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Sarah has $48.

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She wants to save 1/3 of
her money for a trip.

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How many dollars should
she set aside?

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So we essentially want to think
about what 1/3 of 48 is.

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Use 48 as the denominator
and find an

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equivalent fraction to 1/3.

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So what they want us to do in
this problem is they want us

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to say, OK, we want 1/3 of her
money, but we want to write

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this as an equivalent fraction
where we have 48 in the

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denominator.

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So this is equal to something,
some blank up here.

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This is equal to something
over 48.

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So how can we get it to that
something over 48?

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So let's think about what
this means for a second.

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So 1/3, if we were to draw
1/3, it looks like this.

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You could imagine a box
or a pie, I guess.

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So let's say that this is my
pie, and I have it split into

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three pieces.

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So let me split it into
three even pieces.

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And 1/3 is one of those
three pieces.

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That is what 1/3 means.

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Now, if we want express this as
a fraction over 48, how can

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we do that?

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Well, we're going to
have to split this

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thing into 48 pieces.

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How can we split something
into 48?

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Well, 3 times 16 is 48, so if we
split each of these into 16

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pieces-- and it's going
to be hard to draw

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here, but you can imagine.

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Let's see, you split it into
two, now we've split it into

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four, now you split
it into eight.

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You're just going to end up with
a bunch of lines here,

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but you can imagine, you can
just split each of these.

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If you split each of these into
enough, you would have 16

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pieces, so those would
be 16 right there.

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You would have 16 right there
and you have 16 right there.

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And I can just keep doing it.

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Let me do it in the
green over here.

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So if we just kept splitting
it up, we would get 48,

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because you have this first
third would be 16 pieces, the

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second third would be 16,
and then this third

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third would be 16 pieces.

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Altogether, you would
have 48 pieces.

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Now, that 1/3, what does
that represent?

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Well, that represents
16 of the 48.

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It represents these
16 right here.

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It represents these 16 right
there, so 1 over 3 is the

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exact same thing.

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So 1 over 3 is the exact same
thing as 16 over 48.

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Now, we did it just by thinking
about it kind of

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intuitively what 1/3 of 48 is,
but one way to do it more-- I

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guess a process for doing it--
we would say, well, look, to

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get the denominator, the bottom
number, from 3 to 48,

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we multiply by 16.

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3 times 16 is 48.

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And that's literally the process
of going from 3 pieces

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to 48 pieces.

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We have to multiply by 16.

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We have to turn each of our
pieces into 16 pieces.

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That's what we did.

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Now, you can't just multiply
only the denominator by 16.

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You have to multiply the
numerator by the same number.

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And so if each of my pieces
now become 16 pieces, then

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that one piece will
now become 16.

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So one way to think about it,
you just say, well, 3 times 16

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is 48, so 1 times 16 will be my
numerator, so it'll be 16.

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So 1/3 is equal to 16/48.

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And another way you could think
about it, which you'll

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learn in more detail later on,
is we want 1/3 of 48, right?

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That's how much she wants to
save. 1/3 of 48 is equal to

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1/3 times 48.

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And when you multiply-- let me
write it like this-- 1/3 times

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48, and you could rewrite
48 as a fraction 48/1.

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It literally represents
48 wholes.

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And when you multiply fractions,
you can just

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multiply the numerators.

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So this is equal to 48 over--
and then you just multiply the

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denominators.

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48/3, 1 times 48 is 48.

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We'll see this in more
detail in the future.

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Don't worry about it
if it confuses you.

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In the denominator, 3 times 1 is
3, and 48 divided by 3, or

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48/3, is equal to 16.

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So 1/3 of 48 is 16,
or 16/48 is 1/3.

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Hopefully, that make
sense to you.