WEBVTT

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So I've got a whole
pizza here, and let's say

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that I were to cut it
into two equal pieces.

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

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

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

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What fraction of the
pizza have I eaten?

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Well, I took the
whole and I divide it

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into two equal pieces, and
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
of cutting that pizza into only

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2 equal pieces,
let's imagine instead

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that decide to cut it
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
this way and then

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I could cut it once this way.

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And so here I have
4 equal pieces.

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

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

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

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Well, I would eat this piece.

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You could imagine me eating
this piece and this piece right

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over here.

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I've eaten the same
amount of the pizza.

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Each of these pieces you could
imagine got cut into 2 pieces

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when I cut the whole
pizza this way.

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And so now I have to
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
of the 4 slices.

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I'm using different
numbers here.

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Here I'm using a
1 in the numerator

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and 2 in the denominator.

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Here, I'm using a
2 in the numerator

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and a 4 in the denominator.

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These two fractions
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
eat 2 out of 4 equal pieces,

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that's the same
fraction of the pizza

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as if I eat 1 out
of 2 equal pieces.

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So we would say that
these two things

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are equivalent fractions.

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Now let's do another
one like this.

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Instead of just dividing
it into 4 equal pieces,

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let's divide it
into 8 equal pieces.

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So now we could
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
those 4 pieces into 2 pieces.

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

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I want to make
them equal pieces.

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Those don't look as
equal as I would like.

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So that looks more equal, and
that looks reasonably equal.

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So now how many equal
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
the same fraction of the pizza.

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

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

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

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

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is equivalent to 2/4,
which is equivalent to 1/2.

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And you might see a little
bit of a pattern here.

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Going from this scenario
to this scenario,

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I got twice as
many equal slices.

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Because I had twice
as many equal slices,

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I needed to eat two times
the number of slices.

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So I multiply the
denominator by 2,

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and I multiply the
numerator by 2.

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If I multiply the numerator
and the denominator

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by the same number,
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
slices, I cut every slice,

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I turned every slice
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
eat the same amount,

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I have to eat twice
as many pieces.

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So all of these, 1/2, 2/4, four
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
equivalent fractions.

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