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## Arithmetic

### Course: Arithmetic > Unit 18

Lesson 8: Adding & subtracting negative fractions# Adding & subtracting fractions

Add and subtract negative fractions with unlike denominators. Created by Sal Khan.

## Want to join the conversation?

- but the negative + negative = positive .. why you put it as -29 ?(21 votes)
- Negative + negative = a smaller (bigger-looking) negative number. I think you are confusing this with multiplication, where negative x negative = positive. A way to remember is to look at a number line and use easy numbers (1, -1) to figure out the negatives and positives.(20 votes)

- From0:44to0:46, Sal says "then we add 3/4 to -10/6." But why add? Should the distributive property apply and we multiply? Vote up if this is a question you have too, please.(23 votes)
- The distributive property only applies if you're multiplying. Here, you're just adding the three fractions together. It looks confusing because Sal separated two of the fractions and added them together and then he added the third one to those two, but what you're doing to the fractions didn't change -- it's still just three fractions being added.(10 votes)

- Get this comment to 150 votes please!(22 votes)
- i swear if this gets 150(3 votes)

- upvote if

you like water(18 votes) - Is the numerator the only number in the fraction to be negative?(9 votes)
- If one part of a fraction is negative, it means that the whole fraction is negative. It doesn't matter if you put the negative sign in front of the numerator or in front of the denominator, both of them will cause the fraction to be negative. However, you won't see a fraction with both a negative numerator and a negative denominator, because the negatives would cancel each other out and the entire fraction would become positive.(9 votes)

- upvote if u love roblox :P

man i wish i could upvote my own comment(11 votes)- bro is like 8(0 votes)

- Can the denominator of a fraction be negative, or is that a nono?(7 votes)
- The denominator of a fraction can be negative, but it can not be zero.(5 votes)

- This makes honestly no sense to me... HOW DO YOU DO THIS?(8 votes)
- upvote if you love football and gaming(8 votes)
- i like softball and colorgaurd.(2 votes)

- At0:27-0:36, why would you add -3/4 to -7-3/6? I don't get that.(4 votes)
- taking away a positive number from a negative is the same as adding its positive. if you had a problem like -3-4, that would be the same thing as -3 plus -4. just like in the fractions,

-3/4-(-7)-3/6 is the same thing as -3/4 plus -7-3/6.(5 votes)

## Video transcript

We have negative 3/4
minus 7/6 minus 3/6. And there's many
ways to do this. But it immediately
jumps out at me that these last two numbers
have a 6 in the denominator. So I'm going to worry
about these first. I'm going to view this as
negative 7/6 minus 3/6. So if we have negative
7/6 minus 3/6, that's going to be the same
thing as negative 7 minus 3 over 6. And of course, we
have this negative 3/4 out front that
we're going to add to whatever we get over here. So this is these two terms
that I'm adding together. Negative 7 minus
3 is negative 10. So it's negative 10 over 6. And then I'm going to have
to add that to negative 3/4. And now I have to worry about
finding a common denominator. Let me write that so
they have a similar size. So now I have to worry about
finding a common denominator. What is the smallest number that
is a multiple of both 4 and 6? Well, it might jump out
at you that it's 12. You can literally just go
through the multiples of 4. Or you could look at
the prime factorization of both of these numbers. And what's the
smallest number that has all of the prime
factors of both of these? So you need two 2s, and
you need a 2 and a 3. So if you have two 2s and a
3, that's 4 times 3 is 12. So let's rewrite this
as something over 12 plus something over 12. Well, to get your
denominator from 4 to 12, you have to multiply by 3. So let's multiply our
numerator by 3 as well. So if we multiply
negative 3 times 3, you're going to have negative 9. And to get your
denominator from 6 to 12, you have to multiply by 2. So let's multiply our
numerator by 2 as well so that we don't change the
value of the fraction. So that's going
to be negative 20. And now we're ready to add. Our common denominator is 12. And so this is going to be
negative 9 plus negative 20, or we could even write
that as minus 20, over 12, which is equal to--
and we deserve a drum roll now. This is negative 29 over 12. And 29 is a prime
number, so it's not going to share any common
factors other than 1 with 12. So we also have this in
the most simplified form.