0:00:00.680,0:00:02.950
So I've got a whole[br]pizza here, and let's say

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that I were to cut it[br]into two equal pieces.

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Let me cut it right over[br]here into 2 equal pieces.

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And let's say that I ate[br]one of those 2 equal pieces.

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So let's say I ate all[br]of this right over here.

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What fraction of the[br]pizza have I eaten?

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Well, I took the[br]whole and I divide it

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into two equal pieces, and[br]then I ate one of those pieces.

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So I ate 1/2 of the pizza.

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Now, let's imagine that instead[br]of cutting that pizza into only

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2 equal pieces,[br]let's imagine instead

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that decide to cut it[br]into 4 equal pieces.

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So let's draw that.

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So 4 equal pieces.

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So I could cut once[br]this way and then

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I could cut it once this way.

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And so here I have[br]4 equal pieces.

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But let's say that I want to[br]eat the same amount of pizza.

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How many of these 4 equal[br]pieces would I have to eat.

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I encourage you to pause the[br]video and think about that.

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Well, I would eat this piece.

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You could imagine me eating[br]this piece and this piece right

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over here.

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I've eaten the same[br]amount of the pizza.

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Each of these pieces you could[br]imagine got cut into 2 pieces

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when I cut the whole[br]pizza this way.

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And so now I have to[br]eat 2 slices of the 4,

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as opposed to 1 slice of the 2.

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So I just ate 2 out[br]of the 4 slices.

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I'm using different[br]numbers here.

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Here I'm using a[br]1 in the numerator

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and 2 in the denominator.

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Here, I'm using a[br]2 in the numerator

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and a 4 in the denominator.

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These two fractions[br]represent the same quantity.

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I ate the same amount of pizza.

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If I eat 2/4 of a pizza, if I[br]eat 2 out of 4 equal pieces,

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that's the same[br]fraction of the pizza

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as if I eat 1 out[br]of 2 equal pieces.

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So we would say that[br]these two things

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are equivalent fractions.

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Now let's do another[br]one like this.

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Instead of just dividing[br]it into 4 equal pieces,

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let's divide it[br]into 8 equal pieces.

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So now we could[br]cut once like this.

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So now we have 2 equal pieces.

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Cut once like this.

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Now we have 4 equal pieces.

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And then divide each of[br]those 4 pieces into 2 pieces.

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So I'll cut those[br]in-- So let's see.

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I want to make[br]them equal pieces.

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Those don't look as[br]equal as I would like.

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So that looks more equal, and[br]that looks reasonably equal.

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So now how many equal[br]pieces do I have?

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I have 8 equal pieces.

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But let's say I wanted to eat[br]the same fraction of the pizza.

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So I could eat all of these[br]pieces right over here.

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Well, how many of those 8[br]equal pieces have I eaten?

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Well, I've eaten 1, 2, 3,[br]4 of those 8 equal pieces.

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And so once again, this[br]fraction, 4 of 8, or 4/8,

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is equivalent to 2/4,[br]which is equivalent to 1/2.

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And you might see a little[br]bit of a pattern here.

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Going from this scenario[br]to this scenario,

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I got twice as[br]many equal slices.

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Because I had twice[br]as many equal slices,

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I needed to eat two times[br]the number of slices.

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So I multiply the[br]denominator by 2,

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and I multiply the[br]numerator by 2.

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If I multiply the numerator[br]and the denominator

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by the same number,[br]then I'm not changing

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what that fraction represents.

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And you see that over here.

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Going from 4 slices to 8[br]slices, I cut every slice,

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I turned every slice[br]into 2 more slices,

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so I had twice as many slices.

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And then if I want to[br]eat the same amount,

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I have to eat twice[br]as many pieces.

0:04:07.020,0:04:10.590
So all of these, 1/2, 2/4, four[br]4/8, and I could keep going.

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I could do 8/16.

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I could do 16/32.

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All of these would be[br]equivalent fractions.