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## Arithmetic (all content)

# Intro to fractions

Sal divides wholes into equal-sized pieces to create unit fractions. Created by Sal Khan.

## Want to join the conversation?

- how do we simplify :

(5a)^3 divided by 5a ^-1 x 5^-2 a^2(10 votes)- The first thing I like to do is multiply everything out and make all the exponents positive, just so that we can get an idea of what we're working with. You can distribute the exponents to each factor that it's raising:

125a^3 / 5^-1 * a^-1 * 5^-2 * a^2

Now that we have everything all laid out, let's make all the exponents positive, just to simplify the problem a bit more:

= 125a^3 * 5^1 * a^1 * 5^2 / a^2

= 5^3 * 5 * 5^2 * a^3 * a / a^2

Now we can combine the exponents, keeping in mind the rule for doing so:

x^a * x^b = x^(a+b)

x^a / x^b = x^(a-b)

5^(3+1+2) * a^(3+1-2)

= 5^6 * a^2

This means that the final answer is 15,625a^2(15 votes)

- At0:05, why did they use the shapes a rectangle and a square?(1 vote)
- Since both squares and rectangles have congruent (similar) sides, then they can be easily cut into integer (whole number) pieces that make it easier to understand in terms of the overall lesson.(10 votes)

- Hi, this isn't about the video, but is it possible to see a lesson about probability somewhere? I would like to know what or means in probability.(3 votes)
- Hi, Sara! Here's the unit on
**Probability**in the*Statistics & probability*course: https://www.khanacademy.org/math/statistics-probability/probability-library! Happy learning! And have a nice day! :)(2 votes)

- Acording to my calculations the answer to the prolem is 3.5 + ½ ×100937562864657.0986328475024245.547374583 + 364892 + .794750 × 473589374504895723405740938572340540597308546703867034580 -4746574839 :48475.01923-7348392 ×2049875380549384910938574375432095723048759827270823354874873890237985432324592437636384729545489308459 + 452345987458972358273095872438573982754573487543092753498574325 = 394807219084701294872398479238749281749823749812748172498127419280742190784810724721984721487290874298748297498217498724987214782197482947129874289174987443912419274891748913274978123489712042719047210741298470291740871408917238473475634902104 694481354635694605558967340-52830457932044579834275924750943875943875934875984375987573497534759873457348975943287532758437534758473573297473485 73459374. (any body can solve this easily)(2 votes)
- Thanks for the help! Now when I does this next chapter I already understand(2 votes)
- I dont understand fractions because how is it that if you add 1/4+1/4 you get 1/2 the number is now shorter(0 votes)
- Let's see if I can clear this up for you. If you have a pizza, and you cut that pizza into four big slices, each slice is 1/4 of a pizza. Now, here's where you might have been confused. 2 of those 4 slices is the same as 1/2 of a pizza. 1/2 is the same as 2/4. If you had only cut the pizza in half, you would have 2 equal halves. I hope this was helpful, because I know how it is to be confused by fractions.(6 votes)

- what does he mean different ways to think about fractions?(2 votes)
- Can every shape represent unlimited fractions?(1 vote)
- yes since you can always divide it further into more parts.(2 votes)

- What is the fraction of the triangle 😕😕😕 is it 1/2(1 vote)

## Video transcript

What we're going to
talk about in this video is the idea of a fraction. And we'll see there's many
ways to think about a fraction. But first, we'll think
about the most fundamental. So let's say that
I have this square. And we can consider
this a whole. So let me write that down. This is a whole. It is a complete square. Now, what I'm going to do is
divide this into 4 equal parts. So with one cut like that, I've
divided it into 2 equal parts, and then with another
cut like this, I could divide it
into 4 equal parts. So there are 4 equal parts. And now what I'm
going to do is I'm going to select one
of those equal parts, so let's say this
part right over here. I am going to select that. So the question is, what
fraction of the whole is the part that I
have shaded in red? Well, it is 1 out of the
4 equal parts, right? I've shaded in 1 out of
1, 2, 3, 4 equal parts. So we write this
as this fraction. This piece represents
1/4 of the whole. And there's two ways that
you can think about this. You could view this as
1 of the 4 equal parts, or you could view this
as a whole divided by 4 would get you exactly this much. Now let's do another one. And this time, let's
think about how we could represent 1
over 8, so 1 over 8. Well, we could divide
this whole, in this case, the whole is this
rectangle-looking thing. We could divide the
whole into 8 equal parts. So let's do that. So here I've divided
into 2 equal parts. That looks pretty good. And now I can divide each
of those into 2 equal parts to get me 4 equal parts. And then if I were to
divide each of those into 2 equal parts, I
will have 8 equal parts. And it's not exact. Obviously, I've
drawn it by hand, but hopefully this
gets you a sense. So now I have 8 equal parts. And now I'm going to
select exactly one of them. And that'll represent 1/8. And I could select
any one of these, but I'll just do
this one to show you it does not have to be
necessarily the first one. So once again, this
square right over here that I'm shading in red
represents 1/8 of the whole. Now, let's look at
a few more examples where I've shaded
them in ahead of time. And what I want you to do
right now is pause the video, and either in your head
or a piece of paper write down if you consider this
purple thing, the whole, what fraction does this
red part represent? If you consider this
blue part the whole, what fraction does this
red part represent? If you view this yellow
triangle as a whole, what fraction does this
red part represent? And so I encourage you
to pause the video now. Well, let's look
at each of these. So in this case,
for this rectangle, we have 3 equal parts, and
we've shaded in one of them. So this red rectangle
right over here represents 1/3 of the whole. Now, Over here, in this kind
of pie-looking thing, this circle-looking thing, we
have 1, 2, 3, 4, 5 equal parts. And we have shaded in 1
of those 5 equal parts. So this little slice of the
pie, this represents 1/5. This right over here is
1/5 of the entire pie. Now, this one's interesting. You might be tempted to
say, well, I've got 5 parts, and then I've shaded in 1. That must represent 1/4. But remember, it needs
to be 4 equal parts. And it's pretty
clear looking at this that this part right
over here is not equal in size to this part right
over here or this part right over here. These are not 4 equal parts. So we cannot say that this
is 1/4 of the triangle. So you cannot say that.