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Welcome to the presentation
on dividing fractions.

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Let's get started.

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So before I give you the
intuition-- actually, I might

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do that in a different module--
I'm just going to show you the

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mechanics of how you
divide a fraction.

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And it turns out that
it's actually not much

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more difficult than
multiplying fractions.

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If I were to ask you, 1/2
divided by 1/2, whenever you

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divide by a fraction, or
actually, when you divide by

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any number, it's the same thing
as multiplying by its inverse.

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So 1/2 divided by 1/2 is
equal to 1/2 times 2/1.

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We just inverted--
inverse-- the second 1/2.

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And we know from the
multiplication module, 1/2

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times 2/1, well, that's
just equal to 2/2,

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or it's equal to 1.

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And that makes sense because,
actually, any number divided

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by itself is equal to 1.

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1/2 divided by 1/2 is 1, just
like 5 divided by 5 is 1, just

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like 100 divided by 100 is 1.

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And this isn't a new principal.

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Actually, you were
always doing it.

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But isn't this also the
same thing as 2 times the

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inverse of 2, which is 1?

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I'll show it to you.

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Actually, let me give you a
couple more examples to show

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that dividing fractions really
isn't a new concept, this whole

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notion of multiplying
by the inverse.

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If I were to tell you
what is 12 divided by 4?

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Well, we know the answer to
this, but I'm going to show

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you that this is the same
thing as 12 times 1/4.

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12/1 times 1/4 4 is
12/4, which is 3.

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And 12/4 is really just another
way of writing 12 divided by 4,

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so it's kind of a long way of
getting to the same point.

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But I just wanted to show you
that what we're doing in this

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module is nothing new than
what we've always been doing

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when we divide by a number.

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Division is the same thing.

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Dividing by a number is the
same thing as multiplying by

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the inverse of that number.

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And just as a review, an
inverse, if I have a number

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A, the inverse-- inv, short
for inverse-- is 1 over A.

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So the inverse of 2/3 is 3/2,
or the inverse of 5, because 5

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is the same thing as 5/1,
so the inverse is 1/5.

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So let's do some fraction
division problems.

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What is 2/3 divided by 5/6?

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Well, we know that this is the
same thing as 2/3 times 6/5,

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and that's equal to 12/15.

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We can divide the numerator and
denominator by 3, that's 4/5.

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What is 7/8 divided by 1/4?

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Well, that's the same
thing as 7/8 times 4/1.

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Remember, I just
flipped this 1/4.

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Divide by 1/4 is the same
thing as multiplying by 4/1.

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That's all you've got to do.

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And then we could use a little
shortcut we learned in the

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multiplication module.

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8 divided by 4 is 2.

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4 divided by 4 is 1.

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So that equals 7/2.

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Or if you wanted to write that
as a mixed number, this is, of

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course, an improper fraction.

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Improper fractions have
a numerator larger

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than the denominator.

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If you wanted to write that as
a mixed number, 2 goes into 7

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three times with a remainder
of 1, so that's 3 and a half.

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You can write it either way.

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I tend to keep it this
way because it's

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easier to deal with.

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Let's do a ton of more
problems, or at least as many

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more as we can do in the
next four or five minutes.

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What's negative 2/3
divided by 5/2?

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Once again, that's the same
thing as minus 2/3-- whoops--

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as minus 2/3 times what?

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It's times the inverse of
5/2, which is 2/5, and

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that equals minus 4/15.

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What is 3/2 divided by 1/6?

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Well, that's just the same
thing as 3/2 times 6/1,

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I think you might
be getting it now.

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Let's see, let's
do a couple more.

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And, of course, you can always
pause, and look at this whole

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presentation again, so you can
get confused all over again.

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Let's see, let's do minus
5/7 divided by 10/3.

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Well, this is the same thing
as minus 5/7 times 3/10.

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I just multiplied
by the inverse.

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That's all I keep doing
over and over again.

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Minus 5 times 3.

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Minus 15.

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7 times 10 is 70.

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If we divide the numerator
and the denominator by

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5, we get minus 3/14.

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We could have also
just done it here.

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We could have done 5, 2,
and we would have gotten

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minus 3/14 as well.

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Let's do one or two
more problems.

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I think you kind of
get it, though.

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Let's say 1/2
divided by minus 3.

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Ah-ha!

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So what happens when you take a
fraction and you divide it by

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a whole number or an integer?

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Well, we know any whole number
can be written as a fraction.

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This is the same thing as
1/2 divided by minus 3/1.

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And dividing by a fraction is
the same thing as multiplying

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by it's inverse.

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So the inverse of negative 3/1
is negative 1/3, and this

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equals negative 1/6.

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Let's do it the other way.

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What if I had negative
3 divided by 1/2?

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Same thing.

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Negative 3 is the same thing as
minus 3/1 divided by 1/2, which

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is the same thing as minus 3/1
times 2/1, which is equal to

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minus 6/1, which
equals minus 6.

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Now, let me give you a
little bit of intuition

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of why this works.

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Let's say I said 2
divided by 1/3.

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Well, we know that this
is equal to 2/1 times

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3/1, which equals 6.

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So how does 2, 1/3,
and 6 relate?

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Well, let's look
at it this way.

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If I had two pieces of pizza.

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I have two pieces of pizza.

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Here's my two pieces
of pizza right.

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Two right here.

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So I have two pieces of pizza,
and I'm going to divide

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them into thirds.

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So I'm going to divide
each pizza into a third.

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I'll draw the little
Mercedes sign.

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So I'm dividing each pizza
into a third, right?

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How many pieces do I have?

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Let's see, 1, 2, 3, 4, 5, 6.

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I have 6 pieces.

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So you might want to sit and
ponder that for a little bit,

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but I think it might make a
little bit of sense to you.

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Let's do one more just
to tire your brain.

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If I had negative 7/2 divided
by 4/9-- let's pick a negative

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4/9-- well, that's the same
thing as minus 7/2 times

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minus 9/4, right?

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I just multiplied by the
inverse of negative 4/9.

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9 times 7 is equal to--
negative 7 times negative

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9 is positive 63,
and 2 times 4 is 8.

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Hopefully, I think you have a
good idea of how to divide by

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a fraction now, and you can
try out the dividing

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fractions modules.

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Have fun!