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  • If youve been learning math for a while,

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

  • And if youve ever had to break a cookie in half to share with a friend,

  • well then youve used fractions in real life.

  • Ohwell, thank youMmmmm!

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

  • When youre 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.

  • Wellthe 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, nono need to thank me.

  • Ohand 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 likewelltake 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 ofwell, anything!

  • Likelike 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]

  • Okayso 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.

  • Alrightso 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, were 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 finallythe 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

If youve been learning math for a while,

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