So education, I'll
say education,

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because you invest that time
and energy and education, it's

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going to keep paying off.

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Hopefully by doing
that, you're going

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to get better employment
and higher wages

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the rest of your life.

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It will keep paying off.

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So this is the everyday
notion of investment.

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The everyday notion
of consumption,

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the way I think about it,
is you are buying something

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or you're doing something
that you're just

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going to use up
in the short-term.

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And just by using it up,
whatever that object is,

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if you just use it up-- and it's
just going to hopefully benefit

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you in some way, but it's
more of a short-term thing--

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I would consider
that consumption

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in the everyday sense.

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So if you go buy a
candy bar and eat it,

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you have consumed the candy bar.

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You have not made an investment.

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If you go to a movie,
that is consumption.

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And I'm not making
any value judgment

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that one is better
than the other.

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Investment, at the
end of the day,

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you're investing so that you
can get future benefit that

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could lead to consumption.

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Because at the end of
the day, consumption

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is one of the things that might
make your life a little bit

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better off.

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So I'm not saying that one
is better than the other.

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But watching a movie, that
would also be consumption.

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Spending time buying
a book, well, you

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could debate whether
that's education or not.

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But let's say you buy a book
that is not educational,

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that is consumption.

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But it is making you happier.

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Hopefully, it's making your
life better in some way.

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Now, the economic
definitions are

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related to these
everyday definitions,

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but they're a little
bit more precise.

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And they make the
definitions in a way

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that they're easier to account
for if you are a nation.

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They're easier to keep track of.

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So the way an economist
would define it,

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they would define
economic investment

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as spending on
capital equipment.

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Capital equipment are things
like, if you are a factory,

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you will buy the equipment
to run your factory.

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You buy the robots.

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And you buy the assembly line.

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And you buy the wheelbarrows
or whatever else,

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the things that have
to cart things around.

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That is capital equipment.

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It would be things
like inventory.

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So for example, the
inventory-- and this

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is still not so different.

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Both of these things
are being used

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to produce things in the future,
to produce future benefit.

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You're buying that inventory,
sometimes raw material,

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you're going to add value to it.

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And then they're
going to be used

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to produce something
in the future.

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It includes things like even
the structures, the buildings.

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And so for all of this, in
the economic sense, and this

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is why it's easier to account
for, this, for the most part,

00:04:30.880 --> 00:04:32.870
is being done by the firms.

00:04:32.870 --> 00:04:37.810
And it also includes the one
thing that households do,

00:04:37.810 --> 00:04:40.550
which is construction
of new homes.

00:04:44.330 --> 00:04:45.855
This is from the households.

00:04:48.570 --> 00:04:50.720
Actually, the buying
of a house does not

00:04:50.720 --> 00:04:52.440
show up in consumption
or investment,

00:04:52.440 --> 00:04:54.000
because nothing
new was produced.

00:04:54.000 --> 00:04:55.774
Something just exchanged hands.

00:04:55.774 --> 00:04:57.690
So whenever we talk about
any of these things,

00:04:57.690 --> 00:04:59.273
especially when we're
talking about it

00:04:59.273 --> 00:05:01.410
in precise economic
terms, it's the production

00:05:01.410 --> 00:05:04.520
of new capital equipment, new
inventory, new structures,

00:05:04.520 --> 00:05:05.440
new homes.

00:05:05.440 --> 00:05:07.740
If I just buy a factory
from someone else,

00:05:07.740 --> 00:05:09.150
that does not add to GDP.

00:05:09.150 --> 00:05:11.757
It would not be considered
investment or consumption,

00:05:11.757 --> 00:05:13.340
because I'm just
transferring an asset

00:05:13.340 --> 00:05:14.600
from one person to another.

00:05:14.600 --> 00:05:18.050
It would only be added to
GDP when it is first created.

00:05:18.050 --> 00:05:20.620
And on the consumption
side, from an economic point

00:05:20.620 --> 00:05:23.320
of view-- let me draw a little
bit of a line right over here--

00:05:23.320 --> 00:05:32.690
consumption is considered to
be any spending on final goods

00:05:32.690 --> 00:05:38.575
by households except
for new homes.

00:05:43.754 --> 00:05:45.170
And let me make
this even clearer.

00:05:45.170 --> 00:05:47.295
Because remember, if we're
just transferring goods,

00:05:47.295 --> 00:05:48.770
that shouldn't count.

00:05:48.770 --> 00:05:53.700
So let me put it on newly
produced final goods.

00:05:53.700 --> 00:05:55.850
Now, what's unintuitive
a little bit over here

00:05:55.850 --> 00:06:00.010
is, according to the way we
account for GDP, the tuition

00:06:00.010 --> 00:06:01.620
that you spend on a
college education,

00:06:01.620 --> 00:06:04.210
that is new spending
on final goods.

00:06:04.210 --> 00:06:07.310
And here are the final
goods or services.

00:06:07.310 --> 00:06:09.290
The service you're
getting is your education.

00:06:09.290 --> 00:06:11.070
That would be consumption.

00:06:11.070 --> 00:06:13.670
So education would fall
here in the economic sense.

00:06:13.670 --> 00:06:16.590
While in the every day sense, I
would consider education right

00:06:16.590 --> 00:06:17.720
over here.

00:06:17.720 --> 00:06:18.930
Maybe you are buying a car.

00:06:18.930 --> 00:06:20.971
And you're not buying a
car for leisure purposes.

00:06:20.971 --> 00:06:25.612
You're buying a car because you
need your car to go to work.

00:06:25.612 --> 00:06:27.070
There's an argument
that that would

00:06:27.070 --> 00:06:29.620
be an investment in
the everyday sense.

00:06:29.620 --> 00:06:32.390
By having that car,
you have something

00:06:32.390 --> 00:06:34.186
that can take you
to work every day.

00:06:34.186 --> 00:06:35.560
So you're getting
future benefit.

00:06:35.560 --> 00:06:36.970
So there's an argument
that maybe that's

00:06:36.970 --> 00:06:38.640
an investment in
the everyday sense.

00:06:38.640 --> 00:06:43.110
But in the accounting sense,
that car would sit right here.

00:06:43.110 --> 00:06:44.170
You bought a new car.

00:06:44.170 --> 00:06:45.880
But that is considered
consumption.

00:06:45.880 --> 00:06:49.830
You did not buy a new house.

00:06:49.830 --> 00:06:53.180
And the whole reason, at
least as far as I understand,

00:06:53.180 --> 00:06:55.910
why it's set up this way is this
is this easier to account for.

00:06:55.910 --> 00:06:57.860
You look at all of
the spending by firms,

00:06:57.860 --> 00:06:59.000
that's easy to account for.

00:06:59.000 --> 00:07:00.370
You essentially call
that investment.

00:07:00.370 --> 00:07:02.440
Because at the end of
the day, all the spending

00:07:02.440 --> 00:07:04.830
that firms are making
is they're doing

00:07:04.830 --> 00:07:07.070
it to produce some
good or service.

00:07:07.070 --> 00:07:10.070
So we call this investment any
spending that the firms do.

00:07:10.070 --> 00:07:13.190
And on top of that, when
households purchase new homes,

00:07:13.190 --> 00:07:14.850
we also call that investment.

00:07:14.850 --> 00:07:18.000
And that's just easier
for the accounting offices

00:07:18.000 --> 00:07:19.490
of governments to keep track of.

00:07:19.490 --> 00:07:21.370
And everything else
that households do,

00:07:21.370 --> 00:07:23.020
we consider consumption.

00:07:23.020 --> 00:07:24.700
And we'll see in
the next few videos,

00:07:24.700 --> 00:07:26.408
there are a few other
categories in terms

00:07:26.408 --> 00:07:27.830
of things that
the government do.

00:07:27.830 --> 00:07:31.250
And then we'll have to think
about imports and exports.


Fraction to decimal example

WEBVTT
Kind: captions
Language: en

00:00:00.530 --> 00:00:04.090
Let's see if we can write
the fraction 11 over 25,

00:00:04.090 --> 00:00:06.450
or we could call
11/25, to see if we

00:00:06.450 --> 00:00:08.000
can write that as a decimal.

00:00:08.000 --> 00:00:11.200
And we're going to round it to
the nearest thousandths place.

00:00:11.200 --> 00:00:13.780
And so another way of
viewing this is 11 over 25,

00:00:13.780 --> 00:00:16.740
this is the same thing
as 11 divided by 25.

00:00:16.740 --> 00:00:22.520
So we can literally divide 25
into 11, and whatever we get,

00:00:22.520 --> 00:00:26.100
that is going to be the decimal
representation of 11/25.

00:00:26.100 --> 00:00:30.518
And since we're going
to go into the places

00:00:30.518 --> 00:00:32.059
less than the ones
place, we're going

00:00:32.059 --> 00:00:34.170
to go into the tenths
place, the hundredths place,

00:00:34.170 --> 00:00:37.570
and the thousandths place,
let's add some zeroes to this 11

00:00:37.570 --> 00:00:39.700
right over here
after the decimal,

00:00:39.700 --> 00:00:41.750
and now let's start to divide.

00:00:41.750 --> 00:00:43.723
25 doesn't go into 1.

00:00:43.723 --> 00:00:45.880
25 doesn't go into 11.

00:00:45.880 --> 00:00:49.490
25 does go into 110.

00:00:49.490 --> 00:00:52.950
So 25 goes into 110 four times.

00:00:52.950 --> 00:00:54.850
4 times 25 is 100.

00:00:54.850 --> 00:00:57.010
So it goes into it four times.

00:00:57.010 --> 00:00:58.430
Let's keep the decimal up here.

00:00:58.430 --> 00:01:00.231
So we'll write 0.4.

00:01:00.231 --> 00:01:03.910
4 times 25 is 100.

00:01:03.910 --> 00:01:08.890
And now we can subtract
110 minus 100 is 10.

00:01:08.890 --> 00:01:11.870
And now we can bring
down another 0.

00:01:11.870 --> 00:01:16.550
25 goes into 100
exactly four times.

00:01:16.550 --> 00:01:22.607
4 times 25 is 100, and then
you subtract, and you get 0.

00:01:22.607 --> 00:01:24.690
So we actually didn't even
have to round this one.

00:01:24.690 --> 00:01:29.600
This fraction is exactly 0.44.


Converting decimals to fractions example 3

WEBVTT
Kind: captions
Language: en

00:00:00.540 --> 00:00:08.002
Let's see if we can
write 0.36 as a fraction.

00:00:08.002 --> 00:00:09.460
There are several
ways of doing it.

00:00:09.460 --> 00:00:13.380
The way I like to do it
is to say, well, 0.36,

00:00:13.380 --> 00:00:16.300
this is the same thing
as 36 hundredths.

00:00:16.300 --> 00:00:18.230
Or one way to think
about it is this

00:00:18.230 --> 00:00:19.515
is in the hundredths place.

00:00:23.480 --> 00:00:26.110
This is in the
tens place, or you

00:00:26.110 --> 00:00:27.660
could view this
as 30 hundredths.

00:00:27.660 --> 00:00:30.480
You could view this as 3
tens, or 30 hundredths.

00:00:30.480 --> 00:00:33.670
So we could say that this is
the same thing as 36 hundredths,

00:00:33.670 --> 00:00:37.985
or this is equal to 36/100.

00:00:37.985 --> 00:00:40.589
And we've already
expressed it as a fraction,

00:00:40.589 --> 00:00:42.130
but now we could
actually simplify it

00:00:42.130 --> 00:00:46.350
because both 36 and 100
have some common factors.

00:00:46.350 --> 00:00:48.380
They're both divisible
by, well, looks

00:00:48.380 --> 00:00:50.202
like they're both
divisible by 4.

00:00:50.202 --> 00:00:51.660
So if we could
divide the numerator

00:00:51.660 --> 00:00:55.122
by 4 and the
denominator by 4, we're

00:00:55.122 --> 00:00:56.330
doing the same thing to both.

00:00:56.330 --> 00:00:58.490
So we're not changing the
value of the fraction.

00:00:58.490 --> 00:01:04.459
36 divided by 4 is 9, and
then 100 divided by 4 is 25.

00:01:04.459 --> 00:01:06.010
And now these two
characters don't

00:01:06.010 --> 00:01:08.040
seem to share any
other common factors.

00:01:08.040 --> 00:01:11.920
And so we've written
it in simplified form,

00:01:11.920 --> 00:01:13.780
and we're done.


Converting decimals to fractions example 1

WEBVTT
Kind: captions
Language: en

00:00:00.499 --> 00:00:06.040
Let's see if we can
write 0.15 as a fraction.

00:00:06.040 --> 00:00:07.900
So the important
thing here is to look

00:00:07.900 --> 00:00:10.550
at what place these
digits are in.

00:00:10.550 --> 00:00:13.370
So this 1 right over here,
this is in the tenths place,

00:00:13.370 --> 00:00:16.550
so you could view
that as 1 times 1/10.

00:00:16.550 --> 00:00:20.590
This 5 right over here is
in the hundredths place,

00:00:20.590 --> 00:00:23.700
so you could view
that as 5 times 1/100.

00:00:23.700 --> 00:00:26.320
So if I were to rewrite
this, I can rewrite this

00:00:26.320 --> 00:00:30.080
as the sum of-- this 1
represents 1 times 1/10,

00:00:30.080 --> 00:00:33.480
so that would literally
be 1/10 plus--

00:00:33.480 --> 00:00:36.860
and this 5 represents
5 times 1/100,

00:00:36.860 --> 00:00:40.380
so it would be plus 5/100.

00:00:40.380 --> 00:00:41.910
And if we want to
add them up, we

00:00:41.910 --> 00:00:43.870
want to find a
common denominator.

00:00:43.870 --> 00:00:45.890
The common denominator is 100.

00:00:45.890 --> 00:00:49.480
Both 10 and-- the
least common multiple.

00:00:49.480 --> 00:00:52.720
100 is a multiple
of both 10 and 100.

00:00:52.720 --> 00:00:55.734
So we can rewrite this
as something over 100

00:00:55.734 --> 00:00:59.516
plus something over 100.

00:00:59.516 --> 00:01:00.640
This isn't going to change.

00:01:00.640 --> 00:01:02.750
This was already 5/100.

00:01:02.750 --> 00:01:04.650
If we multiply the
denominator here

00:01:04.650 --> 00:01:07.894
by 10-- that's what we did;
we multiplied it by 10--

00:01:07.894 --> 00:01:10.310
then we're going to have to
multiply this numerator by 10.

00:01:10.310 --> 00:01:12.686
And so this is the
same thing as 10/100.

00:01:12.686 --> 00:01:13.810
And now we're ready to add.

00:01:13.810 --> 00:01:20.660
This is the same thing
as-- 10 plus 5 is 15/100.

00:01:20.660 --> 00:01:23.010
And you could have done that
a little bit quicker just

00:01:23.010 --> 00:01:23.860
by inspecting this.

00:01:23.860 --> 00:01:26.109
You would say, look, my
smallest place right over here

00:01:26.109 --> 00:01:27.260
is in the hundredths place.

00:01:27.260 --> 00:01:29.590
Instead of calling this
1/10, I could call this

00:01:29.590 --> 00:01:30.860
literally 10/100.

00:01:30.860 --> 00:01:35.710
Or I could say this
whole thing is 15/100.

00:01:35.710 --> 00:01:37.914
And now if I want to reduce
this to lowest terms,

00:01:37.914 --> 00:01:40.330
we can-- let's see, both the
numerator and the denominator

00:01:40.330 --> 00:01:42.030
are divisible by 5.

00:01:42.030 --> 00:01:44.590
So let's divide them both by 5.

00:01:44.590 --> 00:01:48.410
And so the numerator,
15 divided by 5, is 3.

00:01:48.410 --> 00:01:51.800
The denominator, 100
divided by 5, is 20.

00:01:51.800 --> 00:01:55.890
And that's about as
simplified as we can get.


Converting decimals to fractions example 2

WEBVTT
Kind: captions
Language: en

00:00:00.500 --> 00:00:04.940
Let's write 0.8 as a fraction.

00:00:04.940 --> 00:00:09.910
So 0.8, the 8 right over
here is in the tenths place.

00:00:09.910 --> 00:00:11.100
It is the tenths place.

00:00:11.100 --> 00:00:14.000
So you could read
this as 8 tenths.

00:00:14.000 --> 00:00:18.860
And we can write that literally
as being equal to 8 tenths,

00:00:18.860 --> 00:00:21.136
or 8 over 10.

00:00:21.136 --> 00:00:23.760
And now we've already written it
as a fraction, and if we want,

00:00:23.760 --> 00:00:25.170
we can simplify this down.

00:00:25.170 --> 00:00:27.850
Both 8 and 10 share
common factors.

00:00:27.850 --> 00:00:29.620
They are both divisible by 2.

00:00:29.620 --> 00:00:32.290
So lets divide both the
numerator and the denominator

00:00:32.290 --> 00:00:33.536
by 2.

00:00:33.536 --> 00:00:35.410
We are not changing the
value of the fraction

00:00:35.410 --> 00:00:37.993
because we are dividing both the
numerator and the denominator

00:00:37.993 --> 00:00:38.980
by the same thing.

00:00:38.980 --> 00:00:46.660
8 divided by 2 is 4, 10 divided
by 2 is 5, and we're done.

00:00:46.660 --> 00:00:52.069
0.8 is the same thing as 8/10,
which is the same thing as 4/5.


Converting decimals to fractions 2 (ex 2)

WEBVTT
Kind: captions
Language: en

00:00:00.499 --> 00:00:06.719
Let's see if we can write
12.98 as a mixed number.

00:00:06.719 --> 00:00:08.760
So the first thing you
might want to realize here

00:00:08.760 --> 00:00:14.287
is that this is the exact
same thing as 12 plus 0.98.

00:00:14.287 --> 00:00:16.120
And this simplifies it,
because then we just

00:00:16.120 --> 00:00:18.840
have to write it as 12, and
to some fraction, that's

00:00:18.840 --> 00:00:21.870
the same thing as 0.98.

00:00:21.870 --> 00:00:24.220
So if we could write
0.98 as a fraction,

00:00:24.220 --> 00:00:26.829
then we're almost done.

00:00:26.829 --> 00:00:28.120
So let's see if we can do that.

00:00:28.120 --> 00:00:31.332
So this 9 right over here
is in the tenths place.

00:00:31.332 --> 00:00:32.540
I'll just write it like that.

00:00:32.540 --> 00:00:33.910
Tenths place.

00:00:33.910 --> 00:00:38.040
And this right over here
is in the hundredths place.

00:00:38.040 --> 00:00:40.730
So you could view 0.98
two different ways.

00:00:40.730 --> 00:00:43.910
You could view it as 9/10.

00:00:43.910 --> 00:00:46.000
That's this part
right over here.

00:00:46.000 --> 00:00:53.729
9/10 plus 8/100.

00:00:53.729 --> 00:00:55.770
And if you want to find
a common denominator that

00:00:55.770 --> 00:01:04.620
would be the same thing as
90 over 100 plus 8 over 100,

00:01:04.620 --> 00:01:11.080
which is equal to 98 over 100.

00:01:11.080 --> 00:01:14.649
And so 0.98 is 98/100.

00:01:14.649 --> 00:01:16.690
And another way you could
have said that is look,

00:01:16.690 --> 00:01:19.230
the space right over here
is in the hundredths place,

00:01:19.230 --> 00:01:22.050
and so this is 98/100 or 98/100.

00:01:22.050 --> 00:01:24.020
So you could have skipped
this right over here.

00:01:24.020 --> 00:01:26.145
So if we just wanted to
write it as a mixed number,

00:01:26.145 --> 00:01:29.360
we could just write
it as 12 and, instead

00:01:29.360 --> 00:01:33.440
of 0.98, 12 and 98/100.

00:01:33.440 --> 00:01:36.310
Now we haven't reduced
this to lowest terms yet.

00:01:36.310 --> 00:01:38.140
So let's see if we
can simplify this.

00:01:38.140 --> 00:01:41.600
98 is divisible by
2, and so is 100.

00:01:41.600 --> 00:01:43.780
So let's divide
both of them by 2.

00:01:43.780 --> 00:01:45.310
They have that common factor.

00:01:45.310 --> 00:01:47.570
So we're going to divide
both of them by 2.

00:01:47.570 --> 00:01:53.090
And so this is the same thing as
12, and 98 divided by 2 is 49.

00:01:53.090 --> 00:01:55.856
100 divided by 2 is 50.

00:01:55.856 --> 00:01:57.730
And I think that's about
as far as we can do.

00:01:57.730 --> 00:02:01.950
49 factors, it's divisible
by 7, but 50 isn't, so we've

00:02:01.950 --> 00:02:03.690
put it in lowest terms.

00:02:03.690 --> 00:02:09.449
So 12.98 can be written as a
mixed number, 12 and 49/50.


Converting decimals to percents

WEBVTT
Kind: captions
Language: en

00:00:00.860 --> 00:00:03.996
Percent literally means per 100.

00:00:03.996 --> 00:00:05.370
That's where the
word comes from.

00:00:05.370 --> 00:00:10.540
Cent from cents or century or
any of those words means 100.

00:00:10.540 --> 00:00:13.859
So if someone tells
you 7 per cent--

00:00:13.859 --> 00:00:16.400
and I'm separating the word so
it makes a little more sense--

00:00:16.400 --> 00:00:18.680
they're really saying 7 per 100.

00:00:18.680 --> 00:00:22.260
This is the same
thing as 7 per 100,

00:00:22.260 --> 00:00:27.640
which is the same thing as a
fraction as 7 per 7 per 100.

00:00:27.640 --> 00:00:29.170
With that out of
the way, let's see

00:00:29.170 --> 00:00:36.810
if we can write 0.601
as a percentage.

00:00:36.810 --> 00:00:40.930
Well, we essentially want to
write it as something over 100.

00:00:40.930 --> 00:00:42.730
So you could view
it as-- I'll just

00:00:42.730 --> 00:00:44.800
rewrite this part
right over here.

00:00:44.800 --> 00:00:48.600
You could write it
as 0.601 over 1.

00:00:48.600 --> 00:00:50.152
This is obviously
the same quantity.

00:00:50.152 --> 00:00:51.610
If you divide
anything by 1, you're

00:00:51.610 --> 00:00:53.370
still going to get
that same anything.

00:00:53.370 --> 00:01:00.105
And I'm going to multiply
it by 100 over 100.

00:01:00.105 --> 00:01:01.730
Obviously, this won't
change the value.

00:01:01.730 --> 00:01:03.310
This is just 1 here.

00:01:03.310 --> 00:01:06.000
But what this does is it'll
give us a fraction in term

00:01:06.000 --> 00:01:07.800
with the denominator being 100.

00:01:07.800 --> 00:01:11.790
So the denominator, if I
multiply these two characters

00:01:11.790 --> 00:01:13.530
right over here in
the denominator,

00:01:13.530 --> 00:01:16.480
the denominator of our
product is going to be 100.

00:01:16.480 --> 00:01:21.370
If I multiply 0.0601 times
100, what am I going to get?

00:01:21.370 --> 00:01:24.570
Well, every time I multiply
it by a multiple of 10

00:01:24.570 --> 00:01:26.130
or every time I
multiply it by 10,

00:01:26.130 --> 00:01:28.850
I'm going to shift the decimal
over to the right once.

00:01:28.850 --> 00:01:32.560
So if I multiply it
by 10, I'd get 6.01.

00:01:32.560 --> 00:01:34.070
And if I multiply
it by a 10 again

00:01:34.070 --> 00:01:37.830
or if I multiply it by
100, I'm going to get 60.1.

00:01:37.830 --> 00:01:44.700
So 0.601 times 100 is 60.1.

00:01:44.700 --> 00:01:46.240
Let me rewrite that again.

00:01:46.240 --> 00:01:52.930
If I were to write 0.601, and
I want to multiply it by 100,

00:01:52.930 --> 00:01:55.250
shift the decimal once,
I multiply it by 10.

00:01:55.250 --> 00:01:59.020
If I multiply it by 10 again, or
essentially multiply it by 100,

00:01:59.020 --> 00:02:01.130
I get 60.1.

00:02:01.130 --> 00:02:02.600
So this is times 10.

00:02:02.600 --> 00:02:03.880
This is times 10 again.

00:02:03.880 --> 00:02:05.970
I've essentially
multiplied it by 100.

00:02:05.970 --> 00:02:07.880
But now we have it
in the form we like.

00:02:07.880 --> 00:02:09.919
We have 60.1 over 100.

00:02:09.919 --> 00:02:11.550
Or you could rewrite this.

00:02:11.550 --> 00:02:18.500
This is the same
thing as 60.1 per 100,

00:02:18.500 --> 00:02:24.860
which is the same
thing as 60.1 percent.

00:02:24.860 --> 00:02:28.460
And we'd obviously want to write
it then as 60.1 percent, as one

00:02:28.460 --> 00:02:33.930
word, or 60.1, and we'll
just use the symbol-- 60.1%.

00:02:33.930 --> 00:02:35.940
We are done.


Converting decimals to fractions 2 (ex 1)

WEBVTT
Kind: captions
Language: en

00:00:00.560 --> 00:00:06.742
Let's see if we can write
0.0727 as a fraction.

00:00:06.742 --> 00:00:08.950
Now, let's just think about
what places these are in.

00:00:08.950 --> 00:00:12.130
This is in the tenths place.

00:00:12.130 --> 00:00:13.510
This is in the hundredths place.

00:00:16.550 --> 00:00:18.700
This 2 is in the
thousandths place.

00:00:21.300 --> 00:00:23.640
And this 7 right
here, this last 7,

00:00:23.640 --> 00:00:27.889
is in the ten-thousandths place.

00:00:27.889 --> 00:00:29.680
So there's a couple of
ways we can do this.

00:00:29.680 --> 00:00:31.846
The way I like to think of
this, this term over here

00:00:31.846 --> 00:00:33.390
is in the ten-thousandths place.

00:00:33.390 --> 00:00:35.275
We can view this whole
thing right over here

00:00:35.275 --> 00:00:41.960
as 727 ten-thousandths because
this is the smallest place

00:00:41.960 --> 00:00:42.950
right over here.

00:00:42.950 --> 00:00:44.120
So let's just rewrite it.

00:00:44.120 --> 00:00:53.330
This is equal to
727 over 10,000.

00:00:53.330 --> 00:00:55.280
And we've already
written it as a fraction.

00:00:55.280 --> 00:00:57.840
And I think that's about as
simplified as we can get.

00:00:57.840 --> 00:01:00.590
This number up here
is not divisible by 2.

00:01:00.590 --> 00:01:02.660
It's not divisible by 5.

00:01:02.660 --> 00:01:04.200
In fact, it's not
divisible by 3,

00:01:04.200 --> 00:01:06.300
which means it wouldn't
be divisible by 6 or 9.

00:01:06.300 --> 00:01:09.060
It doesn't even seem
to be divisible by 7.

00:01:09.060 --> 00:01:10.750
It might be a prime number.

00:01:10.750 --> 00:01:13.199
But I think we are done.


Converting decimals to percents example 2

WEBVTT
Kind: captions
Language: en

00:00:00.580 --> 00:00:06.610
Let's see if we can write
1.501 as a percentage.

00:00:06.610 --> 00:00:09.030
Now we really just want
to write this quantity

00:00:09.030 --> 00:00:11.050
as something over 100.

00:00:11.050 --> 00:00:12.880
So what we can do is
we can say that this

00:00:12.880 --> 00:00:16.480
is the same thing
as 1.501 over 1.

00:00:16.480 --> 00:00:17.940
We haven't changed its value.

00:00:17.940 --> 00:00:22.504
And let's multiply
it times 100/100.

00:00:22.504 --> 00:00:24.920
When we do this product-- and
I haven't changed the value.

00:00:24.920 --> 00:00:26.770
This is just multiplying
something times 1.

00:00:26.770 --> 00:00:28.770
But when we do it, we're
going to change the way

00:00:28.770 --> 00:00:29.895
that we're representing it.

00:00:29.895 --> 00:00:33.570
The denominator now is
going to be 1 times 100.

00:00:33.570 --> 00:00:35.000
So that's pretty
straightforward.

00:00:35.000 --> 00:00:36.980
That's just going to be 100.

00:00:36.980 --> 00:00:38.740
And then the
numerator, we're going

00:00:38.740 --> 00:00:42.730
to want to multiply
1.501 times 100.

00:00:42.730 --> 00:00:45.460
And so if we multiply
this times 10,

00:00:45.460 --> 00:00:47.250
we would move the
decimal one over.

00:00:47.250 --> 00:00:48.750
We want to multiply
it by 100, so we

00:00:48.750 --> 00:00:50.600
want to multiply by 10 again.

00:00:50.600 --> 00:00:52.970
So we're going to move the
decimal over to the right

00:00:52.970 --> 00:00:53.470
twice.

00:00:53.470 --> 00:00:56.000
We're multiplying
it by 10 twice,

00:00:56.000 --> 00:00:57.907
or you're multiplying it by 100.

00:00:57.907 --> 00:00:58.990
This is multiplying by 10.

00:00:58.990 --> 00:01:00.310
This is multiplying by 100.

00:01:00.310 --> 00:01:02.310
So this is where the
decimal's going to sit now.

00:01:02.310 --> 00:01:07.060
So we're going to get 150.1.

00:01:07.060 --> 00:01:12.340
And so we've rewritten the
1.501 as 150.1 over 100,

00:01:12.340 --> 00:01:14.731
or 150.1 per 100.

00:01:14.731 --> 00:01:15.480
Let me write that.

00:01:15.480 --> 00:01:22.530
150.1 per 100, which
is the same thing

00:01:22.530 --> 00:01:32.980
as 150.1 per cent, which is
the same thing as 150.1%.

00:01:32.980 --> 00:01:33.687
And we're done.

00:01:33.687 --> 00:01:35.770
And, essentially, all
you're doing-- if you really

00:01:35.770 --> 00:01:38.740
want to simplify the process--
we're multiplying this

00:01:38.740 --> 00:01:41.380
by 100 to get 150.1.

00:01:41.380 --> 00:01:43.575
And then we're saying,
that is the percentage.

00:01:43.575 --> 00:01:45.950
So you want to make sure that
you write the percent there

00:01:45.950 --> 00:01:48.150
or the percent symbol.


Converting percents to decimals

WEBVTT
Kind: captions
Language: en

00:00:00.500 --> 00:00:04.580
Let's see if we can
write 59.2%, if we

00:00:04.580 --> 00:00:07.900
can write this as a decimal.

00:00:07.900 --> 00:00:11.080
Well, 59.2%, this
literally means

00:00:11.080 --> 00:00:15.300
59.2 per cent, which
literally means

00:00:15.300 --> 00:00:23.830
59.2 per 100, which literally
means 59.2 per 100, which

00:00:23.830 --> 00:00:28.290
is the same thing as
59.2 divided by 100.

00:00:28.290 --> 00:00:31.790
And If we were to divide 59.2
by 100, what would we get?

00:00:31.790 --> 00:00:37.500
So this is the same thing
is 59.2 divided by 100.

00:00:37.500 --> 00:00:42.360
So if we were to take 59.2, if
we wanted to divide it by 10,

00:00:42.360 --> 00:00:44.660
we would move the decimal
over to the left once.

00:00:44.660 --> 00:00:46.000
We would get 5.92.

00:00:46.000 --> 00:00:48.470
But we want to divide it by
100, so we move the decimal

00:00:48.470 --> 00:00:49.860
over to the left again.

00:00:49.860 --> 00:00:51.710
We're dividing by 10
once, and then we're

00:00:51.710 --> 00:00:53.440
dividing by 10 again.

00:00:53.440 --> 00:00:56.140
Divide by 10 twice, you're
essentially dividing by 100.

00:00:56.140 --> 00:01:01.580
So you move the decimal to
the left twice, you get 0.592.

00:01:01.580 --> 00:01:04.140
And we'll just put a 0 out
here just to clarify things.

00:01:04.140 --> 00:01:04.959
And we're done.

00:01:04.959 --> 00:01:08.290
We've written
59.2% as a decimal.

00:01:08.290 --> 00:01:11.220
We essentially just
divided this by 100,

00:01:11.220 --> 00:01:13.930
which is dividing by 10
twice, moving the decimal once

00:01:13.930 --> 00:01:15.530
to the left, and
then another time.

00:01:15.530 --> 00:01:18.180
Or since we're dividing by
100, moving the decimal twice

00:01:18.180 --> 00:01:18.710
to the left.

00:01:18.710 --> 00:01:20.630
And we get 0.592.


Converting percents to decimals example 2

WEBVTT
Kind: captions
Language: en

00:00:00.500 --> 00:00:06.370
Let's write 113.9% as a decimal.

00:00:06.370 --> 00:00:09.080
So percent, this
symbol right over here,

00:00:09.080 --> 00:00:10.890
literally means per hundred.

00:00:10.890 --> 00:00:16.400
So this is the same
thing as 113.9 per 100,

00:00:16.400 --> 00:00:22.770
which is the same thing
as 113.9 divided by 100.

00:00:22.770 --> 00:00:25.020
So essentially, if we want
to write this as a decimal,

00:00:25.020 --> 00:00:29.300
we just take a 113.9,
and we divide it by 100.

00:00:29.300 --> 00:00:33.950
And to do that,
113.9 divided by 100.

00:00:33.950 --> 00:00:36.800
If you divide by 10, you move
the decimal once to the left.

00:00:36.800 --> 00:00:39.450
If you divide by 100, you're
moving the decimal twice

00:00:39.450 --> 00:00:39.950
to the left.

00:00:39.950 --> 00:00:42.533
If we're doing it by 1,000, we
would go to the left once more.

00:00:42.533 --> 00:00:44.780
10,000, each time
you divide by 10,

00:00:44.780 --> 00:00:47.410
you'd go one step to the left,
which hopefully makes sense.

00:00:47.410 --> 00:00:49.970
If we were to multiply by 10,
we would be moving the decimal

00:00:49.970 --> 00:00:51.845
over to the right, and
there are other videos

00:00:51.845 --> 00:00:54.240
that go into far more depth
on the intuition behind that.

00:00:54.240 --> 00:00:58.070
But anyway, we're
dividing 113.9 by 100,

00:00:58.070 --> 00:01:00.860
so move the decimal
two spaces to the left.

00:01:00.860 --> 00:01:03.470
So the decimal will
end up right over here.

00:01:03.470 --> 00:01:08.910
So this will be equal to 1.139.

00:01:08.910 --> 00:01:11.598
And we are done.


Adding mixed numbers with like denominators

WEBVTT
Kind: captions
Language: en

00:00:00.570 --> 00:00:02.120
Let's add these
two mixed numbers.

00:00:02.120 --> 00:00:05.615
2 and 5/13 plus 7 and 6/13.

00:00:05.615 --> 00:00:07.490
And the way I like to
think about in my head,

00:00:07.490 --> 00:00:11.250
I like to separate out the mixed
numbers into the whole number

00:00:11.250 --> 00:00:13.450
component and the
fractional component.

00:00:13.450 --> 00:00:20.500
So we can rewrite 2 and
5/13 as 2 plus 5 over 13.

00:00:23.120 --> 00:00:25.240
And then we can write that plus.

00:00:25.240 --> 00:00:31.416
And then 7 and 6/13, we can
rewrite as plus 7 plus 6/13.

00:00:36.800 --> 00:00:38.290
So all I did is I rewrote this.

00:00:38.290 --> 00:00:39.890
And I essentially
expanded it out.

00:00:39.890 --> 00:00:42.070
I broke up the mixed numbers
into their whole number

00:00:42.070 --> 00:00:44.130
parts and their
fractional parts.

00:00:44.130 --> 00:00:45.850
And then what I
like to do is I like

00:00:45.850 --> 00:00:47.480
to add the whole number parts.

00:00:47.480 --> 00:00:51.050
So this 2 plus this
7, so I'll do that.

00:00:51.050 --> 00:00:53.410
So I'll do the 2
plus 7 over here.

00:00:53.410 --> 00:00:54.370
I'll add those up.

00:00:54.370 --> 00:00:56.820
And to that, I will add
the fractional parts.

00:00:56.820 --> 00:01:02.893
So to that, I will add
the 5/13 to the 6/13.

00:01:05.730 --> 00:01:11.180
So if we add the whole
number parts, 2 plus 7 is 9,

00:01:11.180 --> 00:01:12.950
and the fractional
parts, they already

00:01:12.950 --> 00:01:15.270
have the same denominator
in this problem.

00:01:15.270 --> 00:01:19.140
5/13 plus 6/13,
same denominator.

00:01:19.140 --> 00:01:22.750
You're going to get 11/13.

00:01:22.750 --> 00:01:24.080
5 plus 6 is 11.

00:01:24.080 --> 00:01:27.510
So you get 9 plus 11/13.

00:01:27.510 --> 00:01:32.550
Well, that's just the
same thing as 9 and 11/13.

00:01:32.550 --> 00:01:34.560
And we are done.


Subtracting mixed numbers with like denominators

WEBVTT
Kind: captions
Language: en

00:00:00.500 --> 00:00:04.680
Let's figure out what 11 and
12/16 minus 5 and 8/16 is.

00:00:04.680 --> 00:00:06.430
And then we might have
to simplify it down

00:00:06.430 --> 00:00:08.010
to lowest terms.

00:00:08.010 --> 00:00:10.620
So the way I like to do these
is to kind of separate out

00:00:10.620 --> 00:00:12.050
the whole number
part of the mixed

00:00:12.050 --> 00:00:13.950
numbers from the
fractional part.

00:00:13.950 --> 00:00:16.510
So I can rewrite this
number right over here

00:00:16.510 --> 00:00:21.260
as 11 plus 12/16.

00:00:21.260 --> 00:00:23.612
And from that, I am
going to subtract--

00:00:23.612 --> 00:00:25.320
and I'll put parentheses
here because I'm

00:00:25.320 --> 00:00:27.170
going to break this part open.

00:00:27.170 --> 00:00:34.800
I'm going to
subtract 5 plus 8/16.

00:00:34.800 --> 00:00:38.410
5 and 8/16-- same
thing as 5 plus 8/16.

00:00:38.410 --> 00:00:40.580
But I have to remember,
I'm subtracting it.

00:00:40.580 --> 00:00:42.280
I'm subtracting
this whole thing.

00:00:42.280 --> 00:00:45.030
So I could rewrite it as--
I'll rewrite this part--

00:00:45.030 --> 00:00:48.990
11 plus 12/16.

00:00:48.990 --> 00:00:52.050
And I'm subtracting 5 plus 8/16.

00:00:52.050 --> 00:00:54.560
So I can distribute
the negative sign.

00:00:54.560 --> 00:00:59.710
So it's going to be minus
5, negative 1 times 5.

00:00:59.710 --> 00:01:02.470
And then negative 1
times positive 8/16.

00:01:02.470 --> 00:01:05.239
So it's going to be minus 8/16.

00:01:08.819 --> 00:01:11.110
And then I like to do the
whole number parts separately

00:01:11.110 --> 00:01:12.882
and then the fractional
parts separately.

00:01:12.882 --> 00:01:14.340
So let's do the
whole number parts.

00:01:14.340 --> 00:01:16.470
We have 11 minus 5.

00:01:16.470 --> 00:01:20.020
I'll write it here, 11 minus 5.

00:01:20.020 --> 00:01:20.870
We'll do that part.

00:01:20.870 --> 00:01:22.390
That's the whole number part.

00:01:22.390 --> 00:01:26.660
And then we have plus 12/16.

00:01:26.660 --> 00:01:32.896
Let me do this in pink maybe,
plus 12/16, minus 8/16.

00:01:37.410 --> 00:01:41.220
And 11 minus 5 is 6.

00:01:41.220 --> 00:01:43.267
And I have 6 plus.

00:01:43.267 --> 00:01:45.100
And then our denominators
are the same here,

00:01:45.100 --> 00:01:47.118
so we're going to get
something over 16.

00:01:47.118 --> 00:01:50.380
And 12 minus 8 is 4.

00:01:50.380 --> 00:01:52.670
So this is the same
thing as 6 plus 4

00:01:52.670 --> 00:01:55.265
over 16, which is the
same thing as-- writing it

00:01:55.265 --> 00:01:58.455
as a mixed number-- 6 and 4/16.

00:02:01.650 --> 00:02:05.070
And this is the right quantity,
but we can simplify it.

00:02:05.070 --> 00:02:07.000
4/16 can be simplified.

00:02:07.000 --> 00:02:09.419
Both the numerator and the
denominator are divisible by 4.

00:02:09.419 --> 00:02:10.690
They both have the factor 4.

00:02:10.690 --> 00:02:13.420
So let's divide both the
numerator and denominator by 4.

00:02:13.420 --> 00:02:14.680
Divided by 4.

00:02:14.680 --> 00:02:15.222
Divided by 4.

00:02:15.222 --> 00:02:16.846
Since we're dividing
by the same thing,

00:02:16.846 --> 00:02:18.330
we're not changing its quantity.

00:02:18.330 --> 00:02:20.630
And so this is
equal to-- we still

00:02:20.630 --> 00:02:23.470
have the whole number part,
6, but the fraction part

00:02:23.470 --> 00:02:26.790
is now 1, 1/4.

00:02:26.790 --> 00:02:30.400
So we get 6 and 1/4.


How to add mixed numbers that have unlike denominators

WEBVTT
Kind: captions
Language: en

00:00:00.550 --> 00:00:05.400
Let's add 19 and
3/18 to 18 and 2/3.

00:00:05.400 --> 00:00:07.640
So I like to separate out
the whole number parts

00:00:07.640 --> 00:00:08.740
from the fraction parts.

00:00:08.740 --> 00:00:14.590
So 19 and 3/18 is the same
thing as 19 plus 3/18.

00:00:14.590 --> 00:00:18.700
And to that, we are
going to add 18 and 2/3,

00:00:18.700 --> 00:00:23.690
which is the same
thing as 18 plus 2/3.

00:00:23.690 --> 00:00:26.520
Now we can separately add
the whole number parts.

00:00:26.520 --> 00:00:29.295
So we could add
the 19 to the 18.

00:00:29.295 --> 00:00:33.210
So we could do 19 plus 18.

00:00:33.210 --> 00:00:36.960
And then we can add
the fraction parts--

00:00:36.960 --> 00:00:42.896
let me do this in green--
plus 3/18 plus 2/3.

00:00:46.080 --> 00:00:48.970
Now 19/18, pretty
straightforward.

00:00:48.970 --> 00:00:49.830
That is what?

00:00:49.830 --> 00:00:50.330
Let's see.

00:00:50.330 --> 00:00:51.739
19 plus 19 would be 38.

00:00:51.739 --> 00:00:53.405
So this is going to
be 1 less than that.

00:00:53.405 --> 00:00:54.880
It's going to be 37.

00:00:54.880 --> 00:00:57.060
So that gives me 37.

00:00:57.060 --> 00:00:59.830
And then 3/18 plus
2/3, to add them,

00:00:59.830 --> 00:01:01.640
I need to have the
same denominator.

00:01:01.640 --> 00:01:05.530
And the least common
multiple of 18 and 3 is 18.

00:01:05.530 --> 00:01:09.250
So let's convert 2/3
to something over 18.

00:01:09.250 --> 00:01:13.810
So 2/3, if I want to write
it as something over 18,

00:01:13.810 --> 00:01:16.550
well, I multiplied
the denominator by 6,

00:01:16.550 --> 00:01:19.060
so I'd also have to
multiply the numerator by 6.

00:01:19.060 --> 00:01:22.580
So it's the same thing as 12/18.

00:01:22.580 --> 00:01:27.390
So I can rewrite 2/3 as 12/18.

00:01:27.390 --> 00:01:29.390
And now I can add these
two things together.

00:01:29.390 --> 00:01:33.240
That's going to be-- so
I have 37 plus-- it's

00:01:33.240 --> 00:01:37.960
going to be something over
18-- plus something over 18.

00:01:37.960 --> 00:01:42.452
3 plus 12 is 15, plus 15/18.

00:01:42.452 --> 00:01:44.160
And so expressing this
as a mixed number,

00:01:44.160 --> 00:01:48.930
I get 37 and 15/18.

00:01:48.930 --> 00:01:51.050
And that's the right number.

00:01:51.050 --> 00:01:52.520
But we can simplify
it even more.

00:01:52.520 --> 00:01:54.160
We can simplify the 15/18.

00:01:54.160 --> 00:01:58.330
Both the numerator and the
denominator are divisible by 3.

00:01:58.330 --> 00:02:00.084
So let's divide them both by 3.

00:02:00.084 --> 00:02:02.000
And we're not changing
the value because we're

00:02:02.000 --> 00:02:04.680
doing the same thing to the
numerator and the denominator.

00:02:04.680 --> 00:02:09.789
And so this gives us,
we still have our 37,

00:02:09.789 --> 00:02:14.400
but the numerator is now 5,
and the denominator is now 6.

00:02:14.400 --> 00:02:16.020
So we get 37 and 5/6.

00:02:19.080 --> 00:02:20.850
And we're done.


How to subtract mixed numbers that have unlike denominators

WEBVTT
Kind: captions
Language: en

00:00:00.499 --> 00:00:05.040
Let's try to evaluate 7
and 6/9 minus 3 and 2/5.

00:00:05.040 --> 00:00:07.760
So like always, I like to
separate out the whole number

00:00:07.760 --> 00:00:09.410
parts from the fractional parts.

00:00:09.410 --> 00:00:19.320
This is the same thing as 7
plus 6/9 minus 3 minus 2/5.

00:00:19.320 --> 00:00:22.220
And the reason why I'm
saying minus 3 minus 2/5

00:00:22.220 --> 00:00:26.524
is this is the same thing
as minus 3 plus 2/5.

00:00:26.524 --> 00:00:28.190
And so you distribute
the negative sign.

00:00:28.190 --> 00:00:32.004
You're subtracting a 3, and
then you're subtracting the 2/5.

00:00:32.004 --> 00:00:33.920
And so now we can worry
about the whole number

00:00:33.920 --> 00:00:37.340
parts, 7 minus 3.

00:00:37.340 --> 00:00:41.310
Well, 7 minus 3 is
going to give us 4.

00:00:41.310 --> 00:00:43.040
So that's going to give us 4.

00:00:43.040 --> 00:00:48.330
And then we're going
to have 6/9 minus 2/5.

00:00:48.330 --> 00:00:51.330
So let me think about
what 6/9 minus 2/5 are.

00:00:51.330 --> 00:00:54.280
6/9 minus 2/5, well,
we're going to have

00:00:54.280 --> 00:00:55.770
to find a common denominator.

00:00:55.770 --> 00:00:57.680
So this is going to
be the same thing.

00:00:57.680 --> 00:00:59.930
And I think the least
common multiple of 9 and 5

00:00:59.930 --> 00:01:01.812
is going to be 45.

00:01:01.812 --> 00:01:03.020
Literally, you then multiply.

00:01:03.020 --> 00:01:05.180
They have no common factors.

00:01:05.180 --> 00:01:07.380
So it's going to be over 45.

00:01:07.380 --> 00:01:09.830
To go from 9 to 45, I
have to multiply by 5.

00:01:09.830 --> 00:01:12.040
So I'm going to have to
multiply the numerator by 5.

00:01:12.040 --> 00:01:14.120
So 6 times 5 is 30.

00:01:14.120 --> 00:01:15.750
Then I'm going to subtract.

00:01:15.750 --> 00:01:18.584
To go from 5 to 45, I
had to multiply by 9.

00:01:18.584 --> 00:01:20.250
So I have to multiply
the numerator by 9

00:01:20.250 --> 00:01:21.750
if I don't want to
change the value.

00:01:21.750 --> 00:01:25.240
So 2 times 9 is 18.

00:01:25.240 --> 00:01:30.050
And 30/45 minus 18/45 is
going to be something over 45.

00:01:30.050 --> 00:01:34.270
30 minus 18 is 12.

00:01:34.270 --> 00:01:37.400
If I subtract these two
fractions right over here,

00:01:37.400 --> 00:01:41.010
I get 12/45.

00:01:41.010 --> 00:01:42.900
So it's 4 plus 12/45.

00:01:42.900 --> 00:01:45.320
Or if we wanted to write
it as a mixed number,

00:01:45.320 --> 00:01:49.240
this is equal to 4 and 12/45.

00:01:49.240 --> 00:01:50.480
But we're not done yet.

00:01:50.480 --> 00:01:52.070
We can simplify this further.

00:01:52.070 --> 00:01:54.180
12 and 45 have common factors.

00:01:57.030 --> 00:01:58.645
They're both divisible by 3.

00:02:01.660 --> 00:02:03.787
Actually, they're both
divisible by-- well,

00:02:03.787 --> 00:02:05.370
I think we can divide
more after that.

00:02:05.370 --> 00:02:05.911
So let's see.

00:02:05.911 --> 00:02:10.810
If we divide the numerator by
3 and the denominator by 3,

00:02:10.810 --> 00:02:12.370
we end up with 4.

00:02:12.370 --> 00:02:15.880
And 12 divided by 3 is 4.

00:02:15.880 --> 00:02:21.630
And 45 divided by 3 is 15.

00:02:21.630 --> 00:02:23.190
4 and 4/15.

00:02:23.190 --> 00:02:24.410
And actually, we're done.

00:02:24.410 --> 00:02:27.120
These two can't be
simplified anymore.

00:02:27.120 --> 00:02:29.732
4 and 4/15.


Example of adding fractions with unlike denominators

WEBVTT
Kind: captions
Language: en

00:00:00.590 --> 00:00:06.090
Let's add 4/11 to 9/13.

00:00:06.090 --> 00:00:08.210
So in order to add
these two fractions,

00:00:08.210 --> 00:00:09.965
we need to find a
common denominator.

00:00:09.965 --> 00:00:11.340
And that common
denominator needs

00:00:11.340 --> 00:00:14.610
to be the least common
multiple of 11 and 13.

00:00:14.610 --> 00:00:17.520
And these 2 numbers, they
don't share any common factors.

00:00:17.520 --> 00:00:19.520
So their least common
multiple is literally just

00:00:19.520 --> 00:00:22.470
going to be the
product of 11 and 13.

00:00:22.470 --> 00:00:27.440
So we could say 13 times 11.

00:00:27.440 --> 00:00:29.374
13 times 1 is 13.

00:00:29.374 --> 00:00:35.250
13 times another 1 is 13, or you
could say 13 times 10 is 130.

00:00:35.250 --> 00:00:39.410
And we get 3, 4, 1-- 143.

00:00:39.410 --> 00:00:41.746
So that's going to be
our common denominator.

00:00:41.746 --> 00:00:42.870
So I'll write it over here.

00:00:42.870 --> 00:00:48.870
So something over 143 plus
something else over 143.

00:00:48.870 --> 00:00:52.160
And to go from 4/11
to something over 143,

00:00:52.160 --> 00:00:56.060
we multiplied the
11 times 13, or we

00:00:56.060 --> 00:00:57.930
multiplied the
denominator times 13.

00:00:57.930 --> 00:01:00.270
So we're going have to multiply
the numerator times 13,

00:01:00.270 --> 00:01:01.250
as well.

00:01:01.250 --> 00:01:03.100
And 4 times 13, let's see.

00:01:03.100 --> 00:01:04.714
4 times 10 is 40.

00:01:04.714 --> 00:01:06.310
4 times 3 is 12.

00:01:06.310 --> 00:01:07.430
So it gives us 52.

00:01:07.430 --> 00:01:10.230
And you can work that
out by hand if you like.

00:01:10.230 --> 00:01:12.480
4 times 13 is 52.

00:01:12.480 --> 00:01:18.110
And then to go from 13 to
143, we multiplied by 11.

00:01:18.110 --> 00:01:19.990
So if we multiplied
the denominator by 11,

00:01:19.990 --> 00:01:22.198
if we don't want to change
the value of the fraction,

00:01:22.198 --> 00:01:24.490
we have to multiply
the numerator by 11.

00:01:24.490 --> 00:01:27.206
9 times 11 is 99.

00:01:27.206 --> 00:01:28.330
And now we're ready to add.

00:01:28.330 --> 00:01:33.800
This is equal to our
common denominator is 143.

00:01:33.800 --> 00:01:37.900
And 52 plus 99-- 52
plus 100 would be 152,

00:01:37.900 --> 00:01:39.640
and this is going to
be 1 less than that.

00:01:39.640 --> 00:01:42.980
So it's going to be 151.

00:01:42.980 --> 00:01:45.620
And I think that's about as
simplified as we can get.

00:01:45.620 --> 00:01:47.290
As far as I know,
it doesn't look

00:01:47.290 --> 00:01:51.600
like there are any common
factors between 151 and 143.

00:01:51.600 --> 00:01:54.560
So we just get 151/143.

00:01:54.560 --> 00:01:56.910
We can write this
as a mixed number

00:01:56.910 --> 00:02:01.560
because 143 goes
into 151 one time.

00:02:01.560 --> 00:02:04.180
1 times 143 is 143.

00:02:04.180 --> 00:02:06.130
When you subtract, let's see.

00:02:06.130 --> 00:02:07.630
This can become an 11.

00:02:07.630 --> 00:02:08.730
This is a 4.

00:02:08.730 --> 00:02:10.310
11 minus 3 is 8.

00:02:10.310 --> 00:02:11.780
You have a remainder of 8.

00:02:11.780 --> 00:02:13.020
So this is the same thing.

00:02:13.020 --> 00:02:20.740
151/143 is the same
thing as 1 and 8/143.

00:02:20.740 --> 00:02:22.420
And now it becomes
even more clear

00:02:22.420 --> 00:02:25.460
that these can't be
simplified anymore.

00:02:25.460 --> 00:02:26.270
And we are done.

00:02:26.270 --> 00:02:28.820
This is the same thing as
1-- I'll write the 1 a little

00:02:28.820 --> 00:02:32.133
bit bigger-- 1 and 8/143.


Frequency stability property short film

WEBVTT
Kind: captions
Language: en

00:00:00.000 --> 00:00:04.410
[TYPING]

00:00:04.410 --> 00:00:06.070
Consider the following.

00:00:06.070 --> 00:00:07.337
Imagine two rooms.

00:00:07.337 --> 00:00:07.920
[DOOR CLOSING]

00:00:07.920 --> 00:00:08.630
[DOOR CLOSING]

00:00:08.630 --> 00:00:10.375
Inside each room is a switch.

00:00:10.375 --> 00:00:11.206
[CLICK]

00:00:11.206 --> 00:00:13.150
[CLICK]

00:00:13.150 --> 00:00:16.190
In one room, there is a man
who flips his switch according

00:00:16.190 --> 00:00:17.590
to a coin flip.

00:00:17.590 --> 00:00:19.785
If he lands heads,
the switch is on.

00:00:19.785 --> 00:00:22.540
If he lands tails,
the switch is off.

00:00:22.540 --> 00:00:24.720
In the other room, a
woman switches her light

00:00:24.720 --> 00:00:26.410
based on a blind guess.

00:00:26.410 --> 00:00:29.910
She tries to simulate
randomness without a coin.

00:00:29.910 --> 00:00:34.180
Then we start a clock, and they
make their switches in unison.

00:00:34.180 --> 00:00:36.060
[CLICK]

00:00:36.060 --> 00:00:37.470
[CLICK]

00:00:37.470 --> 00:00:38.410
[CLICK]

00:00:38.410 --> 00:00:39.820
[CLICK]

00:00:39.820 --> 00:00:41.560
Can you determine
which light bulb

00:00:41.560 --> 00:00:43.590
is being switched
by a coin flip?

00:00:43.590 --> 00:00:44.898
[CLICK]

00:00:44.898 --> 00:00:46.310
[CLICK]

00:00:46.310 --> 00:00:47.762
[CLICK]

00:00:47.762 --> 00:00:48.730
[CLICK]

00:00:48.730 --> 00:00:51.534
The answer is yes, but how?

00:00:51.534 --> 00:00:53.016
[CLICK]

00:00:53.016 --> 00:00:54.004
[CLICK]

00:00:54.004 --> 00:00:55.486
[CLICK]

00:00:59.440 --> 00:01:02.800
And the trick is to think about
properties of each sequence

00:01:02.800 --> 00:01:05.900
rather than looking for
any specific patterns.

00:01:05.900 --> 00:01:07.980
For example, first,
we may try to count

00:01:07.980 --> 00:01:11.510
the number of 1's and 0's
which occur in each sequence.

00:01:11.510 --> 00:01:13.360
This is close, but
not enough since they

00:01:13.360 --> 00:01:16.230
will both seem fairly even.

00:01:16.230 --> 00:01:20.550
The answer is to count sequences
of numbers, such as runs

00:01:20.550 --> 00:01:22.900
of three consecutive switches.

00:01:22.900 --> 00:01:25.020
A true random sequence
will be equally

00:01:25.020 --> 00:01:28.960
likely to contain every
sequence of any length.

00:01:28.960 --> 00:01:31.960
This is called the
frequency stability property

00:01:31.960 --> 00:01:35.080
and is demonstrated
by this uniform graph.

00:01:35.080 --> 00:01:37.730
The forgery is now obvious.

00:01:37.730 --> 00:01:40.490
Humans favor certain sequences
when they make guesses,

00:01:40.490 --> 00:01:43.750
resulting in uneven patterns
such as we see here.

00:01:43.750 --> 00:01:45.440
One reason this
happens is because we

00:01:45.440 --> 00:01:47.590
make the mistake of
thinking certain outcomes

00:01:47.590 --> 00:01:49.670
are less random than others.

00:01:49.670 --> 00:01:53.640
But realize, there is no
such thing as a lucky number.

00:01:53.640 --> 00:01:57.040
There is no such thing
as a lucky sequence.

00:01:57.040 --> 00:01:59.330
If we flip a coin
10 times, it is

00:01:59.330 --> 00:02:02.340
equally likely to come
up all heads, all tails,

00:02:02.340 --> 00:02:05.510
or any other sequence
you can think of.

00:02:05.510 --> 00:02:06.410
[CLICK]

00:02:06.410 --> 00:02:09.760
[CRICKETS CHIRPING]


More on final and intermediate GDP contributions

WEBVTT
Kind: captions
Language: en

00:00:00.412 --> 00:00:01.870
In the last video,
we touched a bit

00:00:01.870 --> 00:00:05.720
on the idea of final
goods and services.

00:00:05.720 --> 00:00:08.410
And we talked about
the situation in which

00:00:08.410 --> 00:00:10.810
in the given period that
we're calculating GDP.

00:00:10.810 --> 00:00:12.850
So this might be
in a given year.

00:00:12.850 --> 00:00:14.790
If we're essentially
starting from scratch

00:00:14.790 --> 00:00:17.450
and we put in the labor,
the land, we get the cotton.

00:00:17.450 --> 00:00:19.594
The market value of that
is $10, that raw cotton.

00:00:19.594 --> 00:00:22.010
And then we're able to turn
that into thread with a market

00:00:22.010 --> 00:00:23.680
value of $20 and we keep going.

00:00:23.680 --> 00:00:26.360
And we keep on going and
going all the way until we

00:00:26.360 --> 00:00:29.330
get the finished product of
jeans, which has a market

00:00:29.330 --> 00:00:32.980
value of $50, we saw
in the last video

00:00:32.980 --> 00:00:35.340
that the contribution
to GDP will just

00:00:35.340 --> 00:00:36.890
be this final product.

00:00:36.890 --> 00:00:39.270
It will just be the
$50 worth of jeans.

00:00:39.270 --> 00:00:41.270
And we know its value
based on its market value,

00:00:41.270 --> 00:00:43.160
what people are
willing to pay for it.

00:00:43.160 --> 00:00:48.380
We would not count all of
these intermediary goods.

00:00:48.380 --> 00:00:51.180
But that probably raised
the question in your head.

00:00:51.180 --> 00:00:54.750
What if all of this does
not happen in a given year?

00:00:54.750 --> 00:00:59.040
What if the period
ends, what if the year

00:00:59.040 --> 00:01:00.727
were to end right over here?

00:01:00.727 --> 00:01:02.310
So we're thinking
about GDP in a year,

00:01:02.310 --> 00:01:04.559
but we could think about GDP
in a quarter or whatever.

00:01:04.559 --> 00:01:06.870
What if the period under
question ends over here?

00:01:06.870 --> 00:01:08.580
So this is period one.

00:01:08.580 --> 00:01:09.765
Let's call this period one.

00:01:13.120 --> 00:01:16.010
And then this is going
to be period two.

00:01:16.010 --> 00:01:17.960
So in period one,
we get to the point

00:01:17.960 --> 00:01:20.660
that we have a market
value $20 worth of threat.

00:01:20.660 --> 00:01:24.190
And then period two, we get
all the way to the jeans.

00:01:24.190 --> 00:01:26.380
So this is period two over here.

00:01:26.380 --> 00:01:27.550
So this might be one year.

00:01:27.550 --> 00:01:29.520
And then this might be
the year after that.

00:01:29.520 --> 00:01:31.660
What would happen
is in period one,

00:01:31.660 --> 00:01:35.000
we would look at this good,
this intermediary good that's

00:01:35.000 --> 00:01:37.550
sitting in someone's inventory
someplace that's getting ready

00:01:37.550 --> 00:01:40.550
to be used to get
more finished, we

00:01:40.550 --> 00:01:45.000
would say this is the
contribution to GDP.

00:01:45.000 --> 00:01:46.920
And it would be
considered an investment

00:01:46.920 --> 00:01:48.711
because it's going to
be used in the future

00:01:48.711 --> 00:01:49.940
to produce other things.

00:01:49.940 --> 00:01:54.990
So in period one, the
contribution will be $20.

00:01:54.990 --> 00:01:57.910
And then in period
two, the contribution

00:01:57.910 --> 00:02:01.470
won't be just the $50.

00:02:01.470 --> 00:02:04.500
So we do get to a point that
the jeans are worth $50.

00:02:04.500 --> 00:02:07.820
But so that we haven't
double counted the same $20

00:02:07.820 --> 00:02:10.419
in both period one
and period two,

00:02:10.419 --> 00:02:13.310
we'll subtract out what
our starting point was.

00:02:13.310 --> 00:02:15.550
Or essentially,
we'll subtract out

00:02:15.550 --> 00:02:17.910
the contribution, the
intermediary products that

00:02:17.910 --> 00:02:20.320
were already counted
in previous periods.

00:02:20.320 --> 00:02:23.050
Or you could say,
we'll subtract out

00:02:23.050 --> 00:02:26.460
the market value of the
inputs at the beginning

00:02:26.460 --> 00:02:28.110
of that period.

00:02:28.110 --> 00:02:34.100
So you'd say, $50 minus the $20.

00:02:34.100 --> 00:02:36.940
And so you would get
a contribution to GDP

00:02:36.940 --> 00:02:39.810
by taking this $20
intermediary good

00:02:39.810 --> 00:02:43.040
and turning it into
a $50 final good,

00:02:43.040 --> 00:02:48.960
the contribution to GDP in
period two would be $30.


Parsing gross domestic product

WEBVTT
Kind: captions
Language: en

00:00:00.779 --> 00:00:02.286
Narrator: In the last
video we took a look at

00:00:02.286 --> 00:00:05.336
what is probably the
simplest possible economy

00:00:05.336 --> 00:00:07.739
and it's not even clear
that this economy is

00:00:07.739 --> 00:00:10.342
even possible; this one person economy.

00:00:10.342 --> 00:00:13.778
To make it more analogous
to the real world

00:00:13.778 --> 00:00:16.137
where we have household and we have firms.

00:00:16.137 --> 00:00:19.499
In this one island this guy set up a firm

00:00:19.499 --> 00:00:21.924
and he essentially leashed
out all of the factors

00:00:21.924 --> 00:00:25.057
of production to that firm,
including his own labor.

00:00:25.057 --> 00:00:27.528
He leased it out, the rent on his labor

00:00:27.528 --> 00:00:29.925
is essentially his
wages and then he bought

00:00:29.925 --> 00:00:31.924
all of the goods and services he needed

00:00:31.924 --> 00:00:33.994
from that same firm.

00:00:33.994 --> 00:00:37.527
So, his expenditures would be the revenue

00:00:37.527 --> 00:00:40.195
of that firm and then
the revenue of that firm

00:00:40.195 --> 00:00:42.866
would be turned into the expenses

00:00:42.866 --> 00:00:45.209
and the profit of the
firm, so whatever the

00:00:45.209 --> 00:00:47.198
revenue wasn't used in expenses ended up

00:00:47.198 --> 00:00:48.001
being profit.

00:00:48.001 --> 00:00:50.119
Then all of that went back to that one

00:00:50.119 --> 00:00:52.119
household as income.

00:00:52.119 --> 00:00:54.280
When we talked about how we would measure

00:00:54.280 --> 00:00:57.389
the economic activity in this island

00:00:57.389 --> 00:00:58.879
right over here, how would we measure its

00:00:58.879 --> 00:01:00.164
gross domestic product, we said,

00:01:00.164 --> 00:01:02.193
well look we could measure it in multiple

00:01:02.193 --> 00:01:03.133
different ways.

00:01:03.133 --> 00:01:05.629
As it's leaving his
hands, the dollars that is

00:01:05.629 --> 00:01:07.653
going to the firm, you
could view it as the

00:01:07.653 --> 00:01:09.796
total expenditures, or as it's approaching

00:01:09.796 --> 00:01:11.723
the firm that's the
same thing as the total

00:01:11.723 --> 00:01:15.468
revenue for this firm,
total revenue for this

00:01:15.468 --> 00:01:18.795
simplified, one firm economy.

00:01:18.795 --> 00:01:21.136
That total revenue is
the same thing as the

00:01:21.136 --> 00:01:24.991
total expenses plus the
profit for that firm.

00:01:24.991 --> 00:01:27.050
That's the same thing as this one

00:01:27.050 --> 00:01:28.320
households income.

00:01:28.320 --> 00:01:29.657
So, let me write this down.

00:01:29.657 --> 00:01:30.985
The way we looked at it in the last video,

00:01:30.985 --> 00:01:34.654
in the very simple
example, GDP was equal to

00:01:34.654 --> 00:01:39.098
household, household
expenditures which was equal

00:01:39.098 --> 00:01:46.110
to firm, firm revenues
which was equal to firm

00:01:46.110 --> 00:01:51.201
expenses, expenses plus profit,

00:01:51.201 --> 00:01:54.664
which is equal to household income.

00:01:54.664 --> 00:01:57.518
(writing) household income, household ..

00:01:57.518 --> 00:02:00.813
I'll just write inc for
income, household income.

00:02:00.813 --> 00:02:02.654
and of course household income is then,

00:02:02.654 --> 00:02:04.229
at least in this case right over here,

00:02:04.229 --> 00:02:08.530
it ended up being equal
to household expenses.

00:02:08.530 --> 00:02:10.315
What I want to do in this video now is

00:02:10.315 --> 00:02:11.922
think about it in more general terms.

00:02:11.922 --> 00:02:13.779
Let's extend it to a more complex economy,

00:02:13.779 --> 00:02:16.562
to the world we live in and
with that I want to look

00:02:16.562 --> 00:02:19.677
at the more formal definition for GDP.

00:02:19.677 --> 00:02:23.097
This is the more formal definition of GDP,

00:02:23.097 --> 00:02:25.785
or I guess you could say
the definition of GDP

00:02:25.785 --> 00:02:29.718
and it's the market
value of all final goods

00:02:29.718 --> 00:02:31.527
and services, and we're
going to talk about what

00:02:31.527 --> 00:02:34.257
each of these things
mean ... of all, of all

00:02:34.257 --> 00:02:36.196
final goods and services.

00:02:36.196 --> 00:02:40.988
I'll underline all
separately, all final goods

00:02:40.988 --> 00:02:42.385
and services.

00:02:42.385 --> 00:02:44.318
Let me do that in a different color.

00:02:44.318 --> 00:02:48.311
... all final goods and
services produced within

00:02:48.311 --> 00:02:51.116
a country, produced within a country

00:02:51.116 --> 00:02:52.941
in a given period.

00:02:52.941 --> 00:02:54.914
You can have a GDP for a month,

00:02:54.914 --> 00:02:57.648
you could have a GDP
for a quarter of a year

00:02:57.648 --> 00:02:59.455
which would be three
months or you could have

00:02:59.455 --> 00:03:01.385
the GDP in a given year.

00:03:01.385 --> 00:03:02.660
I guess you could even have GDP over a

00:03:02.660 --> 00:03:04.366
10 year period, but it tends to be

00:03:04.366 --> 00:03:06.320
we always think of GDP
in terms of annual GDP

00:03:06.320 --> 00:03:08.517
or quarterly GDP or sometimes even ...

00:03:08.517 --> 00:03:10.448
so there are some estimates
of even monthly GDP

00:03:10.448 --> 00:03:13.657
but it tends to be annually or quarterly.

00:03:13.657 --> 00:03:15.390
Let's parse a little
bit more because these

00:03:15.390 --> 00:03:16.928
little terms can be interesting.

00:03:16.928 --> 00:03:19.280
The first one I'd like
to parse is the idea of

00:03:19.280 --> 00:03:20.655
market value.

00:03:20.655 --> 00:03:22.943
(writing) Market value.

00:03:22.943 --> 00:03:25.454
What this is saying is we
need someway to measure

00:03:25.454 --> 00:03:28.500
what we've produced
and the best way we can

00:03:28.500 --> 00:03:29.783
do it is say, how much
benefit are people getting

00:03:29.783 --> 00:03:31.450
and what they're willing
to pay for it in the

00:03:31.450 --> 00:03:32.945
market is the best way that we can measure

00:03:32.945 --> 00:03:34.988
how much benefit they're actually getting

00:03:34.988 --> 00:03:35.992
out of it.

00:03:35.992 --> 00:03:40.717
For example, if someone in the year,

00:03:40.717 --> 00:03:46.119
I don't know, if an avocado was produced,

00:03:46.119 --> 00:03:49.864
if an avocado is produced in some farm

00:03:49.864 --> 00:03:53.363
and also an orange is produced,

00:03:53.363 --> 00:03:55.791
and an orange is produced,

00:03:55.791 --> 00:03:58.388
we won't say that for each of these,

00:03:58.388 --> 00:04:00.918
we won't say, oh GDP is
increased to buy one fruit

00:04:00.918 --> 00:04:02.529
we'd look at the market value for it.

00:04:02.529 --> 00:04:04.384
If the market value of this avocado is

00:04:04.384 --> 00:04:08.992
$1 and the market value of
this orange is 0.50 cents

00:04:08.992 --> 00:04:13.704
then by producing this fruit the GDP has

00:04:13.704 --> 00:04:15.781
increased by 0.50 cents by producing this

00:04:15.781 --> 00:04:18.971
avocado its GDP has increased by a dollar.

00:04:18.971 --> 00:04:22.652
In the next year, maybe there's whatever,

00:04:22.652 --> 00:04:25.057
demand for avocado's goes down or whatever

00:04:25.057 --> 00:04:27.525
and people pay less for
it and the market value

00:04:27.525 --> 00:04:30.051
of an incremental avocado is 0.50 cents,

00:04:30.051 --> 00:04:32.921
then in the next year
even though the actual

00:04:32.921 --> 00:04:35.331
number of fruit that
was produced is the same

00:04:35.331 --> 00:04:37.531
as the previous year, now all of a sudden

00:04:37.531 --> 00:04:39.534
the contribution from
avocado's might be the same

00:04:39.534 --> 00:04:41.414
as a contribution from oranges.

00:04:41.414 --> 00:04:44.267
It really depends on the market value.

00:04:44.267 --> 00:04:48.698
Then we can focus on this
all, the market value of all

00:04:48.698 --> 00:04:51.603
goods and services,
all goods and services.

00:04:51.603 --> 00:04:53.668
We would do all the different avocado's

00:04:53.668 --> 00:04:55.906
and oranges, but we would do computers,

00:04:55.906 --> 00:04:59.051
we would do cars, we would do tires,

00:04:59.051 --> 00:05:02.789
and we're doing services,
so if you have help

00:05:02.789 --> 00:05:04.667
at home, if you go to the doctor;

00:05:04.667 --> 00:05:07.664
the market value of all of
those things are going to

00:05:07.664 --> 00:05:10.061
be put in to GDP.

00:05:10.061 --> 00:05:12.268
This won't include some things.

00:05:12.268 --> 00:05:16.132
This does not include,
this does not include

00:05:16.132 --> 00:05:17.669
illegal things.

00:05:17.669 --> 00:05:19.076
If someone sells someone else drugs

00:05:19.076 --> 00:05:19.931
we're not keeping track of it.

00:05:19.931 --> 00:05:21.260
Some would argue that maybe it should be

00:05:21.260 --> 00:05:23.062
kept track of in some
way, that you have this

00:05:23.062 --> 00:05:25.371
kind of black market in things,

00:05:25.371 --> 00:05:28.316
but you're not keeping track of illegal,

00:05:28.316 --> 00:05:30.222
(writing) illegal activity.

00:05:30.222 --> 00:05:32.268
And you're also not keeping track of goods

00:05:32.268 --> 00:05:34.338
and services that are produced within

00:05:34.338 --> 00:05:37.137
the household and consumed
within the household.

00:05:37.137 --> 00:05:42.145
For example, if you hire an outside person

00:05:42.145 --> 00:05:46.325
to babysit your child
that would be considered

00:05:46.325 --> 00:05:49.003
part of GDP, that is
a service that you are

00:05:49.003 --> 00:05:52.480
paying for, but if you,
yourself, are babysitting

00:05:52.480 --> 00:05:54.813
your children that is not
going to be considered

00:05:54.813 --> 00:05:56.230
in GDP.

00:05:56.230 --> 00:05:58.143
If I start a lawn-mowing business

00:05:58.143 --> 00:05:59.806
and I go mow other people's lawns,

00:05:59.806 --> 00:06:03.070
or maybe before my wife and I were dating,

00:06:03.070 --> 00:06:05.736
she used to pay me to mow my lawns

00:06:05.736 --> 00:06:07.342
then it would be included in GDP,

00:06:07.342 --> 00:06:09.742
but maybe once we get
married I just mow her lawn

00:06:09.742 --> 00:06:12.878
because we're in the same family now

00:06:12.878 --> 00:06:15.069
then it will not be included in GDP.

00:06:15.069 --> 00:06:18.266
All does include pretty
much everything that

00:06:18.266 --> 00:06:21.952
can be tracked, anything where there is an

00:06:21.952 --> 00:06:24.052
exchange of money, there's some payment

00:06:24.052 --> 00:06:27.364
between two parties for
that good or service.

00:06:27.364 --> 00:06:28.727
Now a really interesting thing

00:06:28.727 --> 00:06:30.183
and this is something I
used to find confusing

00:06:30.183 --> 00:06:32.202
when I first got exposed to GDP,

00:06:32.202 --> 00:06:35.114
is the whole notion of
final goods and services.

00:06:35.114 --> 00:06:37.786
To understand this, let's think about,

00:06:37.786 --> 00:06:41.490
let's think about how
jeans might be produced.

00:06:41.490 --> 00:06:45.725
You have a cotton farmer, a cotton farmer

00:06:45.725 --> 00:06:48.452
and there's some service
that needs to be performed

00:06:48.452 --> 00:06:52.114
so whatever some farming,
some labor that needs

00:06:52.114 --> 00:06:53.286
to be performed.

00:06:53.286 --> 00:06:55.927
Let's say that that is $5 of labor

00:06:55.927 --> 00:06:58.799
and let's say that some
land has to be rented.

00:06:58.799 --> 00:07:01.481
Let's say that that is $5
of ... I'll just make it

00:07:01.481 --> 00:07:04.710
a different number, $4 of land.

00:07:04.710 --> 00:07:05.059
(writing) $4 of land.

00:07:05.059 --> 00:07:06.526
There are other inputs,
but we don't have to

00:07:06.526 --> 00:07:07.523
go into all the details.

00:07:07.523 --> 00:07:09.388
With that, there's going
to be some electricity

00:07:09.388 --> 00:07:11.659
and things like that, but
we won't count all of it.

00:07:11.659 --> 00:07:15.191
You can produce some cotton,
just the plant cotton.

00:07:15.191 --> 00:07:17.444
(writing) you can produce,
you can produce some

00:07:17.444 --> 00:07:18.857
cotton, some raw cotton.

00:07:18.857 --> 00:07:22.251
That raw cotton is worth,
the market value of that

00:07:22.251 --> 00:07:25.448
raw cotton is worth,
let's say it's worth $10.

00:07:25.448 --> 00:07:28.660
So, it's $10 worth of raw cotton.

00:07:28.660 --> 00:07:32.552
Then you can take that raw cotton

00:07:32.552 --> 00:07:35.662
and you could combine
it with some more labor

00:07:35.662 --> 00:07:37.269
(writing) with some more labor

00:07:37.269 --> 00:07:39.131
so let's say you combine
that with another,

00:07:39.131 --> 00:07:41.160
I don't know, $6 of labor.

00:07:41.160 --> 00:07:44.077
(writing) $6 of labor

00:07:44.077 --> 00:07:45.933
and it would also probably require some

00:07:45.933 --> 00:07:47.744
machinery and electricity
and things like that,

00:07:47.744 --> 00:07:50.001
but I won't factor all of
those things in just now.

00:07:50.001 --> 00:07:52.571
We don't need them to
get the point across.

00:07:52.571 --> 00:07:54.995
If I do that, if I combine the $10,

00:07:54.995 --> 00:07:58.527
this intermediate good
with the $6 of labor

00:07:58.527 --> 00:08:01.468
then all of a sudden I
can produce cotton thread.

00:08:01.468 --> 00:08:05.321
(writing) I can produce, I
can produce cotton thread.

00:08:05.321 --> 00:08:07.528
That cotton, the worth of the market value

00:08:07.528 --> 00:08:10.198
of that cotton thread
let's say is now $20.

00:08:10.198 --> 00:08:12.203
(writing) is now $20

00:08:12.203 --> 00:08:13.742
And maybe there is another
intermediate good there,

00:08:13.742 --> 00:08:15.404
maybe it's some dye.

00:08:15.404 --> 00:08:18.266
We'll put the dye in
later, let's do the dye

00:08:18.266 --> 00:08:19.064
in later.

00:08:19.064 --> 00:08:21.532
I have a $20 thread,
and let's say I can take

00:08:21.532 --> 00:08:22.793
that $20 thread.

00:08:22.793 --> 00:08:25.175
(writing) I can take that $20 thread,

00:08:25.175 --> 00:08:28.196
stay with white just
because I started there.

00:08:28.196 --> 00:08:31.546
I can take that $20
thread and I can put in

00:08:31.546 --> 00:08:34.286
some more labor, maybe
I can take $10 of labor

00:08:34.286 --> 00:08:36.752
(writing) $10 of labor

00:08:36.752 --> 00:08:39.008
and then I can essentially create,

00:08:39.008 --> 00:08:42.105
it will essentially create $30 worth of,

00:08:42.105 --> 00:08:44.051
$30 of cotton fabric.

00:08:44.051 --> 00:08:47.072
(writing) $30 worth of cotton fabric.

00:08:47.072 --> 00:08:49.411
Then I can take that $30
worth of cotton fabric

00:08:49.411 --> 00:08:51.593
(writing) $30 worth of cotton fabric

00:08:51.593 --> 00:08:55.737
plus some more labor, let's
say another $5 of labor.

00:08:55.737 --> 00:08:57.861
(writing) $5 of labor

00:08:57.861 --> 00:08:59.996
and let's say we're also going to put in

00:08:59.996 --> 00:09:01.745
$1 of dye.

00:09:01.745 --> 00:09:04.743
(writing) $1 of dye right over here.

00:09:04.743 --> 00:09:06.735
In the process I can create,

00:09:06.735 --> 00:09:09.936
I can create the market value,

00:09:09.936 --> 00:09:11.742
let's say this is $50 worth of blue jeans.

00:09:11.742 --> 00:09:16.821
(writing) $50 worth, worth of, blue jeans,

00:09:16.821 --> 00:09:18.260
blue jeans.

00:09:18.260 --> 00:09:21.075
I do this all over the course of the year,

00:09:21.075 --> 00:09:22.570
so the period in question.

00:09:22.570 --> 00:09:24.127
So the period for this
one I'll assume the period

00:09:24.127 --> 00:09:26.863
is a year, so it's all
happening over the course

00:09:26.863 --> 00:09:28.796
of the period in question.

00:09:28.796 --> 00:09:31.330
We're talking about the GDP in 2012,

00:09:31.330 --> 00:09:33.461
this is all happening in 2012.

00:09:33.461 --> 00:09:36.664
What would be the contribution to GDP.

00:09:36.664 --> 00:09:38.465
If we didn't have the word final here,

00:09:38.465 --> 00:09:40.456
we just had the market value of all goods

00:09:40.456 --> 00:09:42.791
and services then we would add this $5

00:09:42.791 --> 00:09:45.403
to this $4 to this $10 to this $6

00:09:45.403 --> 00:09:48.193
and because of the
production of this jeans

00:09:48.193 --> 00:09:50.128
we would get a very, very large number,

00:09:50.128 --> 00:09:52.826
a very, very large contribution to GDP.

00:09:52.826 --> 00:09:54.992
But that would be, not
even double counting

00:09:54.992 --> 00:09:56.261
that would be triple, or quadrupling,

00:09:56.261 --> 00:09:58.771
or quintuple counting
the value that's actually

00:09:58.771 --> 00:09:59.934
being created because all of this value

00:09:59.934 --> 00:10:04.277
is essentially being
created for in this end $50.

00:10:04.277 --> 00:10:07.605
The actual contribution
to GDP you would only put

00:10:07.605 --> 00:10:10.603
the final good, so you
wouldn't include all of these

00:10:10.603 --> 00:10:12.684
other intermediary goods and services,

00:10:12.684 --> 00:10:15.121
you would just say this
whole chain of event

00:10:15.121 --> 00:10:20.196
results in a $50 increase in GDP.

00:10:20.196 --> 00:10:21.993
In another video we'll
talk about what happens

00:10:21.993 --> 00:10:24.130
if they don't get to this
point during the course

00:10:24.130 --> 00:10:26.404
of the year, if we just stop at one of the

00:10:26.404 --> 00:10:27.608
intermediary goods.

00:10:27.608 --> 00:10:29.605
Assuming you get to this
point, you just include

00:10:29.605 --> 00:10:31.790
the final good in GDP.

00:10:31.790 --> 00:10:36.459
This last part of it is,
produced within a country.

00:10:36.459 --> 00:10:38.082
(writing) produced within a country.

00:10:38.082 --> 00:10:40.149
This is, you might have heard GNP,

00:10:40.149 --> 00:10:41.496
gross national product and that's the

00:10:41.496 --> 00:10:42.417
main difference.

00:10:42.417 --> 00:10:45.619
GDP says, let's say
we're talking about the

00:10:45.619 --> 00:10:48.209
United States, that's my best attempt at

00:10:48.209 --> 00:10:49.185
drawing the United States.

00:10:49.185 --> 00:10:51.686
GDP says look, if it was produced inside

00:10:51.686 --> 00:10:54.257
the country, if it was
produced inside the country,

00:10:54.257 --> 00:10:56.033
we don't care who it was produced by.

00:10:56.033 --> 00:10:57.853
It could have been
produced by someone from

00:10:57.853 --> 00:10:59.395
Mexico, or it could have been produced by

00:10:59.395 --> 00:11:01.307
someone from Canada, it
could have been a factory

00:11:01.307 --> 00:11:03.549
that's owned by the Chinese, but if it was

00:11:03.549 --> 00:11:06.803
produced within the borders
of the United States

00:11:06.803 --> 00:11:08.918
it gets counted as GDP.

00:11:08.918 --> 00:11:11.522
(writing) It gets counted as GDP.

00:11:11.522 --> 00:11:13.801
If an American, if an American who's an

00:11:13.801 --> 00:11:15.796
American national goes overseas

00:11:15.796 --> 00:11:18.055
and produces something,
that is not counted

00:11:18.055 --> 00:11:19.131
as GDP.

00:11:19.131 --> 00:11:21.966
If an American owns a
firm in another country

00:11:21.966 --> 00:11:24.387
and that firm in the
other country produces

00:11:24.387 --> 00:11:26.383
something, that is not the GDP.

00:11:26.383 --> 00:11:28.321
When you focus on peoples' nationality

00:11:28.321 --> 00:11:30.050
that is GNP.

00:11:30.050 --> 00:11:32.798
Not to confuse things,
but if you wanted to

00:11:32.798 --> 00:11:36.054
focus on GNP then you do
care about the earnings

00:11:36.054 --> 00:11:38.721
of American nationals and so you wouldn't

00:11:38.721 --> 00:11:40.803
count the Canadian, but you would include

00:11:40.803 --> 00:11:43.553
the American who's making money overseas.

00:11:43.553 --> 00:11:46.446
GDP fairly simple idea,
you say what's being

00:11:46.446 --> 00:11:47.928
produced within these boundaries,

00:11:47.928 --> 00:11:50.146
we don't care who's doing the producing

00:11:50.146 --> 00:11:52.142
and what their actual nationality is,

00:11:52.142 --> 00:11:54.555
and we're going to ignore production by

00:11:54.555 --> 00:11:58.153
that nationality outside of these borders.