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# Multiplying positive and negative fractions

Video transcript

Let's do a few examples
multiplying fractions. So let's multiply
negative 7 times 3/49. So you might say, I don't
see a fraction here. This looks like an integer. But you just to remind yourself
that the negative 7 can be rewritten as
negative 7/1 times 3/49. Now we can multiply
the numerators. So the numerator is going
to be negative 7 times 3. And the denominator is
going to be 1 times 49. 1 times 49. And this is going to be
equal to-- 7 times 3 is 21. And one of their
signs is negative, so a negative times a positive
is going to be a negative. So this is going
to be negative 21. You could view this as
negative 7 plus negative 7 plus negative 7. And that's going to be over 49. And this is the correct
value, but we can simplify it more because 21 and 49
both share 7 as a factor. That's their greatest
common factor. So let's divide
both the numerator and the denominator by 7. Divide the numerator and
the denominator by 7. And so this gets us
negative 3 in the numerator. And in the
denominator, we have 7. So we could view it
as negative 3 over 7. Or, you could even do
it as negative 3/7. Let's do another one. Let's take 5/9 times-- I'll
switch colors more in this one. That one's a little monotonous
going all red there. 5/9 times 3/15. So this is going
to be equal to-- we multiply the numerators. So it's going to be 5 times 3. 5 times 3 in the numerator. And the denominator is
going to be 9 times 15. 9 times 15. We could multiply them out,
but just leaving it like this you see that there is
already common factors in the numerator
and the denominator. Both the numerator
and the denominator, they're both divisible
by 5 and they're both divisible by 3,
which essentially tells us that they're divisible by 15. So we can divide the numerator
and denominator by 15. So divide the
numerator by 15, which is just like dividing by
5 and then dividing by 3. So we'll just divide by 15. Divide by 15. And this is going to be equal
to-- well, 5 times 3 is 15. Divided by 15 you get
1 in the numerator. And in the denominator,
9 times 15 divided by 15. Well, that's just going to be 9. So it's equal to 1/9. Let's do another one. What would negative 5/9
times negative 3/15 be? Well, we've already
figured out what positive 5/9 times
positive 3/15 would be. So now we just have to
care about the sign. If we were just multiplying the
two positives, it would be 1/9. But now we have to
think about the fact that we're multiplying by a
negative times a negative. Now, we remember
when you multiply a negative times a
negative, it's a positive. The only way that
you get a negative is if one of those two
numbers that you're taking the product of
is negative, not two. If both are positive,
it's positive. If both are negative,
it's positive. Let's do one more example. Let's take 5-- I'm using
the number 5 a lot. So let's do 3/2, just
to show that this would work with
improper fractions. 3/2 times negative 7/10. I'm arbitrarily picking colors. And so our numerator is going
to be 3 times negative 7. 3 times negative 7. And our denominator is
going to be 2 times 10. 2 times 10. So this is going to
be the numerator. Positive times a
negative is a negative. 3 times negative
7 is negative 21. Negative 21. And the denominator, 2 times 10. Well, that is just 20. So this is negative 21/20. And you really can't
simplify this any further.