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Welcome to my presentation on equivalent fractions.

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So equivalent fractions are, essentially what

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they sound like.

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They're two fractions that although they use different

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numbers, they actually represent the same thing.

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Let me show you an example.

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Let's say I had the fraction 1/2.

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Why isn't it writing.

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Let me make sure I get the right color here.

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Let's say I had the fraction 1/2.

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So graphically, if we to draw that, if I had a pie and I

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would have cut it into two pieces.

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That's the denominator there, 2.

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And then if I were to eat 1 of the 2 pieces I would

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have eaten 1/2 of this pie.

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Makes sense.

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Nothing too complicated there.

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Well, what if instead of dividing the pie into two

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pieces, let me just draw that same pie again.

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Instead of dividing it in two pieces, what if I divided

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that pie into 4 pieces?

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So here in the denominator I have a possibility of-- total

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of 4 pieces in the pie.

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And instead of eating one piece, this time I actually

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ate 2 of the 4 pieces.

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Or I ate 2/4 of the pie.

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Well if we look at these two pictures, we can see that

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I've eaten the same amount of the pie.

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So these fractions are the same thing.

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If someone told you that they ate 1/2 of a pie or if they

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told you that they ate 2/4 of a pie, it turns out of that they

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ate the same amount of pie.

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So that's why we're saying those two fractions

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are equivalent.

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Another way, if we actually had-- let's do another one.

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Let's say-- and that pie is quite ugly, but let's assume

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it's the same type of pie.

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Let's say we divided that pie into 8 pieces.

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And now, instead of eating 2 we ate 4 of those 8 pieces.

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So we ate 4 out of 8 pieces.

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Well, we still ended up eating the same amount of the pie.

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We ate half of the pie.

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So we see that 1/2 will equal 2/4, and that equals 4/8.

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Now do you see a pattern here if we just look at the

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numerical relationships between 1/2, 2/4, and 4/8?

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Well, to go from 1/2 to 2/4 we multiply the denominator-- the

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denominator just as review is the number on the bottom

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of the fraction.

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We multiply the denominator by 2.

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And when you multiply the denominator by 2, we also

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multiply the numerator by 2.

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We did the same thing here.

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And that makes sense because well, if I double the number of

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pieces in the pie, then I have to eat twice as many pieces to

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eat the same amount of pie.

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Let's do some more examples of equivalent fractions

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and hopefully it'll hit the point home.

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Let me erase this.

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Why isn't it letting me erase?

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Let me use the regular mouse.

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OK, good.

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Sorry for that.

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So let's say I had the fraction 3/5.

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Well, by the same principle, as long as we multiply the

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numerator and the denominator by the same numbers, we'll

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get an equivalent fraction.

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So if we multiply the numerator times 7 and the denominator

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times 7, we'll get 21-- because 3 times 7 is 21-- over 35.

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And so 3/5 and 21/35 are equivalent fractions.

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And we essentially, and I don't know if you already know how to

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multiply fractions, but all we did is we multiplied 3/5

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times 7/7 to get 21/35.

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And if you look at this, what we're doing here isn't magic.

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7/7, well what's 7/7?

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If I had 7 pieces in a pie and I were to eat 7 of

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them; I ate the whole pie.

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So 7/7, this is the same thing as 1.

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So all we've essentially said is well, 3/5 and we

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multiplied it times 1.

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Which is the same thing as 7/7.

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Oh boy, this thing is messing up.

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And that's how we got 21/35.

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So it's interesting.

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All we did is multiply the number by 1 and we know

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that any number times 1 is still that number.

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And all we did is we figured out a different way

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of writing 21/35.

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Let's start with a fraction 5/12.

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And I wanted to write that with the denominator-- let's say I

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wanted to write that with the denominator 36.

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Well, to go from 12 to 36, what do we have to multiply by?

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Well 12 goes into 36 three times.

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So if we multiply the denominator by 3, we also have

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to multiply the numerator by 3.

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Times 3.

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We get 15.

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So we get 15/36 is the same thing as 5/12.

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And just going to our original example, all that's saying

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is, if I had a pie with 12 pieces and I ate 5 of them.

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Let's say I did that.

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And then you had a pie, the same size pie, you had a

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pie with 36 pieces and you ate 15 of them.

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Then we actually ate the same amount of pie.

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