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### Course: Algebra basics>Unit 1

Lesson 6: 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
• 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.
• At , 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? :(
• 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
• At , Sal. says that we cannot simplify 21/20 anymore. Can't we turn it into a mixed number, say 1 1/20?
• 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.
• What would happen if you multiply a negative fraction and a positive fraction?
• 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
• 5/9 X 3/15 . I don't understand the step where they both were divided by 15 in the above video.
• 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?
• whats the answer or work show for 7/2 x 1/6
• 7/2 x 1/6 = 7/12
You would multiply the two denominators and the two numerators to get 7/12.

If this helped I would really appreciate an upvote :)
• Can someone help I do not get this.
At all
• How would you draw a model for -7/10?
• at a negative times a negative= a positive so the answer would just be 1/9.
• Hi there!

I'm just a little confused. In the video "adding fractions with different signs" (not this video) we were taught to find the common denominator before addressing the numerator. However, here we aren't finding a common denominator first. What am I missing?

Thanks!
• Are you trying to compare adding fractions to multiplying fractions? They are not the same operation.

## 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.