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# Dividing negative fractions

Created by Sal Khan.

Video transcript

Let's do some examples
dividing fractions. Let's say that I have negative
5/6 divided by positive 3/4. Well, we've already talked about
when you divide by something, it's the exact same thing as
multiplying by its reciprocal. So this is going to be the
exact same thing as negative 5/6 times the reciprocal
of 3/4, which is 4/3. I'm just swapping the
numerator and the denominator. So this is going to be 4/3. And we've already seen lots of
examples multiplying fractions. This is going to be the
numerators times each other. So we're going to multiply
negative 5 times 4. I'll give the
negative sign to the 5 there, so negative 5 times 4. Let me do 4 in
that yellow color. And then the denominator
is 6 times 3. Now, in the numerator here, you
see we have a negative number. You might already know
that 5 times 4 is 20, and you just have to
remember that we're multiplying a negative
times a positive. We're essentially going to
have negative 5 four times. So negative 5 plus negative 5
plus negative 5 plus negative 5 is negative 20. So the numerator
here is negative 20. And the denominator here is 18. So we get 20/18, but
we can simplify this. Both the numerator
and the denominator, they're both divisible by 2. So let's divide them both by 2. Let me give myself
a little more space. So if we divide both the
numerator and the denominator by 2, just to
simplify this-- and I picked 2 because
that's the largest number that goes
into both of these. It's the greatest common
divisor of 20 and 18. 20 divided by 2 is 10,
and 18 divided by 2 is 9. So negative 5/6 divided
by 3/4 is-- oh, I have to be very careful here. It's negative 10/9, just
how we always learned. If you have a negative
divided by a positive, if the signs are
different, then you're going to get a negative value. Let's do another example. Let's say that I have negative
4 divided by negative 1/2. So using the exact
logic that we just said, we say, hey look,
dividing by something is equivalent to multiplying
by its reciprocal. So this is going to be
equal to negative 4. And instead of writing
it as negative 4, let me just write
it as a fraction so that we are clear
what its numerator is and what its denominator is. So negative 4 is the exact
same thing as negative 4/1. And we're going to multiply
that times the reciprocal of negative 1/2. The reciprocal of negative
1/2 is negative 2/1. You could view it
as negative 2/1, or you could view it as
positive 2 over negative 1, or you could view
it as negative 2. Either way, these are
all the same value. And now we're ready to multiply. Notice, all I did here,
I rewrote the negative 4 just as negative 4/1. Negative 4 divided
by 1 is negative 4. And here, for the negative
1/2, since I'm multiplying now, I'm multiplying
by its reciprocal. I've swapped the denominator
and the numerator. Or I swapped the denominator
and the numerator. What was the denominator
is now the numerator. What was the numerator
is now the denominator. And I'm ready to multiply. This is going to be equal to--
I gave both the negative signs to the numerator
so it's going to be negative 4 times negative
2 in the numerator. And then in the denominator,
it's going to be 1 times 1. Let me write that down. 1 times 1. And so this gives us,
so we have a negative 4 times a negative 2. So it's a negative
times a negative, so we're going to get
a positive value here. And 4 times 2 is 8. So this is a positive 8 over 1. And 8 divided by 1
is just equal to 8.