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# 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(14 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(19 votes)

- At0:05, why did they use the shapes a rectangle and a square?(6 votes)
- 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.(14 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.(7 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! :)(7 votes)

- Why do fractions help us in life?(5 votes)
- well, fractions are very usefull. take money. i need to pay my bill of $100 by the end of the month. i have $35 so far. so i have 35/100 of what i need.(1 vote)

- Hii! um...how do you divide fractions? also i think it is very fun to multiply fractions so may u please make a video on that? Thank you!(5 votes)
- to multiply fractions, simply multiply the numerators, and put that over the product of the denominators. For example, lets say we have 1/5*2/3, 1(2) = 2 and 5(3) = 15, so you get 2/15, and when you divide fractions, you simply take the recipricol of the dividend and then multiply.(2 votes)

- Go me+smart group!(4 votes)
- It looks like the triangle that Sal show last could be divided into 8 equal parts. I think the top of the red colored triangle starts at the middle of the side of the big triangle. So the small triangle would be 1/8 of the larger triangle. Anyone agree?(3 votes)
- Is the triangle 1/6 equal part? If not, what is it? I'd like to know what part of the triangle was shaded and how it was derived. I'll have a hard time sleeping until I understand how to figure out what fractional part of that triangle was shaded.(3 votes)
- Sadly,i don't understand what you mean,please be more understandable(1 vote)

- why do we have fractions ?(3 votes)
- Sometimes we have to represent numbers that are not whole. If you eat a slice of pizza, you didn't eat 1 whole pizza, you likely ate 1/8 of the pizza.(3 votes)

- Why did you make Khan Academy anyway because most things I get wrong I am on fraction?(3 votes)

## 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.