Khan Stories: Mrs. Hengels' class

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Language: en

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- With my students, a lot
of them have not had a lot

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of academic success.

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They've faced a lot of obstacles.

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(chiming)

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That's what's great about Khan Academy is

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they have success.

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So I think that really builds them up.

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They're all working on the same program,

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but they're working on
very different things

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and the great thing about that is,

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there's no judgment.

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(cheering)

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They actually love Khan
Academy so much that they

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approached me to start a club that was

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specifically doing Khan Academy.

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They're asking to do math work

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outside of the regular school day,

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like totally their own motivation.

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These kids are creating social connections

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and boosting their self esteem

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and just feeling great about themselves

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all through the connection
of doing Khan Academy.

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(light music)


Introducing: Khan Academy Kids!

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Language: en

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- Hi everyone, Sal here with
my three year old son, Azad

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and we're excited to announce
the launch of Khan Academy

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Kids, which is designed to take
students like Azad ages 2-5

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to become lifelong learners.

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- Hi friend, welcome to my room.

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- [Sal] Kids love this program
because it's really fun.

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- Awesome!

00:00:16.902 --> 00:00:19.390
- [Sal] Friendly characters
like our narrator, Kody Bear--

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- Welcome to Khan Academy Kids.

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- [Sal] Interact with them throughout the

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learning experience.

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And we've combined tasks
like math and reading with

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activities like drawing and story telling.

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We really think parents and
teachers are going to love

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Khan Academy Kids because
it's aligned with important

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standards, like common core
and the Headstarts Learning

00:00:36.120 --> 00:00:37.370
Outcome's framework.

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There are thousands of
activities and original books in

00:00:39.900 --> 00:00:40.733
the program.

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Khan Academy Kids also promotes
social emotional development

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through topics like empathy and sharing.

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And what's more, we've partnered
with Super Simple songs,

00:00:49.380 --> 00:00:52.490
Bellwether Media, and National
Geographic Young Explorer

00:00:52.490 --> 00:00:55.970
magazine to provide learning
materials kids will love.

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Khan Academy Kids is a free
mobile app available in the App

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Store, Google Play, and Amazon.

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Download today, let the
joyful learning begin!

00:01:03.517 --> 00:01:05.300
(children laughing)

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Hi everyone, Sal here.

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I'm here to announce--

00:01:07.443 --> 00:01:08.276
(child squeals)

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(children laughing)

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Shh.

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Hi everyone, I'm here with my
son Azad, who's three years

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old, to announce the launch
of Khan Academy Kids, which is

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designed--

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(child squeals)

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(child laughing)

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Kids 2-5 ready to become
learners for life.

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(child chattering)

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Say it loud and funny!

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- Download today!

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- Download today and let
the joyful learning begin!

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(child squeals)

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How do they do this in movies?

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(child laughing)


Khan Stories: Isai Baltezar's class

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(light music)

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- In my classroom, I always
ask them, who are you.

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They know to respond, "I am
the leader of the world."

00:00:06.870 --> 00:00:08.614
And it's true, they are the future.

00:00:08.614 --> 00:00:11.870
(light music)

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The importance of
teachers is unquantifiable

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for this excess of students
because we do not just teach,

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but we really care about our students.

00:00:20.906 --> 00:00:23.620
(light music)

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We're also their mentors,
we're also their friends.

00:00:26.092 --> 00:00:28.592
(light music)

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Every teacher uses different tools

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to be an effective teacher.

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One of those tools that I choose to use

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because I believe the curriculum,

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the rigor in it is Khan Academy.

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So, it gives me immediate feedback

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of okay, this person understands,
or this person doesn't.

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Every student, every child, every life

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has a possibility to create something.

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Everyone deserves access
to free, quality education.

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Then we can really see the
power of education blossom.


Rounding to the nearest 10

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Language: en

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- [Instructor] In this video,

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we're going to be doing some rounding,

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which you're probably not
familiar with just yet

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but you'll see that it's
pretty straightforward

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and we're going to start by
rounding to the nearest 10.

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So the first question is,

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what is rounding and
why is it even useful?

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Well, let's say that
you have the number 37.

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It's a fine number.

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But let's say that you
have to do some math

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with the number 37

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and you can do a lot of
math with the number 37.

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But let's say you just wanna estimate

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what something might be.

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Let's say that if someone
says, hey, I have 37 pickles

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and you have 39 pickles,

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roughly, how many do we have together?

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We don't have to have it down

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to the exact number of pickles.

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Well then, rounding will
actually be a very useful tool.

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But let's just focus on what it means

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to round to the nearest 10.

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So when they're talking about
rounding to the nearest 10,

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we're gonna be thinking about
the tens place of the number.

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So we can see right over here

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in our tens place, we have a three.

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And so that three represents three tens.

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So the number 37, it's
three tens and seven ones,

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so it is more than three tens

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and it's gonna be less than four tens.

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So this number is going to
be more than three tens,

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I could do it like this.

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It's gonna be more than three tens,

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which we can represent like
that, three tens and zero ones,

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or you might know that as 30,

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and it's going to be less than four tens

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or also known as 40.

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And so, when you're rounding,

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you're either going to
round to the number of tens

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that is right below this number

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or the number of tens
that is right above that.

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But how do we know whether 37

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rounded to the nearest 10
is going to be 30 or 40?

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Well, to answer that question,

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let's first just do it
visually on a number line.

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And then we can come up with
some rules for ourselves.

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And so, first of all,
let's just count by tens

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and we make sure we include 30 and 40.

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So, if we start at zero, 10,

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20, actually, let me have
a little bit more space

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'cause I wanna see the interesting things

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that are going to go on.

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Zero, 10,

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20, 30,

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40, that's enough, but
I could just go to 50

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just to complete this number line.

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And so, where is 37 on this number line?

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Well, it's between 30 and 40,

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and if I wanted to make
it a little bit clear,

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if I said that this is
35 right over there,

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right in between 30 and 40,

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then 37 is going to be right about,

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right about here.

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So, that is 37.

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And so, when you're
rounding to the nearest 10,

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and remember, we're picking

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between three tens and four tens,

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you say which 10 is it closest to.

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Is it closer to three tens
or is it closer to four tens?

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Well, you can just look at this

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and say, hey, it looks a
lot closer to four tens.

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And so in this situation,

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37 rounded to the nearest 10

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is going to be 40.

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And so, you might ask a question,

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well, give me another number.

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What if someone said 32

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rounded to the nearest 10?

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Well, 32 is going to be right over here.

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And then you'd say, all right,

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well, that's between
three tens and four tens,

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but it's a lot closer to three tens,

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so 32 rounded to the
nearest 10 is going to be,

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is going to be 30.

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Now, an interesting question
that you might be wondering

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is what if you're right in between?

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What if we wanted to round
35 to the nearest 10?

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35, once again, it's between
three tens and four tens,

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between 30 and 40.

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Which one do we round to

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if we wanna round to the nearest 10?

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Well, the rule is, and this
is really just something

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that the society has decided on

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is that if you're right in
the middle, you round up,

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so the number 35 is
going to round up to 40.

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Even though it's exactly five away

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from each of these numbers,

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35, if you're right in between,
is going to round up to 40.

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If you're a little bit less than 35,

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then you're going to round down to 30.

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With that out of the way,
let's do some more examples.

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Let's do, actually, let's do an example

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of a three-digit number,

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where we're rounding to the nearest 10.

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Let's say that we want
to round the number 124

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to the nearest 10.

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Well, there's a couple of ways

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that you could think about this.

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You could say that this is
100, two tens and four ones.

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Or you could even view this
as 12 tens and four ones.

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So you could say, hey, this is in between,

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12 tens and four ones,
it's greater than 12 tens,

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which is 120, and it's less than 13 tens,

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which is 130.

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These are the two tens that
are closest to this number.

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And then to decide which one it rounds to,

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you might already be
able to think about it

00:05:19.300 --> 00:05:21.370
based on some of the
rules we came up with,

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but let me draw it on
a number line for you.

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So we draw a number line,

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and I'm not going to start at zero,

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because we have to get all the way to 130,

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so let's just start,
I'll start at a hundred.

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So, this is 100, 110,

00:05:36.700 --> 00:05:39.373
let me draw the number line,
we're going to have 120,

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then we go to 130.

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I'll just do 140 here

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just for filling out the number
line that I've drawn so far.

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And then I'll draw the
halfway mark, which is 125.

00:05:53.390 --> 00:05:54.900
And then, see its halfway,

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so maybe a little bit closer to there.

00:05:57.490 --> 00:06:00.750
And then 124, we do it in this red color,

00:06:00.750 --> 00:06:03.520
124 is right over there.

00:06:03.520 --> 00:06:05.690
124.

00:06:05.690 --> 00:06:09.410
And so, if we're trying to
pick between 120 and 130,

00:06:09.410 --> 00:06:14.410
between 12 tens and 13 tens,
which one is it closer to?

00:06:14.500 --> 00:06:17.030
Well, we can see it's
only four away from 120

00:06:17.030 --> 00:06:21.420
while it's six away from
130, so we would round down,

00:06:21.420 --> 00:06:25.640
we're going to round down
to 120 in this situation

00:06:25.640 --> 00:06:28.670
if we're rounding to the nearest 10.

00:06:28.670 --> 00:06:31.627
If this was 125 or 126

00:06:31.627 --> 00:06:36.020
or 127 or 128 or 129, well
then, we would round to 130.

00:06:36.020 --> 00:06:41.020
And of course, if it was 130,
we would round it to 130.

00:06:41.090 --> 00:06:43.270
Let's do one more example.

00:06:43.270 --> 00:06:45.570
And actually, I'm going
to do a one-digit number.

00:06:45.570 --> 00:06:48.990
Let's say we wanna round
seven to the nearest 10.

00:06:48.990 --> 00:06:53.990
I'll write it out, round
seven to the nearest,

00:06:54.860 --> 00:06:56.160
nearest 10.

00:06:56.160 --> 00:06:58.360
Pause this video and
see if you can do that.

00:06:59.690 --> 00:07:04.390
All right, well, seven
is between what two tens?

00:07:04.390 --> 00:07:08.880
Well, seven is less than one ten,

00:07:08.880 --> 00:07:13.090
so it's less than one ten, and
it's greater than zero tens.

00:07:13.090 --> 00:07:15.800
So, it's between zero
tens, which is just zero,

00:07:15.800 --> 00:07:19.800
and one ten, which is 10, but
which one does it round to?

00:07:19.800 --> 00:07:22.763
Well here, once again, we
can draw our number line.

00:07:23.850 --> 00:07:28.180
So, we'll do zero and then this is five

00:07:28.180 --> 00:07:30.290
and then this is 10,

00:07:30.290 --> 00:07:33.410
and seven is right about there.

00:07:33.410 --> 00:07:34.810
That is where seven is.

00:07:34.810 --> 00:07:37.060
And we can either visually see that seven

00:07:37.060 --> 00:07:38.567
is closer to 10 than it is to zero.

00:07:38.567 --> 00:07:40.330
It's only three away from 10

00:07:40.330 --> 00:07:42.110
while it's seven away from zero,

00:07:42.110 --> 00:07:45.000
so you would round up to 10.

00:07:45.000 --> 00:07:47.270
Or you can use the rule
that we just thought about.

00:07:47.270 --> 00:07:51.270
Seven is greater than or equal to five,

00:07:51.270 --> 00:07:53.160
so you round up.

00:07:53.160 --> 00:07:56.610
You round to the 10 that
is higher than this number.

00:07:56.610 --> 00:08:01.140
If this number was, if in
this ones place, I can say,

00:08:01.140 --> 00:08:04.200
if your ones place is between zero,

00:08:04.200 --> 00:08:06.350
it's greater than or equal to zero

00:08:06.350 --> 00:08:10.050
but less than five, then you round down.

00:08:10.050 --> 00:08:12.630
And you can see that happens
in all of these situations.

00:08:12.630 --> 00:08:16.180
If you look at 37, you
look at the ones place

00:08:16.180 --> 00:08:20.170
and your ones place here is
greater than or equal to five,

00:08:20.170 --> 00:08:22.130
so you round up.

00:08:22.130 --> 00:08:25.520
Here, if your ones
place, it's greater than

00:08:25.520 --> 00:08:28.540
or equal to five, it's five
exactly in that situation,

00:08:28.540 --> 00:08:31.580
so it's equal to five,
once again, you round up.

00:08:31.580 --> 00:08:35.100
If your ones place is less than five,

00:08:35.100 --> 00:08:38.160
well, in this situation, we round down.

00:08:38.160 --> 00:08:42.660
If your ones place is less
than five, you round down.

00:08:42.660 --> 00:08:44.930
Your ones place, and here,
you only have a ones place,

00:08:44.930 --> 00:08:48.423
but it's greater than or
equal to five, we round it up.


Three digit addition word problems

WEBVTT
Kind: captions
Language: en

00:00:00.500 --> 00:00:01.420
- [Instructor] We're told,

00:00:01.420 --> 00:00:05.900
the table gives the amounts
of materials Aya recycled.

00:00:05.900 --> 00:00:07.550
So we have the different materials here,

00:00:07.550 --> 00:00:09.260
and then it gives the various amounts.

00:00:09.260 --> 00:00:13.890
How many kilograms of paper
and aluminum did Aya recycle?

00:00:13.890 --> 00:00:17.410
So pause this video and see
if you can figure this out.

00:00:17.410 --> 00:00:20.950
Okay, so we're thinking
about paper and aluminum,

00:00:20.950 --> 00:00:24.000
so paper is right over here.

00:00:24.000 --> 00:00:27.950
She recycled 277 kilograms of paper.

00:00:27.950 --> 00:00:30.750
And aluminum is right over here.

00:00:30.750 --> 00:00:33.640
She recycled 134 kilograms of aluminum.

00:00:33.640 --> 00:00:36.260
And so we want the
combination, or the sum,

00:00:36.260 --> 00:00:39.540
of paper and aluminum, so it's going to be

00:00:39.540 --> 00:00:44.540
277 kilograms plus 134 kilograms.

00:00:46.880 --> 00:00:50.680
So we really need to figure
out what 277 plus 134 is,

00:00:50.680 --> 00:00:52.330
and in multiple videos, we have talked

00:00:52.330 --> 00:00:55.470
about how there's many different
ways of approaching this.

00:00:55.470 --> 00:00:58.930
We could say, well let's
just break up the 134.

00:00:58.930 --> 00:01:01.680
We could start at, actually let
me do this on a number line.

00:01:01.680 --> 00:01:03.750
That sometimes is a fun thing to do.

00:01:03.750 --> 00:01:07.420
So if we were to just say,
this is our number line,

00:01:07.420 --> 00:01:11.603
and we're going to start
at 277 right over there.

00:01:12.570 --> 00:01:16.780
So first, we could add
100, because we have 100

00:01:16.780 --> 00:01:18.490
right over there, so let's do that.

00:01:18.490 --> 00:01:23.240
If we add 100, so plus
100, where does it get us?

00:01:23.240 --> 00:01:27.720
Well if we add 100 here, we get to 377.

00:01:27.720 --> 00:01:32.290
So 300, I'll just write, 77.

00:01:32.290 --> 00:01:36.410
And then we could add three 10s, or 30.

00:01:36.410 --> 00:01:38.610
So then we're going to add 30.

00:01:38.610 --> 00:01:43.610
So let's add 30, so plus 30.

00:01:44.260 --> 00:01:45.790
What does that get us?

00:01:45.790 --> 00:01:47.500
So this is interesting.

00:01:47.500 --> 00:01:52.500
If you add 30 to 370,

00:01:52.870 --> 00:01:56.510
you would get to 400,

00:01:56.510 --> 00:01:58.240
and then we have another seven there,

00:01:58.240 --> 00:02:01.790
so that gets us to 407.

00:02:01.790 --> 00:02:04.250
So then we get to 407.

00:02:04.250 --> 00:02:05.960
And once again, this is just one way

00:02:05.960 --> 00:02:06.960
to try to think about it.

00:02:06.960 --> 00:02:10.670
And then, last but not
least, we could add the four.

00:02:10.670 --> 00:02:12.820
So then you say, we're there right now,

00:02:12.820 --> 00:02:16.630
and then we add plus four,
and seven plus four is 11,

00:02:16.630 --> 00:02:20.590
so 407 plus four is 411.

00:02:20.590 --> 00:02:24.730
So how many kilograms of paper
and aluminum did Aya recycle?

00:02:24.730 --> 00:02:27.940
Would be 411 kilograms.

00:02:27.940 --> 00:02:31.203
Kilo, kilograms, and we're done.


Estimating adding large numbers by rounding

WEBVTT
Kind: captions
Language: en

00:00:00.240 --> 00:00:02.310
- [Instructor] Let's say
that we run an egg farm,

00:00:02.310 --> 00:00:06.380
and yesterday, we went out
and we collected 398 eggs

00:00:06.380 --> 00:00:08.170
from the chickens, and then today,

00:00:08.170 --> 00:00:12.690
we went out and we collected
251 eggs from the chickens.

00:00:12.690 --> 00:00:14.350
And what we're curious about is,

00:00:14.350 --> 00:00:17.100
roughly how many eggs do we now have

00:00:17.100 --> 00:00:19.430
that we've collected
over the last two days?

00:00:19.430 --> 00:00:21.630
Well, there's a few ways we could do that.

00:00:21.630 --> 00:00:25.200
We could just add 398 to 251,

00:00:25.200 --> 00:00:27.920
and figure out what that is equal to.

00:00:27.920 --> 00:00:29.670
But let's say that we
don't have a lot of time,

00:00:29.670 --> 00:00:32.150
and we don't have paper, and
we want to do it in our heads,

00:00:32.150 --> 00:00:34.210
and we don't care about the exact number.

00:00:34.210 --> 00:00:37.820
We want to know roughly
how many eggs do we have?

00:00:37.820 --> 00:00:41.390
Well, that's where the tool
of estimating is useful.

00:00:41.390 --> 00:00:43.920
So instead of saying the
exact amount of eggs,

00:00:43.920 --> 00:00:46.050
we could say, how many do we roughly have?

00:00:46.050 --> 00:00:48.580
And that's what this
squiggly equal sign means,

00:00:48.580 --> 00:00:50.940
it means, hey, we don't have
to get the exact number,

00:00:50.940 --> 00:00:52.710
but how many do we roughly have?

00:00:52.710 --> 00:00:54.920
And so we will be estimating.

00:00:54.920 --> 00:00:57.170
And the way that we can do that

00:00:57.170 --> 00:00:59.880
is that we can round each of these numbers

00:00:59.880 --> 00:01:02.350
to a number that is close to them,

00:01:02.350 --> 00:01:05.130
but that's easier to add in our heads,

00:01:05.130 --> 00:01:07.160
and then we add those two numbers.

00:01:07.160 --> 00:01:09.810
So pause this video, and see
if you can do that on your own

00:01:09.810 --> 00:01:11.540
before we do it together.

00:01:11.540 --> 00:01:13.570
Alright, now let's do this together.

00:01:13.570 --> 00:01:18.570
Let's start with 398, and let's
round it to the nearest 10.

00:01:19.430 --> 00:01:21.730
So, 398, you can view this as,

00:01:21.730 --> 00:01:23.580
we have a nine in the 10s place,

00:01:23.580 --> 00:01:28.210
but you could view this
as 39 10s, and eight.

00:01:28.210 --> 00:01:30.970
The 10 that it is right directly above

00:01:30.970 --> 00:01:35.800
is exactly 39 10s and zero ones, or 390,

00:01:35.800 --> 00:01:40.640
and then the next ten would
be if we go up to 40 10s,

00:01:40.640 --> 00:01:44.440
which would be the same thing as 400.

00:01:44.440 --> 00:01:47.370
Now, which one would we round to?

00:01:47.370 --> 00:01:52.370
Well, 398 is closer to
400 than it is to 390,

00:01:52.730 --> 00:01:54.610
and we've talked about
in the rounding videos

00:01:54.610 --> 00:01:56.050
that you can see that this right over here

00:01:56.050 --> 00:01:59.970
is five or greater, so we
would round the 10s place up.

00:01:59.970 --> 00:02:02.187
So we would round to 400.

00:02:03.630 --> 00:02:07.720
And so, 398, we round to 400.

00:02:07.720 --> 00:02:11.020
And then we're going to add that to 251,

00:02:11.020 --> 00:02:13.410
what's that rounded to the nearest 10?

00:02:13.410 --> 00:02:15.000
So I'll do that again, right over here.

00:02:15.000 --> 00:02:15.833
251.

00:02:17.440 --> 00:02:21.670
The 10 that is right below
that is going to be 250.

00:02:21.670 --> 00:02:23.860
The 10 that is right above that

00:02:23.860 --> 00:02:26.233
is going to be 260.

00:02:27.610 --> 00:02:30.440
Once again, you could view
this as 25 10s and one.

00:02:30.440 --> 00:02:35.440
And 251 is clearly closer
to 250, we can round down.

00:02:35.470 --> 00:02:38.510
Another way to think about it
is, you look at the 10s place,

00:02:38.510 --> 00:02:40.210
and then you look at the ones place,

00:02:40.210 --> 00:02:43.410
and you say, hey, this is less than five,

00:02:43.410 --> 00:02:46.240
so I'm gonna round down
to on the 10s place,

00:02:46.240 --> 00:02:47.940
so we get to 250.

00:02:47.940 --> 00:02:51.430
So when you round 251 to the nearest 10,

00:02:51.430 --> 00:02:53.790
you're going to get 250.

00:02:53.790 --> 00:02:57.010
Now, I encourage you, add
these two in your head.

00:02:57.010 --> 00:02:58.913
What would this be equal to?

00:03:00.080 --> 00:03:01.780
Well, the way that I
think about it in my head,

00:03:01.780 --> 00:03:05.060
and there's a lot of different
ways to approach addition,

00:03:05.060 --> 00:03:06.520
but you could say, alright,

00:03:06.520 --> 00:03:09.880
I can think about the hundreds.

00:03:09.880 --> 00:03:12.650
I have four hundreds, and I'm
adding that to two hundreds,

00:03:12.650 --> 00:03:15.020
and let me do this in a new color.

00:03:15.020 --> 00:03:16.330
So if I have four hundreds,

00:03:16.330 --> 00:03:17.820
and I'm adding it to two hundreds,

00:03:17.820 --> 00:03:20.250
well, that's going to be six hundreds.

00:03:20.250 --> 00:03:25.130
And if I have zero 10s, and
if I'm adding it to five 10s,

00:03:25.130 --> 00:03:27.780
well, I'm still going to have five 10s,

00:03:27.780 --> 00:03:29.790
and then I have zero ones in either cases,

00:03:29.790 --> 00:03:31.740
so I'm still going to have zero ones.

00:03:31.740 --> 00:03:32.630
And so there you have it.

00:03:32.630 --> 00:03:37.630
We were able to estimate 398
plus 251 as being roughly 650.


Three digit subtraction word problems

WEBVTT
Kind: captions
Language: en

00:00:00.490 --> 00:00:03.050
- [Instructor] There are
461 homes in the part

00:00:03.050 --> 00:00:04.990
of town where Samir lives.

00:00:04.990 --> 00:00:09.300
He counted that 352 of
those homes are apartments.

00:00:09.300 --> 00:00:11.890
How many of the homes are not apartments?

00:00:11.890 --> 00:00:14.710
So like always, pause this video and see

00:00:14.710 --> 00:00:17.060
if you can work through it on your own.

00:00:17.060 --> 00:00:19.780
All right, now let's do this together.

00:00:19.780 --> 00:00:22.720
So we're starting with 461 homes.

00:00:22.720 --> 00:00:25.570
So we have 461, and we wanna know how many

00:00:25.570 --> 00:00:27.270
are not apartments.

00:00:27.270 --> 00:00:29.080
So what we wanna do is take out the number

00:00:29.080 --> 00:00:30.200
that are apartments.

00:00:30.200 --> 00:00:34.000
And they tell us that 352 of
those homes are apartments.

00:00:34.000 --> 00:00:36.690
So we'll take out the
number that are apartments

00:00:36.690 --> 00:00:39.000
and what we will left it with is going

00:00:39.000 --> 00:00:40.970
to be the number that are not apartments.

00:00:40.970 --> 00:00:45.490
So we really just have to
evaluate 461 minus 352.

00:00:45.490 --> 00:00:47.570
And as we've talked about in other videos

00:00:47.570 --> 00:00:49.840
there's many techniques for doing this.

00:00:49.840 --> 00:00:53.840
We could break apart 352 into
the various place values.

00:00:53.840 --> 00:00:56.680
So we could say that
this is the same thing

00:00:56.680 --> 00:01:01.680
as 461 minus, we'll do
this in different colors,

00:01:02.170 --> 00:01:07.170
minus three hundreds,
or 300, minus five tens,

00:01:08.420 --> 00:01:13.420
or 50, and then minus
two, and then minus two

00:01:15.930 --> 00:01:17.020
right over there.

00:01:17.020 --> 00:01:18.720
And then you might be able to figure out

00:01:18.720 --> 00:01:23.470
that 461 minus 300, that
that is going to be,

00:01:23.470 --> 00:01:25.610
I'm just taking three 100s from this,

00:01:25.610 --> 00:01:28.640
so that's going to be 161.

00:01:28.640 --> 00:01:31.980
And then if I subtract 50 from that, well,

00:01:31.980 --> 00:01:34.280
what's 61 minus 50?

00:01:34.280 --> 00:01:35.520
Well, that would be 11.

00:01:35.520 --> 00:01:38.550
So 161 minus 50 would be 111.

00:01:38.550 --> 00:01:40.010
Or another way of thinking about it

00:01:40.010 --> 00:01:42.470
is if you take these five 10s away

00:01:42.470 --> 00:01:45.150
from these six 10s, you'll
be left with one 10,

00:01:45.150 --> 00:01:48.180
so that would be 100, one 10, and one one.

00:01:48.180 --> 00:01:49.860
So you have 111.

00:01:49.860 --> 00:01:52.410
And then you want to subtract that two,

00:01:52.410 --> 00:01:55.680
last but not least, and 11
minus two would be nine.

00:01:55.680 --> 00:01:58.697
So 111 minus two would be equal to 109.

00:02:01.280 --> 00:02:03.620
But I mentioned there's many other ways

00:02:03.620 --> 00:02:06.580
that you might try to
approach something like this.

00:02:06.580 --> 00:02:09.010
You could say, hey, well maybe it's easier

00:02:09.010 --> 00:02:13.940
to subtract 50, or 350
I should say, then 352

00:02:13.940 --> 00:02:16.800
and so you could subtract two
from both of these numbers.

00:02:16.800 --> 00:02:20.120
So if you subtract two
from 461, if you subtract

00:02:20.120 --> 00:02:23.630
one you get to 460, you
subtract two you get to 459.

00:02:23.630 --> 00:02:28.630
459 minus, you subtract two
from this you get to 350.

00:02:28.880 --> 00:02:30.020
And this is all about the idea

00:02:30.020 --> 00:02:31.810
that the difference doesn't change as long

00:02:31.810 --> 00:02:34.090
as you add or subtract
the same number to both.

00:02:34.090 --> 00:02:36.290
And so here we might say that four 100s

00:02:36.290 --> 00:02:38.270
minus three 100s is 100.

00:02:38.270 --> 00:02:42.110
And then 59 minus 50 is nine.

00:02:42.110 --> 00:02:43.970
So we would get the same result.

00:02:43.970 --> 00:02:45.730
The thing to appreciate
is that this is all

00:02:45.730 --> 00:02:49.590
about subtracting 352
from 461 and that there's

00:02:49.590 --> 00:02:52.633
multiple ways of calculating this.


Rounding to the nearest 100

WEBVTT
Kind: captions
Language: en

00:00:00.330 --> 00:00:02.860
- [Narrator] At this point,
you are likely already familiar

00:00:02.860 --> 00:00:05.320
with the idea of rounding.

00:00:05.320 --> 00:00:07.210
Probably, you have had some practice

00:00:07.210 --> 00:00:09.870
rounding to the nearest 10.

00:00:09.870 --> 00:00:12.270
Now we're gonna do
another type of rounding.

00:00:12.270 --> 00:00:15.567
We are now going to
round to the nearest 100.

00:00:16.940 --> 00:00:18.750
So let's just start with an example,

00:00:18.750 --> 00:00:20.160
and you'll see that in a lot of ways,

00:00:20.160 --> 00:00:22.920
it's very similar to
rounding to the nearest 10,

00:00:22.920 --> 00:00:26.260
we're just looking at
different place values now.

00:00:26.260 --> 00:00:29.237
So let's say we have the number 345.

00:00:32.650 --> 00:00:37.270
And we want to round
this to the nearest 100.

00:00:37.270 --> 00:00:40.000
So pause this video, and
see, I know I haven't even

00:00:40.000 --> 00:00:42.880
taught you how to do that,
but what's your intuition?

00:00:42.880 --> 00:00:47.243
What is the nearest 100 to 345?

00:00:48.120 --> 00:00:49.860
Okay, now let's do this together.

00:00:49.860 --> 00:00:53.090
And what we wanna do is
first look at the 100s place.

00:00:53.090 --> 00:00:58.090
And you can see 345 is three
100s, four 10s, and five ones.

00:00:58.870 --> 00:01:03.670
So 345, the 100, the number of 100s,

00:01:03.670 --> 00:01:08.670
that is right below 345 is three 100s,

00:01:08.970 --> 00:01:12.870
so it's between three 100s,
zero 10s, and zero ones,

00:01:12.870 --> 00:01:14.980
and then the number of 100s

00:01:14.980 --> 00:01:17.800
that's right above this number is 400.

00:01:17.800 --> 00:01:21.080
We're in between three 100s and four 100s.

00:01:21.080 --> 00:01:22.850
And 400.

00:01:22.850 --> 00:01:24.690
So if we're gonna round
this to the nearest 100,

00:01:24.690 --> 00:01:27.470
it's gonna go to one of these two.

00:01:27.470 --> 00:01:29.380
Well, to think about
which one we round to,

00:01:29.380 --> 00:01:32.400
we have to think about
well, is 345 closer to 400,

00:01:32.400 --> 00:01:34.250
or is it closer to 300?

00:01:34.250 --> 00:01:35.730
And to think about that,

00:01:35.730 --> 00:01:39.220
we can draw ourselves a number line.

00:01:39.220 --> 00:01:43.110
And so let me just start
my number line here at,

00:01:43.110 --> 00:01:44.470
I'll just start it at 200.

00:01:44.470 --> 00:01:47.983
So that's 200, let's make this 300,

00:01:50.100 --> 00:01:53.273
and then this would be 400.

00:01:54.120 --> 00:01:56.640
And then since we, let's just see,

00:01:56.640 --> 00:01:58.980
this would be about 350 right over here,

00:01:58.980 --> 00:02:00.970
so I'll do the 50s right over there.

00:02:00.970 --> 00:02:02.210
So that 350.

00:02:02.210 --> 00:02:04.880
So where would 345 sit?

00:02:04.880 --> 00:02:07.820
Well, 345 is a little bit less than 350.

00:02:07.820 --> 00:02:11.450
It's going to be roughly right over there.

00:02:11.450 --> 00:02:13.700
So which 100 is it closer to?

00:02:13.700 --> 00:02:17.470
Are we closer to 300,
or are we closer to 400?

00:02:17.470 --> 00:02:20.900
Well, you can visually see,
350 is right in between.

00:02:20.900 --> 00:02:24.300
It's 50 away from 300,
and 50 away from 400.

00:02:24.300 --> 00:02:28.590
So 345 is going to be a
little bit closer to 300.

00:02:28.590 --> 00:02:31.910
So in this situation, if we're
rounding to the nearest 100,

00:02:31.910 --> 00:02:36.700
we would round down to 300.

00:02:36.700 --> 00:02:38.820
Now another way that you could do this,

00:02:38.820 --> 00:02:41.220
and it's very similar
to what we thought about

00:02:41.220 --> 00:02:42.620
when we rounded to the nearest 10,

00:02:42.620 --> 00:02:46.000
is okay, we're rounding
to the nearest 100,

00:02:46.000 --> 00:02:49.400
so this is either going to be
rounded to a three or a four,

00:02:49.400 --> 00:02:51.760
and to decide on that,

00:02:51.760 --> 00:02:54.950
we go to one place value less than that.

00:02:54.950 --> 00:02:58.150
So to decide on that, we
would go to the 10s place.

00:02:58.150 --> 00:02:59.730
Let me do this in a different color.

00:02:59.730 --> 00:03:01.090
Go to the 10s place.

00:03:01.090 --> 00:03:03.710
And in our 10s place right over here,

00:03:03.710 --> 00:03:08.700
if this is less than
five, then we round down.

00:03:08.700 --> 00:03:12.880
If it is greater than or
equal to five, we round up.

00:03:12.880 --> 00:03:16.220
So in this situation,
it is less than five,

00:03:16.220 --> 00:03:18.320
so we round down.

00:03:18.320 --> 00:03:21.700
If this was 365, well then that would be

00:03:21.700 --> 00:03:23.400
greater than or equal to five,

00:03:23.400 --> 00:03:24.740
so then we would round up.

00:03:24.740 --> 00:03:27.180
And that makes sense, because
365 would be over here,

00:03:27.180 --> 00:03:29.370
and it would be closer to 400.

00:03:29.370 --> 00:03:30.620
Let's do another example.

00:03:30.620 --> 00:03:32.350
We'll do it both with
what I just described,

00:03:32.350 --> 00:03:33.880
and we'll do it with a number line.

00:03:33.880 --> 00:03:35.940
And I'll actually do a
four digit number now,

00:03:35.940 --> 00:03:38.930
just to just mix things up a little bit.

00:03:38.930 --> 00:03:41.373
Let's say we have the number 7,652.

00:03:48.350 --> 00:03:50.080
Pause this video, and see if you can

00:03:50.080 --> 00:03:53.323
round this number to the nearest 100.

00:03:55.660 --> 00:03:58.160
Alright, now let's do it together.

00:03:58.160 --> 00:04:00.300
Now, we're thinking about the 100s place,

00:04:00.300 --> 00:04:01.720
so right over there.

00:04:01.720 --> 00:04:04.520
You can view this as seven
thousands and six 100s.

00:04:04.520 --> 00:04:07.330
Or you could even view this as 76 100s.

00:04:07.330 --> 00:04:10.870
So what are the closest
100s to this number?

00:04:10.870 --> 00:04:12.920
Well, this is, you could either view this

00:04:12.920 --> 00:04:16.170
as 76 100s and five 10s and two ones,

00:04:16.170 --> 00:04:19.850
or seven thousands, six
100s, five 10s, and two ones.

00:04:19.850 --> 00:04:23.670
And so either way, the 100s
that are right below this

00:04:23.670 --> 00:04:28.670
is 76 100s, or 7,600,

00:04:28.740 --> 00:04:30.620
and the 100s that are right above this,

00:04:30.620 --> 00:04:33.970
well you would just take
one more than this six,

00:04:33.970 --> 00:04:38.970
so that would be 7700, 7700.

00:04:39.590 --> 00:04:42.583
And so, which one would it round to?

00:04:43.470 --> 00:04:45.430
Well, we could use the technique
that I just showed you.

00:04:45.430 --> 00:04:48.810
You go one place value less than the 100s,

00:04:48.810 --> 00:04:51.060
which in this case is in the 10s position,

00:04:51.060 --> 00:04:52.220
and you would say, alright,

00:04:52.220 --> 00:04:54.410
is this greater than or equal to five?

00:04:54.410 --> 00:04:55.900
If it is, we round up.

00:04:55.900 --> 00:04:57.600
Is this less than five?

00:04:57.600 --> 00:04:58.840
Then we round down.

00:04:58.840 --> 00:05:01.410
This is greater than or equal to five.

00:05:01.410 --> 00:05:02.720
It's equal to five.

00:05:02.720 --> 00:05:07.150
So in this situation, we round up to 7700.

00:05:07.150 --> 00:05:09.860
And we can see that on
a number line as well.

00:05:09.860 --> 00:05:12.133
Let me draw a number line here.

00:05:13.550 --> 00:05:18.550
And so let me just start at,
let's say that this is 7500,

00:05:20.360 --> 00:05:25.360
this is 7600, or 7,600, and
this right over here is 7,700.

00:05:33.780 --> 00:05:38.550
And this would be 7,650 right over here.

00:05:38.550 --> 00:05:42.410
And so 7,652 is going to be
a little bit more than that.

00:05:42.410 --> 00:05:44.100
It's going to be a little bit more.

00:05:44.100 --> 00:05:46.710
And since you can see, it's
either right in the middle,

00:05:46.710 --> 00:05:48.800
or to the right of right in the middle,

00:05:48.800 --> 00:05:52.450
we would round up to 7700,

00:05:52.450 --> 00:05:55.440
which is exactly what we just did.

00:05:55.440 --> 00:05:58.680
Now let me give you another
interesting example.

00:05:58.680 --> 00:06:03.680
Let's say we wanted to round
to the nearest 100 for 982.

00:06:08.360 --> 00:06:09.793
What would that be?

00:06:11.280 --> 00:06:13.940
Well once again, we
look at the 100s place.

00:06:13.940 --> 00:06:17.260
Well what's 100 that's right below 982?

00:06:17.260 --> 00:06:18.770
Well if you just get rid of the 82,

00:06:18.770 --> 00:06:20.400
you're just left with nine 100s,

00:06:20.400 --> 00:06:22.700
so that would be 900 if you round down.

00:06:22.700 --> 00:06:24.220
And if you were to round up,

00:06:24.220 --> 00:06:26.840
what's the 100s right above this?

00:06:26.840 --> 00:06:30.180
Well, you could go from
nine 100s to 10 100s,

00:06:30.180 --> 00:06:33.413
and that would be the same thing as 1,000.

00:06:34.480 --> 00:06:36.250
And so I wanted to show this example

00:06:36.250 --> 00:06:38.070
because when you're rounding up here,

00:06:38.070 --> 00:06:42.370
the next 100 is 10 100s, or 1,000.

00:06:42.370 --> 00:06:44.540
And so we can see very clearly here

00:06:44.540 --> 00:06:46.403
that if we look at the 10s place,

00:06:47.270 --> 00:06:50.400
the eight is greater
than or equal to five,

00:06:50.400 --> 00:06:52.600
so we are going to round up.

00:06:52.600 --> 00:06:57.213
So 982 rounded to the
nearest 100s is 1,000.


Methods for subracting 3 digit numbers

WEBVTT
Kind: captions
Language: en

00:00:00.450 --> 00:00:01.330
- [Instructor] Hello.

00:00:01.330 --> 00:00:03.990
In this video, we're going
to think about techniques

00:00:03.990 --> 00:00:06.660
for subtracting three-digit numbers.

00:00:06.660 --> 00:00:10.983
So let's say we wanted to figure
out what 357 minus 156 is.

00:00:12.500 --> 00:00:13.390
Pause this video,

00:00:13.390 --> 00:00:15.250
and see if you can
somehow figure this out.

00:00:15.250 --> 00:00:17.270
And you don't have to be able to

00:00:17.270 --> 00:00:18.900
because we're going to walk,
work through it together,

00:00:18.900 --> 00:00:21.250
but it doesn't hurt to try a little bit.

00:00:21.250 --> 00:00:22.770
All right, now let's do it together.

00:00:22.770 --> 00:00:24.690
And one way to think about it is

00:00:24.690 --> 00:00:27.420
what if we were to break up the 156

00:00:27.420 --> 00:00:29.560
into its different place values?

00:00:29.560 --> 00:00:32.580
So we view it as 100 and 50

00:00:32.580 --> 00:00:33.770
and six.

00:00:33.770 --> 00:00:37.940
So then this could be rewritten as 357

00:00:37.940 --> 00:00:40.400
minus 100,

00:00:40.400 --> 00:00:42.480
minus 100,

00:00:42.480 --> 00:00:44.630
minus 50,

00:00:44.630 --> 00:00:47.420
minus 50, that's five 10s right there,

00:00:47.420 --> 00:00:50.200
and then minus six.

00:00:50.200 --> 00:00:51.210
Now does this help us?

00:00:51.210 --> 00:00:53.020
Pause this video, and see if you can

00:00:53.020 --> 00:00:54.933
figure out what this would be.

00:00:56.040 --> 00:00:57.780
Well, many of you
probably said, all right,

00:00:57.780 --> 00:00:59.900
if I have three hundreds and 57

00:00:59.900 --> 00:01:02.230
and if I were to take away 100,

00:01:02.230 --> 00:01:04.303
well, then I'm going to be left with 257.

00:01:05.873 --> 00:01:08.933
And then if I take 50 away from that,

00:01:10.010 --> 00:01:13.530
250 away from 257,

00:01:13.530 --> 00:01:14.820
well, I have five 10s here,

00:01:14.820 --> 00:01:15.960
and I'm gonna take away five 10s,

00:01:15.960 --> 00:01:17.520
so I'm gonna be left with zero 10s.

00:01:17.520 --> 00:01:19.573
I'm gonna be left with 207.

00:01:21.268 --> 00:01:25.230
And then if I took 207 and
I subtracted six from that,

00:01:25.230 --> 00:01:27.840
so 207 minus six,

00:01:27.840 --> 00:01:30.690
that, of course, is
going to be equal to 201.

00:01:30.690 --> 00:01:32.300
I just took away those six ones,

00:01:32.300 --> 00:01:34.750
and I had seven ones on top
of the two hundreds before,

00:01:34.750 --> 00:01:36.510
to get us to 201.

00:01:36.510 --> 00:01:39.310
So this is one very good technique

00:01:39.310 --> 00:01:41.190
for being able to subtract numbers,

00:01:41.190 --> 00:01:43.380
and it doesn't just apply
to three-digit numbers.

00:01:43.380 --> 00:01:45.430
You could do this with many-digit numbers.

00:01:45.430 --> 00:01:48.170
But there's other things
that you could be doing.

00:01:48.170 --> 00:01:50.950
You could, for example,
try to adjust the numbers

00:01:50.950 --> 00:01:52.820
to make the subtraction easier.

00:01:52.820 --> 00:01:55.590
For example, you could say,
hey, wouldn't it be nice

00:01:55.590 --> 00:01:59.710
if instead of subtracting 156,
I only had to subtract 150?

00:01:59.710 --> 00:02:01.300
And there is a way that you could do that.

00:02:01.300 --> 00:02:03.470
As long as whatever you add or subtract

00:02:03.470 --> 00:02:05.500
to one of these numbers
you do to the other,

00:02:05.500 --> 00:02:07.580
then the difference will be the same.

00:02:07.580 --> 00:02:10.420
So there is a situation where
you subtract six from both

00:02:10.420 --> 00:02:13.300
of these numbers before you
try to find the difference.

00:02:13.300 --> 00:02:15.340
So then let me write this out.

00:02:15.340 --> 00:02:19.100
So let's say you wanted to subtract six

00:02:19.100 --> 00:02:21.223
from both.

00:02:22.390 --> 00:02:23.350
What would this be?

00:02:23.350 --> 00:02:26.670
Well, 357 minus six,
well, we're just going

00:02:26.670 --> 00:02:28.580
to take six ones away
from the seven ones here,

00:02:28.580 --> 00:02:31.080
so it's going to be 351

00:02:31.080 --> 00:02:33.280
minus 156

00:02:33.280 --> 00:02:34.500
minus six.

00:02:34.500 --> 00:02:37.580
Well, that just gets us to 150.

00:02:37.580 --> 00:02:39.720
And this might be, for many of y'all,

00:02:39.720 --> 00:02:42.590
a little bit more
straightforward to compute.

00:02:42.590 --> 00:02:44.670
You might realize, all right,
if I have three hundreds

00:02:44.670 --> 00:02:48.090
and I take away one of those
hundreds, I get two hundreds.

00:02:48.090 --> 00:02:51.050
If I have five 10s and if
I take away those five 10s,

00:02:51.050 --> 00:02:52.950
I'm going to be left with zero 10s.

00:02:52.950 --> 00:02:56.570
And if I have one one and
if I take away no ones,

00:02:56.570 --> 00:02:57.980
I'm still gonna have one one.

00:02:57.980 --> 00:03:00.950
Or you could say, look,
300 minus a hundred is 200,

00:03:00.950 --> 00:03:04.060
51 minus 50 is just one.

00:03:04.060 --> 00:03:05.480
So that was pretty helpful.

00:03:05.480 --> 00:03:08.910
Another technique is to,
instead of going to 150,

00:03:08.910 --> 00:03:11.610
you might say, well, what
if I wanted to subtract 160?

00:03:12.510 --> 00:03:13.530
Well, in that situation,

00:03:13.530 --> 00:03:16.010
you could add four to
both of these numbers.

00:03:16.010 --> 00:03:18.080
Add four

00:03:18.080 --> 00:03:19.513
to both.

00:03:20.630 --> 00:03:21.500
What would happen then?

00:03:21.500 --> 00:03:23.750
Pause this video, and
try to figure that out.

00:03:23.750 --> 00:03:26.010
Well, what's 357 plus four?

00:03:26.010 --> 00:03:29.210
357 plus three gets us to 360,

00:03:29.210 --> 00:03:32.790
plus another one gets us to 361.

00:03:32.790 --> 00:03:37.081
And if I add four to 156, that is 160.

00:03:37.081 --> 00:03:38.470
And since I added four to both,

00:03:38.470 --> 00:03:40.280
I added the same amount to both,

00:03:40.280 --> 00:03:42.230
the difference is going to be the same.

00:03:42.230 --> 00:03:43.960
And so if you look through this,

00:03:43.960 --> 00:03:46.880
300 minus 100 is two hundreds left.

00:03:46.880 --> 00:03:51.210
And then 61 minus 60, that gets us to,

00:03:51.210 --> 00:03:52.720
that gets us to 201.

00:03:52.720 --> 00:03:54.840
And what I just kind of
did in my head, if I wanted

00:03:54.840 --> 00:03:58.480
to write it out, we could say
this is the same thing as 361

00:03:58.480 --> 00:04:00.680
minus 100,

00:04:00.680 --> 00:04:02.470
minus 100.

00:04:02.470 --> 00:04:06.040
And I could break it out
completely, like I did up here,

00:04:06.040 --> 00:04:07.280
or I could break it out partially.

00:04:07.280 --> 00:04:08.910
I could just break out the hundreds place

00:04:08.910 --> 00:04:12.170
and then break out the 60,

00:04:12.170 --> 00:04:13.370
so minus 60.

00:04:13.370 --> 00:04:15.290
I guess you could view
that as I broke out the 10s

00:04:15.290 --> 00:04:17.190
and I didn't write the ones.

00:04:17.190 --> 00:04:20.580
But you can see 361 minus
a hundred would be 261,

00:04:20.580 --> 00:04:22.590
and then you take 60 away from that.

00:04:22.590 --> 00:04:25.833
Once again, you would be left with 201.

00:04:27.060 --> 00:04:29.730
So the big takeaway here is
there's many different ways

00:04:29.730 --> 00:04:32.760
to approach subtraction with
however many digits you have,

00:04:32.760 --> 00:04:36.300
and this just gets you a
glimpse of different methods.

00:04:36.300 --> 00:04:39.480
And some will be more convenient
in different situations

00:04:39.480 --> 00:04:41.893
depending on what numbers
you are dealing with.


Subtraction by breaking apart

WEBVTT
Kind: captions
Language: en

00:00:00.420 --> 00:00:02.470
- [Instructor] We're told
that Linde isn't sure

00:00:02.470 --> 00:00:05.513
how to subtract 853.

00:00:07.100 --> 00:00:09.670
We are told Linde isn't sure

00:00:09.670 --> 00:00:10.783
how to subtract 853

00:00:11.860 --> 00:00:14.250
minus 283.

00:00:14.250 --> 00:00:16.300
Help Linde by choosing an expression

00:00:16.300 --> 00:00:18.213
that is the same as 853

00:00:19.130 --> 00:00:21.760
minus 283.

00:00:21.760 --> 00:00:22.820
So pause this video

00:00:22.820 --> 00:00:24.190
and see if you can answer it on your own

00:00:24.190 --> 00:00:25.940
before we work through it together.

00:00:26.870 --> 00:00:27.703
All right.

00:00:27.703 --> 00:00:28.750
Now when we look at all of the choices,

00:00:28.750 --> 00:00:30.087
they all start with 853.

00:00:31.230 --> 00:00:35.010
Now, this first choice,
they subtract out 200.

00:00:35.010 --> 00:00:38.680
That makes sense 'cause we
have 200s right over there.

00:00:38.680 --> 00:00:43.136
Then they subtract out 50 and
then they subtract out three.

00:00:43.136 --> 00:00:46.140
So the 200 and the three make sense.

00:00:46.140 --> 00:00:49.240
You can view 853 minus 283

00:00:49.240 --> 00:00:52.360
as 853

00:00:52.360 --> 00:00:54.080
minus 200s

00:00:55.130 --> 00:00:56.870
minus 80,

00:00:56.870 --> 00:00:59.320
eight 10s right here, minus three.

00:00:59.320 --> 00:01:00.470
But that's not what they wrote in here.

00:01:00.470 --> 00:01:02.380
Instead of putting an
80 here, they put a 50,

00:01:02.380 --> 00:01:03.980
so we can rule that out.

00:01:03.980 --> 00:01:08.822
Here we have 853 minus
20 minus 800 minus three.

00:01:08.822 --> 00:01:10.710
Well, this is a little bit strange

00:01:10.710 --> 00:01:13.800
because we don't have
two 10s, we have 200s,

00:01:13.800 --> 00:01:16.850
and we don't have 800s, we have eight 10s,

00:01:16.850 --> 00:01:19.110
so this is also incorrect.

00:01:19.110 --> 00:01:20.450
Now, it's probably going to be this one,

00:01:20.450 --> 00:01:23.210
but let's just make sure we
feel comfortable with this.

00:01:23.210 --> 00:01:25.360
So this one has 853

00:01:25.360 --> 00:01:26.860
minus 200

00:01:26.860 --> 00:01:29.030
minus 50

00:01:29.030 --> 00:01:31.260
minus 30.

00:01:31.260 --> 00:01:33.306
Does that make sense?

00:01:33.306 --> 00:01:35.350
Well, let's think about it.

00:01:35.350 --> 00:01:36.183
What they're doing

00:01:36.183 --> 00:01:38.550
is that they're subtracting
out first the 200,

00:01:38.550 --> 00:01:40.110
so that's this part right over here,

00:01:40.110 --> 00:01:40.943
so that makes sense,

00:01:40.943 --> 00:01:42.680
they're subtracting out first that.

00:01:42.680 --> 00:01:44.580
And then they're subtracting out 53

00:01:44.580 --> 00:01:46.900
and then they're subtracting out 30.

00:01:46.900 --> 00:01:50.467
Well, that is the same
thing as subtracting out 83

00:01:50.467 --> 00:01:52.570
'cause subtracting 83 is the same thing

00:01:52.570 --> 00:01:54.880
as subtracting out 53,
and then subtracting 30.

00:01:54.880 --> 00:01:57.780
53 plus 30 is 83.

00:01:57.780 --> 00:01:58.613
Now, you might be wondering,

00:01:58.613 --> 00:02:00.620
why would they even do it this way?

00:02:00.620 --> 00:02:01.930
What's easier to do in your head?

00:02:01.930 --> 00:02:05.110
853 minus 200

00:02:05.110 --> 00:02:07.450
is 653.

00:02:07.450 --> 00:02:11.820
You take away 53 from that,
so you take away 53 from that,

00:02:11.820 --> 00:02:14.920
and you're going to be left with 600,

00:02:14.920 --> 00:02:18.880
and then 600 minus 30,
you might recognize that,

00:02:18.880 --> 00:02:22.120
you could use the 60 10s minus three 10s,

00:02:22.120 --> 00:02:23.820
this is gonna be 57 10s

00:02:23.820 --> 00:02:25.160
or you might be able
to do it in your head,

00:02:25.160 --> 00:02:26.650
600 minus 30

00:02:26.650 --> 00:02:28.500
is 570.

00:02:28.500 --> 00:02:29.476
So that's why they broke out,

00:02:29.476 --> 00:02:31.710
they broke up the 83.

00:02:31.710 --> 00:02:34.200
Instead of just breaking
it up into 80 and three,

00:02:34.200 --> 00:02:36.480
they broke it up into 53 and 30

00:02:36.480 --> 00:02:38.450
to match this 53 over here,

00:02:38.450 --> 00:02:40.910
and so it was easier
to work out the result.

00:02:40.910 --> 00:02:42.869
Let's do another example.

00:02:42.869 --> 00:02:45.110
So here we're asked to fill in the blank.

00:02:45.110 --> 00:02:50.110
They say 143 minus 79 is
the same as blank minus 80.

00:02:50.290 --> 00:02:53.040
So pause this video and see
if you can figure this out.

00:02:54.100 --> 00:02:56.120
So the key here is to realize

00:02:56.120 --> 00:02:57.720
is that when you have a difference here,

00:02:57.720 --> 00:02:59.110
as long as you add or subtract

00:02:59.110 --> 00:03:00.990
the same amount to both of these,

00:03:00.990 --> 00:03:02.850
the difference will be the same.

00:03:02.850 --> 00:03:06.690
So it looks like they
tried to turn the 79 into,

00:03:06.690 --> 00:03:11.690
it looks like they turned the
79 into an 80 by adding one,

00:03:12.360 --> 00:03:14.690
and so if we want the
difference to be the same,

00:03:14.690 --> 00:03:18.560
we would add one to the 143 as well.

00:03:18.560 --> 00:03:21.690
So 143 plus one is 144.

00:03:21.690 --> 00:03:23.440
If we add one to both of these numbers,

00:03:23.440 --> 00:03:25.770
the difference would be the same.

00:03:25.770 --> 00:03:27.030
And we're done.

00:03:27.030 --> 00:03:29.293
So, it's 144 minus 80.


Missing numbers in three digit subtraction

WEBVTT
Kind: captions
Language: en

00:00:00.600 --> 00:00:04.290
- [Instructor] Let's say
that we are told that 495

00:00:04.290 --> 00:00:09.213
is equal to 621 minus blank.

00:00:10.280 --> 00:00:12.340
What would blank be?

00:00:12.340 --> 00:00:15.680
Pause this video and see
if you can figure that out.

00:00:15.680 --> 00:00:17.490
Okay, now let's do this together,

00:00:17.490 --> 00:00:18.660
and one technique is to try

00:00:18.660 --> 00:00:21.280
to visualize this on a number line.

00:00:21.280 --> 00:00:26.210
495 is what you get when you
subtract something from 621,

00:00:26.210 --> 00:00:28.820
so let me put those two
numbers on a number line.

00:00:28.820 --> 00:00:31.230
So, let me do the number line like this.

00:00:31.230 --> 00:00:34.150
So we're gonna start at
621, and subtract blank,

00:00:34.150 --> 00:00:36.420
to get to 495.

00:00:36.420 --> 00:00:41.420
So if this is 621, we're
going to subtract some amount

00:00:42.510 --> 00:00:45.810
to get to 495.

00:00:45.810 --> 00:00:48.907
So let's say this right over here is 495.

00:00:51.220 --> 00:00:53.150
Now, what amount did we subtract?

00:00:53.150 --> 00:00:55.720
So here we are subtracting blank,

00:00:55.720 --> 00:00:57.430
that's my blank over there,

00:00:57.430 --> 00:01:00.310
and so we need to figure out what that is.

00:01:00.310 --> 00:01:05.310
So how do you go from 621 to 495?

00:01:05.580 --> 00:01:07.290
Well, one way that my brain does it,

00:01:07.290 --> 00:01:11.440
first, we can subtract 21 to get to 600.

00:01:11.440 --> 00:01:16.340
So let me do minus 21,
would get us to 600.

00:01:16.340 --> 00:01:19.970
Then, we could subtract
another 100 to get to 500.

00:01:19.970 --> 00:01:24.470
So then we could subtract
another 100, so minus 100,

00:01:24.470 --> 00:01:26.670
to get us to 500.

00:01:26.670 --> 00:01:29.010
And then, to go from 500 to 495,

00:01:29.010 --> 00:01:31.520
we would subtract another five.

00:01:31.520 --> 00:01:34.550
So to go from 621 to 495, and I picked

00:01:34.550 --> 00:01:36.320
these numbers intentionally, I picked 21

00:01:36.320 --> 00:01:39.627
to subtract to get to 600,
I picked 100 to get to 500,

00:01:39.627 --> 00:01:42.460
and then I picked five to get 495,

00:01:42.460 --> 00:01:46.040
I subtracted a total of
21, then I subtract 100,

00:01:46.040 --> 00:01:47.140
then I subtracted five.

00:01:47.140 --> 00:01:52.140
So I subtracted 100, I subtracted
21, and I subtracted five,

00:01:52.530 --> 00:01:56.160
and so, how much did I subtract in total?

00:01:56.160 --> 00:01:58.130
So let me put it this way,
this is the same thing

00:01:58.130 --> 00:02:02.420
as 621 minus these things,

00:02:02.420 --> 00:02:04.810
that's equal to 495.

00:02:04.810 --> 00:02:08.860
So in total, let's see, if I
subtract 21 and I subtract five

00:02:08.860 --> 00:02:12.310
that is subtracting 26,

00:02:12.310 --> 00:02:15.360
and so I subtract 126.

00:02:15.360 --> 00:02:17.373
So I subtracted a total of 126.

00:02:19.140 --> 00:02:23.927
So 495 is equal to 621 minus 126.

00:02:26.040 --> 00:02:27.020
Let's do another example.

00:02:27.020 --> 00:02:29.200
Let's say we wanna figure out,

00:02:29.200 --> 00:02:34.200
if someone tells us blank minus 435

00:02:34.380 --> 00:02:39.380
is equal to 210, what is
blank in this situation?

00:02:40.020 --> 00:02:42.000
Well, this is a little bit different now,

00:02:42.000 --> 00:02:43.450
because now, we're not
trying to figure out

00:02:43.450 --> 00:02:46.230
what to subtract from the larger number,

00:02:46.230 --> 00:02:47.360
in this situation, we're trying

00:02:47.360 --> 00:02:48.620
to figure out the larger number.

00:02:48.620 --> 00:02:51.810
The larger number minus
something is equal to 210.

00:02:51.810 --> 00:02:55.010
But as always, it's useful to
draw this on a number line,

00:02:55.010 --> 00:02:57.040
just to make sure we're
thinking about things

00:02:57.040 --> 00:02:58.560
in a reasonable way.

00:02:58.560 --> 00:03:02.470
So we're going to start
at blank, take out 435,

00:03:02.470 --> 00:03:04.470
and then we're going to get to 210.

00:03:04.470 --> 00:03:06.540
So we're starting here, maybe I'll put

00:03:06.540 --> 00:03:08.760
a question mark there
so we know that point,

00:03:08.760 --> 00:03:13.760
we're starting there,
we are subtracting 435,

00:03:13.780 --> 00:03:17.010
so that's minus 435,

00:03:17.010 --> 00:03:20.520
and we are getting to 210.

00:03:20.520 --> 00:03:23.350
So, to figure out blank, we
could go the other way around.

00:03:23.350 --> 00:03:27.290
We could start at 210, and then just add,

00:03:27.290 --> 00:03:32.173
and then just add 435.

00:03:33.590 --> 00:03:35.587
So, what's 210 plus 435?

00:03:36.800 --> 00:03:38.280
Well, there's many ways of doing it,

00:03:38.280 --> 00:03:39.440
but I encourage you to pause this video

00:03:39.440 --> 00:03:41.660
and see if you can work that out.

00:03:41.660 --> 00:03:45.310
Well, one way to do it
is, first we can add 400,

00:03:45.310 --> 00:03:46.460
and I'll do this in another color,

00:03:46.460 --> 00:03:48.750
just for a little bit of variety.

00:03:48.750 --> 00:03:51.233
So, first I'll add 400.

00:03:52.360 --> 00:03:56.520
So, if I add 400 plus 400,

00:03:56.520 --> 00:03:57.890
that would get us, let's see,

00:03:57.890 --> 00:03:59.070
if you add four hundreds to that,

00:03:59.070 --> 00:04:00.563
that would get you to 610.

00:04:01.450 --> 00:04:04.540
And then, if I add 30 to that,

00:04:04.540 --> 00:04:08.850
so if I add plus 30, and
I haven't drawn it exact,

00:04:08.850 --> 00:04:11.040
but this is just to help
us think about things,

00:04:11.040 --> 00:04:13.290
that's three more 10s,
and I already have one 10,

00:04:13.290 --> 00:04:16.710
so 10 plus 30 is 40,
so that gets us to 640,

00:04:16.710 --> 00:04:18.860
and then I'm going to add the five.

00:04:18.860 --> 00:04:22.483
So this right over here, if
I add five to it, is 645.

00:04:23.370 --> 00:04:24.490
So there you have it.

00:04:24.490 --> 00:04:29.490
645 minus 435 is equal to 210.


Writing: Sentence Boundaries — Harder Example

WEBVTT
Kind: captions
Language: en

00:00:00.380 --> 00:00:03.350
- [Instructor] In response to
fears of a chocolate shortage,

00:00:03.350 --> 00:00:06.150
farmers are looking to
a high-yielding variety

00:00:06.150 --> 00:00:07.528
of cocoa tree.

00:00:07.528 --> 00:00:12.528
Which was developed by Ecuadorian
agronomist Homero Castro.

00:00:13.870 --> 00:00:17.370
So this was a bit strange
that we end a sentence,

00:00:17.370 --> 00:00:19.280
and then we start a sentence with,

00:00:19.280 --> 00:00:24.170
which was developed by Ecuadorian
agronomist Homero Castro.

00:00:24.170 --> 00:00:27.140
Because this right by itself,
this isn't a sentence,

00:00:27.140 --> 00:00:29.140
this isn't a sentence by itself.

00:00:29.140 --> 00:00:31.170
This feels like this which is referring,

00:00:31.170 --> 00:00:36.170
it's giving us more explanation
of this high-yielding

00:00:36.440 --> 00:00:38.100
variety of cocoa tree.

00:00:38.100 --> 00:00:39.500
So I definitely don't wanna separate it

00:00:39.500 --> 00:00:41.810
as a separate sentence
so I'm gonna change it,

00:00:41.810 --> 00:00:43.440
so I'm gonna scratch out no change.

00:00:43.440 --> 00:00:45.530
So let's look at this choice, so this say,

00:00:45.530 --> 00:00:47.760
farmers are looking to
a high-yielding variety

00:00:47.760 --> 00:00:49.920
of cocoa tree comma,

00:00:49.920 --> 00:00:54.100
which was developed by Ecuadorian
agronomist Homero Castro.

00:00:54.100 --> 00:00:55.910
So this one feels quite good.

00:00:55.910 --> 00:00:58.340
I would use a comma and just
go straight to the which,

00:00:58.340 --> 00:01:00.007
so this one looks right.

00:01:00.007 --> 00:01:02.479
Let's look at the other choices.

00:01:02.479 --> 00:01:04.890
Farmers are looking to
a high-yielding variety

00:01:04.890 --> 00:01:09.400
of cocoa tree, and that tree was developed

00:01:09.400 --> 00:01:11.760
by Ecuadorian agronomist Homero Castro.

00:01:11.760 --> 00:01:13.280
Well this is just unnecessarily wordy,

00:01:13.280 --> 00:01:16.680
we're using the word tree
twice, so I don't like that one.

00:01:16.680 --> 00:01:18.840
And this last choice is
just like the second choice,

00:01:18.840 --> 00:01:21.260
but instead of a comma
we have a semicolon.

00:01:21.260 --> 00:01:24.370
And the reason why I like a
comma more than a semicolon,

00:01:24.370 --> 00:01:27.360
I imagine, I view a semicolon
as separating two clauses

00:01:27.360 --> 00:01:29.790
that can almost stand on
themselves, and in fact,

00:01:29.790 --> 00:01:31.630
sometimes they can stand on themselves,

00:01:31.630 --> 00:01:33.030
but there's a semicolon to kind of show

00:01:33.030 --> 00:01:34.500
that they are related.

00:01:34.500 --> 00:01:36.730
While a comma is, for the most part,

00:01:36.730 --> 00:01:38.700
separating clauses that can't stand,

00:01:38.700 --> 00:01:40.760
the first one can stand
alone by themselves.

00:01:40.760 --> 00:01:42.840
In response to fears of
a chocolate shortage,

00:01:42.840 --> 00:01:44.869
farmers are looking to
a high-yielding variety

00:01:44.869 --> 00:01:45.870
of cocoa tree.

00:01:45.870 --> 00:01:47.280
That can stand by itself.

00:01:47.280 --> 00:01:49.500
But the second clause has
trouble standing by itself,

00:01:49.500 --> 00:01:51.290
in fact, it can't stand as a sentence,

00:01:51.290 --> 00:01:54.770
which was developed by Ecuadorian
agronomist Homero Castro.

00:01:54.770 --> 00:01:58.076
So I feel good about the
comma right over here.

00:01:58.076 --> 00:02:00.460
No need to over-complicate things,

00:02:00.460 --> 00:02:02.933
if the simpler tool works.


Khan Stories: Claudia

WEBVTT
Kind: captions
Language: en

00:00:00.180 --> 00:00:01.900
- My name's Claudia, and I am currently

00:00:01.900 --> 00:00:03.850
a freshman at MIT.

00:00:03.850 --> 00:00:07.574
I'm from South Florida, and
now my journey continues here.

00:00:07.574 --> 00:00:10.407
(uplifting music)

00:00:11.620 --> 00:00:13.730
My family is from the Azores islands,

00:00:13.730 --> 00:00:15.220
which are in the middle of the Atlantic.

00:00:15.220 --> 00:00:17.570
Just knowing that where
my family comes from

00:00:17.570 --> 00:00:19.890
and the lack of education,
they've built me up

00:00:19.890 --> 00:00:22.640
with such important
skills of interpersonal

00:00:22.640 --> 00:00:25.210
communication, team building, leadership

00:00:25.210 --> 00:00:26.930
and now it's just my turn to take

00:00:26.930 --> 00:00:28.887
this and put it in an academic context.

00:00:28.887 --> 00:00:32.470
(uplifting music)

00:00:32.470 --> 00:00:35.010
Being a first-generation
high school graduate,

00:00:35.010 --> 00:00:36.860
first-generation college student,

00:00:36.860 --> 00:00:38.280
I didn't really have that background

00:00:38.280 --> 00:00:40.580
of really good testing
skills or just the role

00:00:40.580 --> 00:00:41.980
models around me to really show

00:00:41.980 --> 00:00:43.910
me how to do things academically.

00:00:43.910 --> 00:00:46.270
Getting the academic support
had to come from somewhere,

00:00:46.270 --> 00:00:49.000
and Khan Academy being online, being free

00:00:49.000 --> 00:00:50.790
and available, having SAT prep,

00:00:50.790 --> 00:00:52.910
even pairing up with the College Board,

00:00:52.910 --> 00:00:56.270
I was able to get accurate
very, very closely-related

00:00:56.270 --> 00:00:58.170
questions, so when I was on the test,

00:00:58.170 --> 00:00:59.357
nothing was a surprise.

00:00:59.357 --> 00:01:02.453
(uplifting music)

00:01:02.453 --> 00:01:04.930
So whenever it's free,
it's open, it's fair.

00:01:04.930 --> 00:01:06.290
And I have that fire in my stomach

00:01:06.290 --> 00:01:08.050
that I know that this
is where I want to be,

00:01:08.050 --> 00:01:09.220
this is what I want to do.

00:01:09.220 --> 00:01:12.150
I have so many opinions and so many things

00:01:12.150 --> 00:01:14.410
I find wrong with the
world, and I really know

00:01:14.410 --> 00:01:16.740
that this is a place where I can grow,

00:01:16.740 --> 00:01:18.390
learn, and gain even more skills

00:01:18.390 --> 00:01:19.511
to be able to do just that.

00:01:19.511 --> 00:01:22.344
(inspiring music)


Khan Stories: Shrey

WEBVTT
Kind: captions
Language: en

00:00:00.000 --> 00:00:00.833
(upbeat music)

00:00:00.833 --> 00:00:01.666
- It was amazing.
- One sentence,

00:00:01.666 --> 00:00:03.100
I don't think I'll ever forget in my life,

00:00:03.100 --> 00:00:04.460
Mom, I made it to Harvard.

00:00:04.460 --> 00:00:08.079
It was like a Bollywood
Hollywood kind of a sentence.

00:00:08.079 --> 00:00:09.297
- Well I'm Shrey.

00:00:09.297 --> 00:00:12.100
I'm a freshman in Harvard, Class of 2022.

00:00:12.100 --> 00:00:14.270
And I'm from New Delhi, India.

00:00:14.270 --> 00:00:16.650
I've been using Khan
Academy for quite a while,

00:00:16.650 --> 00:00:18.637
6th grade, probably.

00:00:18.637 --> 00:00:21.470
(uplifting music)

00:00:22.520 --> 00:00:24.623
Chemistry is a subject that,

00:00:25.490 --> 00:00:27.850
if you're not clear with the fundamentals

00:00:27.850 --> 00:00:29.640
or the building blocks,

00:00:29.640 --> 00:00:31.650
you will really struggle a lot

00:00:31.650 --> 00:00:34.730
when you get to the higher concepts.

00:00:34.730 --> 00:00:36.560
When I struggled with Chemistry,

00:00:36.560 --> 00:00:40.640
it was more about not
getting enough attention

00:00:40.640 --> 00:00:43.420
on the basic fundamental things,

00:00:43.420 --> 00:00:47.303
or the class being just
too fast-paced for me.

00:00:47.303 --> 00:00:50.600
(upbeat music)

00:00:50.600 --> 00:00:54.470
Khan Academy eliminated that
for me to a great extent,

00:00:54.470 --> 00:00:56.550
'cause I didn't have to feel bad

00:00:56.550 --> 00:00:59.500
about watching the same
video over and over again.

00:00:59.500 --> 00:01:01.380
I could watch it at a slower pace.

00:01:01.380 --> 00:01:04.660
I could do millions of questions

00:01:04.660 --> 00:01:07.240
at the same level, at
the fundamental level,

00:01:07.240 --> 00:01:08.660
and that was great, actually,

00:01:08.660 --> 00:01:10.883
'cause I was learning at my own pace.

00:01:12.005 --> 00:01:13.470
(electronic chime)

00:01:13.470 --> 00:01:15.420
Khan Academy teaching just eliminates

00:01:15.420 --> 00:01:17.120
any sort of learning gap.

00:01:17.120 --> 00:01:20.570
- This access to education
is the greatest gift

00:01:20.570 --> 00:01:22.180
which we can give to our kids,

00:01:22.180 --> 00:01:24.040
wherever they are in this world.

00:01:24.040 --> 00:01:26.400
If they have access to
this kind of education

00:01:26.400 --> 00:01:28.850
through technology, through digital means,

00:01:28.850 --> 00:01:30.750
through platforms like Khan Academy,

00:01:30.750 --> 00:01:32.250
they can achieve anything.

00:01:32.250 --> 00:01:34.120
A child sitting in any
corner of the world,

00:01:34.120 --> 00:01:36.730
if they have this access
to these resources,

00:01:36.730 --> 00:01:37.780
anything is possible.


Types of competition and marginal revenue

WEBVTT
Kind: captions
Language: en

00:00:00.370 --> 00:00:01.970
- [Instructor] We've
already had several videos

00:00:01.970 --> 00:00:05.410
where we talk about the types of markets

00:00:05.410 --> 00:00:07.240
that we might look at in economics.

00:00:07.240 --> 00:00:10.580
At one end, you might
have perfect competition,

00:00:10.580 --> 00:00:12.630
let's write perfect comp,

00:00:12.630 --> 00:00:15.810
and this is where you have many firms,

00:00:15.810 --> 00:00:18.330
what they produce is not differentiated,

00:00:18.330 --> 00:00:20.630
there is no barriers to entry,

00:00:20.630 --> 00:00:22.950
and in that situation, we have looked at

00:00:22.950 --> 00:00:24.270
that the market price,

00:00:24.270 --> 00:00:26.400
the firms just have to
take that market price,

00:00:26.400 --> 00:00:29.260
and that market price is
going to describe what

00:00:29.260 --> 00:00:31.630
their marginal revenue is going to be.

00:00:31.630 --> 00:00:34.800
No matter how much each of
those individual firms produce,

00:00:34.800 --> 00:00:36.610
they're just going to
get that market price,

00:00:36.610 --> 00:00:40.070
so that marginal revenue
will be that market price,

00:00:40.070 --> 00:00:41.300
but then we looked at a whole

00:00:41.300 --> 00:00:45.150
sort of what we could call
imperfectly competitive firms,

00:00:45.150 --> 00:00:49.240
imperfectly, imperfect competition.

00:00:49.240 --> 00:00:52.250
At the extreme, you have the monopoly,

00:00:52.250 --> 00:00:54.480
where you only have
one firm in the market,

00:00:54.480 --> 00:00:56.650
huge barriers to entry and

00:00:56.650 --> 00:01:00.260
so that company or that firm
essentially is the market

00:01:00.260 --> 00:01:03.660
and so their demand curve
for their product essentially

00:01:03.660 --> 00:01:05.880
is the market demand curve.

00:01:05.880 --> 00:01:07.160
But in between, you have things

00:01:07.160 --> 00:01:10.370
like monopolistic
competition right over there,

00:01:10.370 --> 00:01:12.380
and in monopolistic competition,

00:01:12.380 --> 00:01:14.610
you have many firms that are competing

00:01:14.610 --> 00:01:16.460
but they are all
differentiated in some way,

00:01:16.460 --> 00:01:17.910
and there are some barriers to entry.

00:01:17.910 --> 00:01:19.960
A good example of monopolistic competition

00:01:19.960 --> 00:01:24.050
or imperfect competition might
be the athletic shoe market.

00:01:24.050 --> 00:01:25.050
In the athletic shoe market,

00:01:25.050 --> 00:01:26.140
you have many competitors,

00:01:26.140 --> 00:01:27.740
you have your Nike, Adidas,

00:01:27.740 --> 00:01:30.740
Reebok, and I could keep listing names,

00:01:30.740 --> 00:01:32.360
and they are all differentiated
in their own way,

00:01:32.360 --> 00:01:34.110
they all have their own brands,

00:01:34.110 --> 00:01:35.750
which they have built up over time,

00:01:35.750 --> 00:01:37.940
they have associations with
certain sports figures,

00:01:37.940 --> 00:01:40.560
some their shoes might
be perceived as better

00:01:40.560 --> 00:01:42.480
in certain categories, but they

00:01:42.480 --> 00:01:44.620
are also competing with each other.

00:01:44.620 --> 00:01:45.950
So the competition is that they

00:01:45.950 --> 00:01:46.940
are competing with each other

00:01:46.940 --> 00:01:48.910
but you could consider
monopolistic competition

00:01:48.910 --> 00:01:50.470
because only Nike can sell,

00:01:50.470 --> 00:01:54.210
well, Nike shoes, and so you
could imagine a demand curve

00:01:54.210 --> 00:01:56.490
for say only Nike shoes,

00:01:56.490 --> 00:01:58.130
so in imperfect competition,

00:01:58.130 --> 00:02:00.800
every firm would have their
own unique demand curve,

00:02:00.800 --> 00:02:05.330
and how much they produce
actually will affect the price

00:02:05.330 --> 00:02:07.700
that they get for the
product or the service,

00:02:07.700 --> 00:02:09.680
and what we're going to
see in this video is when

00:02:09.680 --> 00:02:11.880
we are dealing with imperfect competition,

00:02:11.880 --> 00:02:13.990
the demand curve, the price,

00:02:13.990 --> 00:02:17.010
isn't exactly what marginal
revenue is going to be,

00:02:17.010 --> 00:02:20.093
and to understand that, let's
look at a simple model here.

00:02:21.150 --> 00:02:24.600
So right over here, I
have a very simple model

00:02:24.600 --> 00:02:26.570
of a demand curve for a firm

00:02:26.570 --> 00:02:28.880
in an imperfectly competitive market,

00:02:28.880 --> 00:02:30.900
and you can see here that the more

00:02:30.900 --> 00:02:33.420
that that firm produces of its goods,

00:02:33.420 --> 00:02:36.810
the lower price it can get for that good,

00:02:36.810 --> 00:02:38.590
and we can see very clearly this

00:02:38.590 --> 00:02:41.600
is a classic downward
sloping demand curve,

00:02:41.600 --> 00:02:44.040
but what's going to be really
interesting is to think about,

00:02:44.040 --> 00:02:45.850
what is going to be the marginal revenue,

00:02:45.850 --> 00:02:47.810
especially the marginal revenue in a world

00:02:47.810 --> 00:02:49.750
where if they sell one unit,

00:02:49.750 --> 00:02:52.000
they get 32.50, but when
they sell two units,

00:02:52.000 --> 00:02:54.610
it's not like they'll get
32.50 for one of those units

00:02:54.610 --> 00:02:56.940
and then they'll get
25 for the second unit.

00:02:56.940 --> 00:03:00.150
If you have a market price
out there for $25, you're

00:03:00.150 --> 00:03:02.380
going to get $25 on all two units,

00:03:02.380 --> 00:03:05.130
so even though someone was
willing to pay 32.50 for one,

00:03:05.130 --> 00:03:05.963
they are still only going

00:03:05.963 --> 00:03:08.250
to pay $25, so let's think about what

00:03:08.250 --> 00:03:09.520
that does to the marginal revenue.

00:03:09.520 --> 00:03:10.550
I encourage you to pause this video

00:03:10.550 --> 00:03:11.610
and try to fill out this table

00:03:11.610 --> 00:03:13.363
yourself before I do it with you.

00:03:14.270 --> 00:03:15.920
All right, now let's do it together,

00:03:15.920 --> 00:03:18.360
so our total revenue,
obviously when we sell nothing,

00:03:18.360 --> 00:03:20.310
we have, let me do this in another color,

00:03:20.310 --> 00:03:22.300
we have zero total revenue.

00:03:22.300 --> 00:03:24.580
Now, when we sell one unit at 32.50, well,

00:03:24.580 --> 00:03:25.810
then our total revenue is

00:03:25.810 --> 00:03:28.370
going to be 32.50, no surprise there.

00:03:28.370 --> 00:03:29.990
Now it's going to get interesting.

00:03:29.990 --> 00:03:31.610
When we sell two units,

00:03:31.610 --> 00:03:33.730
what's going to be our total revenue?

00:03:33.730 --> 00:03:37.280
Well, both of those units
are gonna be sold at $25,

00:03:37.280 --> 00:03:38.640
it's not like, as I just said, it's not

00:03:38.640 --> 00:03:41.130
like that first person is
still willing to pay 32.50,

00:03:41.130 --> 00:03:43.170
like hey, your market price is $25,

00:03:43.170 --> 00:03:44.690
that's what everyone is going to pay,

00:03:44.690 --> 00:03:49.520
so now your total revenue
is $50, two times $25.

00:03:49.520 --> 00:03:52.200
Now when you go to three,

00:03:52.200 --> 00:03:55.130
the market price that you
can get is 17.50, let's see,

00:03:55.130 --> 00:03:58.503
that is going to be, 52.50.

00:04:00.135 --> 00:04:01.950
52.50 of total revenue,

00:04:01.950 --> 00:04:05.550
and then if you, if your
market price was $10, you could

00:04:05.550 --> 00:04:06.640
have a quantity of four.

00:04:06.640 --> 00:04:08.500
If you wanted to sell four,

00:04:08.500 --> 00:04:09.890
you could do so at a price

00:04:09.890 --> 00:04:11.820
of $10, you can do it in either way,

00:04:11.820 --> 00:04:14.217
but then your total
revenue is going to be $40.

00:04:15.460 --> 00:04:16.920
Now, from this, we can think about, well,

00:04:16.920 --> 00:04:18.780
what's our marginal revenue?

00:04:18.780 --> 00:04:21.520
Well, our marginal revenue
for that first unit

00:04:21.520 --> 00:04:23.360
is the same as what the price

00:04:23.360 --> 00:04:26.520
of that first unit is, we
went from zero to 32.50 with

00:04:26.520 --> 00:04:31.440
that first unit, so that's
32.50 right over here,

00:04:31.440 --> 00:04:32.710
but what about as we go

00:04:32.710 --> 00:04:35.900
from that first unit to that second unit?

00:04:35.900 --> 00:04:37.840
Well, our units go up by one,

00:04:37.840 --> 00:04:41.773
but our revenue from 32.50
to 50 goes up by 17.50,

00:04:42.960 --> 00:04:44.440
and so we are already seeing

00:04:44.440 --> 00:04:46.670
that there is a discrepancy
between our marginal revenue

00:04:46.670 --> 00:04:49.600
and our price, and we can going.

00:04:49.600 --> 00:04:51.590
When we go from two to three units,

00:04:51.590 --> 00:04:54.170
our revenue only goes up by 2.50,

00:04:54.170 --> 00:04:57.630
and so that's going to
be our marginal revenue,

00:04:57.630 --> 00:04:59.980
and then something very
interesting happens.

00:04:59.980 --> 00:05:02.270
As we go from three units to four units,

00:05:02.270 --> 00:05:04.420
our total revenue actually goes down,

00:05:04.420 --> 00:05:09.420
it goes down by 12.50,
negative 12.50 right over here,

00:05:10.890 --> 00:05:13.450
and that's because when
the price gets that low,

00:05:13.450 --> 00:05:15.770
you are taking a hit on all of the units

00:05:15.770 --> 00:05:17.820
that you are selling, so
you'll actually get a lower

00:05:17.820 --> 00:05:21.040
total revenue right over
here, and if we plotted,

00:05:21.040 --> 00:05:24.030
we'll see very clearly that
the marginal revenue curve,

00:05:24.030 --> 00:05:27.100
the parts from the demand
curve for that firm

00:05:27.100 --> 00:05:30.100
that's competing in an
imperfectly competitive market,

00:05:30.100 --> 00:05:32.880
and so we can see here at one unit,

00:05:32.880 --> 00:05:36.650
our marginal revenue is
the same, but at two units,

00:05:36.650 --> 00:05:41.650
our marginal revenue is
17.50, at three units,

00:05:42.640 --> 00:05:45.980
our marginal revenue is 2.50,

00:05:45.980 --> 00:05:48.520
and so we have a marginal revenue curve

00:05:48.520 --> 00:05:52.430
that looks more like this.

00:05:52.430 --> 00:05:53.900
So the big takeaway is here

00:05:53.900 --> 00:05:57.480
that a firm that's operating
in an imperfectly market.

00:05:57.480 --> 00:05:59.110
It isn't just a price taker,

00:05:59.110 --> 00:06:00.970
it's not that no matter
how much it produces it's

00:06:00.970 --> 00:06:02.420
going to get the same price,

00:06:02.420 --> 00:06:04.730
it's going to have its
own unique demand curve,

00:06:04.730 --> 00:06:06.910
because there is some
differentiation in the market,

00:06:06.910 --> 00:06:10.660
and so it's going to have a
downward sloping demand curve,

00:06:10.660 --> 00:06:13.390
and because of that downward
sloping demand curve,

00:06:13.390 --> 00:06:14.360
you are also going to have

00:06:14.360 --> 00:06:16.560
a downward sloping marginal revenue curve

00:06:16.560 --> 00:06:18.360
and that marginal
revenue curve is actually

00:06:18.360 --> 00:06:21.570
going to be downward
sloping at a steeper rate,

00:06:21.570 --> 00:06:23.750
so when we start doing the firm analysis

00:06:23.750 --> 00:06:25.870
of marginal cost and
where does it intersect

00:06:25.870 --> 00:06:28.240
the marginal revenue, if
you're dealing with a firm

00:06:28.240 --> 00:06:30.380
that's operating in a
perfectly competitive market,

00:06:30.380 --> 00:06:32.270
that marginal revenue curve
when we've seen it before

00:06:32.270 --> 00:06:34.310
was horizontal, but when we think about

00:06:34.310 --> 00:06:36.110
that marginal revenue curve for a firm

00:06:36.110 --> 00:06:37.710
in an imperfectly competitive market,

00:06:37.710 --> 00:06:39.230
that's going to be downward sloping,

00:06:39.230 --> 00:06:41.250
it's going to be sloping downward faster

00:06:41.250 --> 00:06:42.793
than its demand curve.


Marginal revenue and marginal cost in imperfect competition

WEBVTT
Kind: captions
Language: en

00:00:00.210 --> 00:00:02.270
- [Instructor] In this video,
we're going to think about

00:00:02.270 --> 00:00:04.530
marginal revenue and marginal cost

00:00:04.530 --> 00:00:07.840
for a firm in an imperfectly
competitive market.

00:00:07.840 --> 00:00:10.160
But before we do that, I just
want to be able to review

00:00:10.160 --> 00:00:12.080
and compare to what we already know

00:00:12.080 --> 00:00:14.850
about a firm in a perfectly
competitive market.

00:00:14.850 --> 00:00:18.150
So right over here, we're
analyzing the firm's economics.

00:00:18.150 --> 00:00:20.780
This shows the marginal cost
as a function of quantity,

00:00:20.780 --> 00:00:22.530
and we've talked about this before.

00:00:22.530 --> 00:00:24.760
Oftentimes, it will trend down initially,

00:00:24.760 --> 00:00:27.640
as you have better specialization
and some efficiencies,

00:00:27.640 --> 00:00:29.340
and then it might start trending up,

00:00:29.340 --> 00:00:30.820
as there are just coordination costs

00:00:30.820 --> 00:00:33.310
or other costs that make
the marginal cost go up.

00:00:33.310 --> 00:00:35.560
And we have talked about this notion that,

00:00:35.560 --> 00:00:37.560
in a perfectly competitive market,

00:00:37.560 --> 00:00:39.460
the firm is a price-taker.

00:00:39.460 --> 00:00:41.660
There's going to be some market price,

00:00:41.660 --> 00:00:44.530
let's call this P sub m,

00:00:44.530 --> 00:00:45.850
some price in the market

00:00:45.850 --> 00:00:47.490
for the good that they are producing,

00:00:47.490 --> 00:00:49.310
and there's many producers
who are producing this good.

00:00:49.310 --> 00:00:50.310
And they're undifferentiated,

00:00:50.310 --> 00:00:51.890
and there's no barriers to entry.

00:00:51.890 --> 00:00:53.630
And so they just have to
be price-takers there.

00:00:53.630 --> 00:00:55.870
No matter how many units they produce,

00:00:55.870 --> 00:00:58.680
they're just going to be able
to get that same market price.

00:00:58.680 --> 00:01:01.320
So a firm in a perfectly
competitive market,

00:01:01.320 --> 00:01:04.550
that market price defines
their marginal revenue curve.

00:01:04.550 --> 00:01:05.990
Their marginal revenue
curve will essentially

00:01:05.990 --> 00:01:09.130
just be a horizontal line like this,

00:01:09.130 --> 00:01:11.310
and we've already studied
this in previous videos.

00:01:11.310 --> 00:01:13.380
And we talked about that here,

00:01:13.380 --> 00:01:16.450
if this firm was trying
to maximize its profit

00:01:16.450 --> 00:01:19.590
and if it was rational, it
would produce the quantity

00:01:19.590 --> 00:01:22.520
where marginal cost is
equal to marginal revenue.

00:01:22.520 --> 00:01:26.200
So it would produce this
quantity right over here.

00:01:26.200 --> 00:01:28.650
But now let's think about how
things are a bit different

00:01:28.650 --> 00:01:31.620
for a firm in an imperfectly
competitive market.

00:01:31.620 --> 00:01:33.670
In a previous video, we talked about how,

00:01:33.670 --> 00:01:35.250
in an imperfectly competitive market,

00:01:35.250 --> 00:01:36.850
there's some differentiation

00:01:36.850 --> 00:01:39.620
amongst the various
players who are competing,

00:01:39.620 --> 00:01:44.260
and so their market price
is a function of quantity.

00:01:44.260 --> 00:01:47.150
If they just produce a
bunch of their product,

00:01:47.150 --> 00:01:51.050
the price that they get in the
market is likely to go down.

00:01:51.050 --> 00:01:55.030
So they will have their own
firm-specific demand curve.

00:01:55.030 --> 00:01:57.870
Maybe it looks something like this.

00:01:57.870 --> 00:02:00.310
So that is their demand curve.

00:02:00.310 --> 00:02:03.090
And we also saw in that
video that that demand curve,

00:02:03.090 --> 00:02:05.510
essentially the price that
they could get at any quantity,

00:02:05.510 --> 00:02:06.900
that that's not going to be the same

00:02:06.900 --> 00:02:08.180
as the marginal revenue curve.

00:02:08.180 --> 00:02:10.600
If the demand curve is
downward-sloping like that,

00:02:10.600 --> 00:02:12.810
the marginal revenue curve is likely

00:02:12.810 --> 00:02:15.130
to be even more downward-sloping.

00:02:15.130 --> 00:02:17.450
So it's going to look something like this.

00:02:17.450 --> 00:02:19.560
That would be the marginal revenue curve.

00:02:19.560 --> 00:02:20.490
Now in this situation,

00:02:20.490 --> 00:02:23.100
what would be rational for the firm to do?

00:02:23.100 --> 00:02:25.900
Well, once again, it would
want to produce the quantity

00:02:25.900 --> 00:02:29.600
where the marginal cost is
equal to the marginal revenue.

00:02:29.600 --> 00:02:32.650
So they would want to produce
this quantity right over here.

00:02:32.650 --> 00:02:34.660
But you see something interesting here.

00:02:34.660 --> 00:02:36.570
If they produce at this quantity,

00:02:36.570 --> 00:02:39.360
notice the price that
they can get in the market

00:02:39.360 --> 00:02:41.050
is much higher than that.

00:02:41.050 --> 00:02:42.660
The price that they get in the market

00:02:42.660 --> 00:02:44.880
is higher than the marginal cost

00:02:44.880 --> 00:02:46.820
and the marginal revenue at that point.

00:02:46.820 --> 00:02:48.520
And because we see a situation

00:02:48.520 --> 00:02:51.420
where price is greater
than your marginal cost,

00:02:51.420 --> 00:02:53.470
versus in a perfectly competitive market

00:02:53.470 --> 00:02:56.060
where you see that price
is equal to marginal cost,

00:02:56.060 --> 00:02:57.670
that that is the optimal quantity,

00:02:57.670 --> 00:02:59.710
but because you have this gap,

00:02:59.710 --> 00:03:03.280
that people are willing to pay
more than that marginal cost.

00:03:03.280 --> 00:03:05.180
But you still aren't going to
be able to produce any more

00:03:05.180 --> 00:03:06.500
because it doesn't make sense

00:03:06.500 --> 00:03:08.340
from a marginal revenue point of view.

00:03:08.340 --> 00:03:09.280
This gap,

00:03:09.280 --> 00:03:11.810
the difference between the
price and the marginal cost

00:03:11.810 --> 00:03:14.930
at this rational quantity for this firm

00:03:14.930 --> 00:03:17.510
in an imperfectly competitive
market to produce,

00:03:17.510 --> 00:03:20.560
economists would refer to
this as an inefficiency,

00:03:20.560 --> 00:03:22.310
inefficiency.

00:03:22.310 --> 00:03:24.510
Folks are willing to pay
more than that marginal cost,

00:03:24.510 --> 00:03:28.140
but you still have no
motivation to produce more.

00:03:28.140 --> 00:03:29.350
Because if you produce more,

00:03:29.350 --> 00:03:31.720
even though the price is
higher than the marginal cost,

00:03:31.720 --> 00:03:33.140
your marginal revenue is going

00:03:33.140 --> 00:03:34.890
to be below the marginal cost,

00:03:34.890 --> 00:03:36.670
and so you would be taking a hit

00:03:36.670 --> 00:03:38.873
in aggregate on those extra units.


Khan Stories: Jordan

WEBVTT
Kind: captions
Language: en

00:00:00.350 --> 00:00:02.700
- I'm Jordan, I'm a sophomore at Harvard.

00:00:02.700 --> 00:00:04.200
I'm first-generation college student.

00:00:04.200 --> 00:00:05.600
My dad works two, three jobs.

00:00:05.600 --> 00:00:07.040
My mom's still working.

00:00:07.040 --> 00:00:08.740
My grandparents, coming from Puerto Rico,

00:00:08.740 --> 00:00:11.390
and that kind of thing, and
not having any education.

00:00:11.390 --> 00:00:14.570
So from two generations
ago, my grandparents,

00:00:14.570 --> 00:00:17.170
not even going to middle
school, to me being at Harvard,

00:00:17.170 --> 00:00:19.230
I think that is not only symbolic

00:00:19.230 --> 00:00:21.110
of the hard work that it took to get here,

00:00:21.110 --> 00:00:23.940
but it just shows that you work hard,

00:00:23.940 --> 00:00:24.973
you can really do anything.

00:00:24.973 --> 00:00:25.990
(uplifting, exciting music)

00:00:25.990 --> 00:00:27.360
With my dad always telling me, you know,

00:00:27.360 --> 00:00:30.010
education is what's gonna
take you to the next level.

00:00:30.980 --> 00:00:32.210
No matter where you go to school,

00:00:32.210 --> 00:00:33.780
no matter if you're in high school,

00:00:33.780 --> 00:00:35.710
no matter if you're at the
best university in the world,

00:00:35.710 --> 00:00:37.510
Khan Academy can be used anywhere.

00:00:37.510 --> 00:00:40.430
Just having that 24 hour,
free online resource

00:00:40.430 --> 00:00:43.830
that I have used in the past
and am going to continue using,

00:00:43.830 --> 00:00:45.770
to eventually help me reach my goals

00:00:45.770 --> 00:00:46.960
of one day going to medical school.

00:00:46.960 --> 00:00:49.060
And one day, eventually becoming a doctor.

00:00:50.190 --> 00:00:51.470
Being the first doctor in my family

00:00:51.470 --> 00:00:53.770
is going to be something
that's remarkable,

00:00:53.770 --> 00:00:55.983
and it's gonna mean a lot to my family.


Profit maximization worked example Free Response Question

WEBVTT
Kind: captions
Language: en

00:00:00.140 --> 00:00:02.810
- [Instructor] We're
told corn is used as food

00:00:02.810 --> 00:00:05.480
and as an input in the
production of ethanol,

00:00:05.480 --> 00:00:07.040
an alternative fuel.

00:00:07.040 --> 00:00:12.020
Assume corn is produced in a
perfectly competitive market.

00:00:12.020 --> 00:00:15.290
Draw correctly labeled side-by-side graphs

00:00:15.290 --> 00:00:19.670
for the corn market and a
representative corn farmer.

00:00:19.670 --> 00:00:22.260
On your graphs show each of the following:

00:00:22.260 --> 00:00:25.310
The equilibrium price and
quantity in the corn market,

00:00:25.310 --> 00:00:29.580
labeled P sub M and Q sub M, respectively.

00:00:29.580 --> 00:00:33.440
The profit-maximizing
quantity of corn produced

00:00:33.440 --> 00:00:37.110
by the representative farmer
earning zero economic profit,

00:00:37.110 --> 00:00:39.010
labeled Q sub F.

00:00:39.010 --> 00:00:41.350
So like always, pause this
video and see if you can do this

00:00:41.350 --> 00:00:44.190
on your own before we
work through it together.

00:00:44.190 --> 00:00:45.820
All right, now let's
work through it together.

00:00:45.820 --> 00:00:50.270
So we're going to do correctly
labeled side-by-side graphs.

00:00:50.270 --> 00:00:54.300
So let me do, ooh, this is
going to be my horizontal axis

00:00:54.300 --> 00:00:55.950
for the market.

00:00:55.950 --> 00:00:58.724
And then this is going
to be the horizontal axis

00:00:58.724 --> 00:01:01.090
for the farmer.

00:01:01.090 --> 00:01:06.090
And this is going to be quantity
in the market, quantity.

00:01:07.180 --> 00:01:10.080
Quantity, and then this
is going to be quantity

00:01:10.080 --> 00:01:13.760
for the farmer, quantity.

00:01:13.760 --> 00:01:17.710
And then this is going to
be price in the market.

00:01:17.710 --> 00:01:19.240
And whatever the market price is,

00:01:19.240 --> 00:01:20.580
that's also going to be the price

00:01:20.580 --> 00:01:21.840
that the farmer has to take,

00:01:21.840 --> 00:01:24.340
because it says it's a
perfectly competitive market.

00:01:24.340 --> 00:01:26.913
So the farmer's going to
be a price taker here.

00:01:27.840 --> 00:01:30.400
So let me make these axes.

00:01:30.400 --> 00:01:33.290
So this is price right over here.

00:01:33.290 --> 00:01:35.700
And this is price over here.

00:01:35.700 --> 00:01:38.020
So first let's draw the corn market.

00:01:38.020 --> 00:01:42.280
So let me label this corn market.

00:01:42.280 --> 00:01:44.710
And we've done this
multiple times already.

00:01:44.710 --> 00:01:47.360
Our demand curve might
look something like this.

00:01:47.360 --> 00:01:49.333
This is our demand curve.

00:01:50.280 --> 00:01:54.290
As when price is high,
low quantity demanded.

00:01:54.290 --> 00:01:56.510
When price is low, high quantity demanded.

00:01:56.510 --> 00:01:58.530
And supply goes the other way around.

00:01:58.530 --> 00:02:02.140
So our supply curve would
look something like this.

00:02:02.140 --> 00:02:05.450
And then this point,
this helps us figure out

00:02:05.450 --> 00:02:07.960
this is going to be our equilibrium price,

00:02:07.960 --> 00:02:11.600
so that's P sub M, P sub M.

00:02:11.600 --> 00:02:15.890
And then this is going to
be our equilibrium quantity,

00:02:15.890 --> 00:02:18.360
so Q sub M.

00:02:18.360 --> 00:02:23.320
Now this graph over here, we
are going to draw the farmer.

00:02:23.320 --> 00:02:26.423
So this is going to be the farmer,

00:02:27.600 --> 00:02:29.980
the farmer's firm right over here.

00:02:29.980 --> 00:02:31.690
So the farmer's going to be a price taker,

00:02:31.690 --> 00:02:33.748
so whatever the equilibrium
price in the market,

00:02:33.748 --> 00:02:36.470
that is going to be the
price that the farmer

00:02:36.470 --> 00:02:38.080
is going to have to take.

00:02:38.080 --> 00:02:39.890
That market price is going to be

00:02:39.890 --> 00:02:42.510
the farmer's marginal revenue.

00:02:42.510 --> 00:02:44.730
Now they say the
profit-maximizing quantity

00:02:44.730 --> 00:02:48.530
of corn produced by the
representative farmer

00:02:48.530 --> 00:02:53.160
earning zero economic
profit, labeled Q sub F.

00:02:53.160 --> 00:02:55.560
So we're going to have some
quantity right over here.

00:02:55.560 --> 00:02:58.020
It is the profit-maximizing quantity,

00:02:58.020 --> 00:03:01.460
but it's also zero economic profit.

00:03:01.460 --> 00:03:04.210
So the zero economic profit tells us

00:03:04.210 --> 00:03:09.210
that the price must be equal
to the average total cost

00:03:09.235 --> 00:03:11.090
at that quantity.

00:03:11.090 --> 00:03:13.210
So I can make an average total cost curve

00:03:13.210 --> 00:03:15.053
that looks something like this.

00:03:16.410 --> 00:03:18.250
And I'm going to make its minimum point

00:03:18.250 --> 00:03:21.600
intersect that market price,

00:03:21.600 --> 00:03:24.850
because we know from previous videos

00:03:24.850 --> 00:03:27.440
that the profit-maximizing quantity

00:03:27.440 --> 00:03:30.060
happens where the marginal cost

00:03:30.060 --> 00:03:32.270
intersects the marginal
revenue, which, in this case,

00:03:32.270 --> 00:03:34.780
would be the price that
the farmer has to take

00:03:34.780 --> 00:03:35.613
from the market.

00:03:35.613 --> 00:03:37.380
And we know that the marginal cost curve

00:03:37.380 --> 00:03:39.460
intersects the average total cost curve

00:03:39.460 --> 00:03:41.430
at this minimum point right over here.

00:03:41.430 --> 00:03:44.740
So I could draw a marginal cost curve.

00:03:44.740 --> 00:03:47.290
It might look something like this.

00:03:47.290 --> 00:03:50.120
So that is our marginal cost curve.

00:03:50.120 --> 00:03:52.140
And notice, the marginal cost curve

00:03:52.140 --> 00:03:54.810
intersects the average total
cost at that minimum point.

00:03:54.810 --> 00:03:57.660
We explained that in
multiple videos already.

00:03:57.660 --> 00:04:00.160
And we've explained in a previous video

00:04:00.160 --> 00:04:02.350
that the profit-maximizing quantity

00:04:02.350 --> 00:04:04.500
is the quantity at which the marginal cost

00:04:04.500 --> 00:04:06.690
and the marginal revenue meet.

00:04:06.690 --> 00:04:09.180
And the price is the marginal revenue.

00:04:09.180 --> 00:04:11.940
Beyond that point, every incremental unit

00:04:11.940 --> 00:04:13.410
the corn farmer's going to take a loss.

00:04:13.410 --> 00:04:15.630
It's gonna take him more resources

00:04:15.630 --> 00:04:17.100
to produce that corn

00:04:17.100 --> 00:04:20.020
than they're going to
able to get in the market.

00:04:20.020 --> 00:04:22.400
And we also mentioned that
this has to be a situation

00:04:22.400 --> 00:04:24.220
of zero economic profit.

00:04:24.220 --> 00:04:27.930
So the average total cost
has to be at that price,

00:04:27.930 --> 00:04:30.470
at that marginal revenue
right at that point.

00:04:30.470 --> 00:04:32.600
So this right over here

00:04:32.600 --> 00:04:37.600
would be our Q sub capital F.

00:04:38.270 --> 00:04:39.103
And we're done.