If you’ve been learning math for a while,

then you probably already know a thing or two about fractions.

And if you’ve ever had to break a cookie in half to share with a friend,

well then you’ve used fractions in real life.

Oh… well, thank you… Mmmmm!

That’s because fractions are used to represent smaller pieces or parts of things.

When you’re first learning about fractions, it can help to draw pictures to see how they work.

So let’s start by drawing a circle.

This circle represents what we call a whole.

No, not the kind of hole that you could fall into!

More like a whole cookie, or a whole pizza.

Now, if we divide that circle, or whole amount, into four parts,

then we call each of those parts a fraction of the original whole circle.

Because this is Math class and not Art, we can’t just keep on drawing pictures.

We need to learn how to write out fractions using the language of math.

Yep, you guessed it! That means using numbers.

Unlike a regular number, to write a fraction you need two numbers;

one number on top, one number on bottom, and a line between them.

I’ll explain exactly what the line is for later in the video,

but for now, let’s figure out what the two numbers mean.

Remember, fractions are used to represent parts of something,

and the number on the bottom tells us how many parts that something is divided into.

The number on top tells us how many of those parts we have.

['elevator' music]

For example, let’s write a fraction for our drawing here.

I divided the circle into four parts, right?

So the number on the bottom will be ‘4’.

And I still have all four of those parts, so the number on top will also be ‘4’.

I have ‘4’ out of ‘4’ parts. That means I still have a whole circle.

But what if someone came by and took away one part from the circle.

Well… the circle is still divided into four parts, so the bottom number would still be ‘4’.

But I only have three of those parts left, so that means the top number will change to ‘3’.

So I have ‘3’ over ‘4’, or three-fourths of the circle.

…make sense so far?

Good! Let’s try another example.

Let’s say that I divide a rectangle up into eight parts, and I give you three of those parts.

Since the total number of parts is eight, the bottom number will be ‘8’,

and since you have three of those parts, the top number will be ‘3’.

So the fraction I’m giving you is… ‘3’ over ‘8’, or three-eighths of the rectangle.

No, no, no… no need to thank me.

Oh… and it’s important to remember that for fractions to work right,

the parts that you divide the whole up into have to be equal.

We can’t take like… well… take a candy bar and say,

“well I’m gonna divide it into two parts. So this is your half, and here's my half”.

Let’s look at a few more examples

so you can really see the pattern of how fractions can represent parts of objects.

This rectangle is divided up into three equal parts, and two of them are shaded red.

So ‘2’ over ‘3’, or two-thirds of the rectangle is shaded red.

This circle is divided into twelve equal parts, and seven of those parts are shaded green.

So, ‘7’ over ’12’, or seven-twelfths of the circle is shaded green.

This hexagon is divided into six equal parts, and five of those parts are shaded blue.

So ‘5’ over ‘6’, or five-sixths of the hexagon is shaded blue.

Alright, so you can see how fractions can be used to represent parts of objects like circles and rectangles,

but fractions can be used for more than that.

They can be used to represent parts of… well, anything!

Like… like pets for example.

Let’s say you have seven pets;

four dogs,

two cats,

and a big, fat, hamster.

That means that ‘4’ over ‘7’, or four-sevenths of your pets are dogs,

and ‘2’ over ‘7’, or two-sevenths of your pets are cats,

and ‘1’ over ‘7’, or one-sevenths of your pets are hamsters.

It also means that your house probably smells like a pet store. [laughter]

Okay… so fractions can be used to represent anything from parts of a circle to kitty-cats.

But did you know that fractions can also be used represent things you can’t even see?

Well, like a test score for example…

Let’s say you take a math test and there’s 20 questions on the test,

and you get 17 of those questions right.

That means that you got ’17’ over ’20’ , or seventeen-twentieths of the questions right.

Alright…so that’s the basic idea of how fractions can be used to represent parts of things,

but there’s a lot more to fractions than that.

In the next section, we’re going to be looking at some of the other things we can do with fractions.

But before that, let’s review…

Fractions are used to represent parts of a whole.

Fractions are written in the form of a top number over a bottom number with a line between them.

The bottom number represents how many parts the whole is divided into.

And the top number represents how many of those parts you have.

And finally… the parts that a whole is divided up into must be equal for fractions to work right.

To really understand how fractions are used to represent parts of things,

be sure to do the exercises, and I’ll see you in section two.

Learn more at www.mathantics.com