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## Arithmetic

### Course: Arithmetic > Unit 19

Lesson 5: Multiply & divide negative fractions# Multiplying positive and negative fractions

See examples of multiplying and dividing fractions with negative numbers. Created by Sal Khan.

## Want to join the conversation?

- So if you add a negative to a negative, you get more negatives? Because I thought a negative plus a negative is a positive. I'm really confused(13 votes)
- Addition an subtraction can be seen as movement along the number line. Subtraction means move to the left of the line, while addition means move to the right. While the negative symbol on a number means move the opposite direction as you normally one.

Imagine this as a number line:

-5, -4, -3,-2,-1, 0 -1, 2, 3, 4, 5

if you have (-2) - 2 =?

You start at -2, move to the left two places, and your answer is -4.

If you have 5 - 7 =?

Then you start at 5, move to the left 7 places which places you at -2

If you're given 1 + (-2)=?

You start at 1, and with addition you usually move to the right, but it's a negative, or opposite to, so you move to the LEFT instead, ending at -1.(34 votes)

- At4:30, why does Sal say that you can't simplify -21/20? Can't you simplify it to

-1 1/20? Or is it -21 over +20? :((11 votes)- The fraction is fully reduced as -21/20 (no common factors in numerator & denominator).

You can convert it to a mixed number, which you did correctly. It does become -1 1/20(12 votes)

- At4:31, Sal. says that we cannot simplify 21/20 anymore. Can't we turn it into a mixed number, say 1 1/20?(11 votes)
- Good question! Yes, we can turn into a mixed number, but it is simplified as a fraction. numerator and denominator do not have any common factors other than 1.(3 votes)

- 5/9 X 3/15 . I don't understand the step where they both were divided by 15 in the above video.(5 votes)
- They were both divided by 15 because 5 times 3 is 15 and 9 times 15 is 135. Since both numbers had a GCF (Greatest Common Factor) of 15, Sal divided by 15 and received an answer of 1/9 because 15 divided by 15 is 1 and 135 divided by 15 is 9.

Unless you were looking for some other answer I suppose?(8 votes)

- What would happen if you multiply a negative fraction and a positive fraction?(6 votes)
- If you multiply a negative by a positive you will always get a negative no matter if there is a decimal, fraction or whole number(7 votes)

- whats the answer or work show for 7/2 x 1/6(5 votes)
- Can someone help I do not get this.

At all(5 votes) - How would you draw a model for -7/10?(4 votes)
- at3:00a negative times a negative= a positive so the answer would just be 1/9.(4 votes)

- How are you guys and girls? Are you guys strangers or by people that I know!

:) but mostly absotually :((5 votes) - Can you multiply a positive and a positive? Or a negitive and a negitive or no?(4 votes)
- Yes just like even and odd whenever you come across a problem like that you can think of even and odd(2 votes)

## 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.