WEBVTT

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Divide and write the answer
as a mixed number.

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And we have 3/5 divided
by 1/2.

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Now, whenever you're dividing
any fractions, you just have

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to remember that dividing by a
fraction is the same thing as

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multiplying by its reciprocal.

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So this thing right here is the
same thing as 3/5 times--

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so this is our 3/5 right here,
and instead of a division

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sign, you want a multiplication
sign, and

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instead of a 1/2, you want to
take the reciprocal of 1/2,

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which would be 2/1--
so times 2/1.

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So dividing by 1/2 is the
exact same thing as

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multiplying by 2/1.

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And we just do this as a
straightforward multiplication

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problem now.

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3 times 2 is 6, so our
new numerator is 6.

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5 times 1 is 5.

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So 3/5 divided by 1/2 as an
improper fraction is 6/5.

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Now, they want us to write
it as at mixed number.

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So we divide the 5 into
the 6, figure out how

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many times it goes.

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That'll be the whole number
part of the mixed number.

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And then whatever's left over
will be the remaining

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numerator over 5.

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So what we'll do is
take 5 into 6.

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5 goes into 6 one time.

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1 times 5 is 5.

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Subtract.

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You have a remainder of 1.

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So 6/5 is equal to one whole,
or 5/5, and 1/5.

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This 1 comes from whatever
is left over.

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And now we're done!

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3/5 divided by 1/2
is 1 and 1/5.

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Now, the one thing that's not
obvious is why did this work?

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Why is dividing by 1/2 the
same thing as multiplying

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essentially by 2.

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2/1 is the same thing as 2.

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And to do that, I'll do a little
side-- fairly simple--

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example, but hopefully, it
gets the point across.

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Let me take four objects.

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So we have four objects:
one, two, three, four.

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So I have four objects, and if
I were to divide into groups

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of two, so I want to divide
it into groups of two.

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So that is one group of two and
then that is another group

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of two, how many groups
do I have?

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Well, 4 divided by 2, I have two
groups of two, so that is

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equal to 2.

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Now, what if I took those
same four objects:

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one, two, three, four.

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So I'm taking those
same four objects.

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Instead of dividing them into
groups of two, I want to

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divide them into groups of 1/2,
which means each group

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will have half of
an object in it.

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So let's say that would be
one group right there.

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That is a second group.

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That is a third group.

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I think you see each group has
half of a circle in it.

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That is the fourth.

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That's the fifth.

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That's the sixth.

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That's the seventh, and then
that's the eighth.

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You have eight groups of 1/2,
so this is equal to 8.

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And notice, now each of the
objects became two groups.

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So you could say how many
groups do you have?

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Well, you have four objects
and each of

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them became two groups.

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I'm looking for a
different color.

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Each of them became
two groups, and so

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you also have eight.

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So dividing by 1/2 is the same
thing as multiplying by 2.

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And you could think about it
with other numbers, but

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hopefully, that gives you a
little bit of an intuition.

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