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Adding & subtracting fractions

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

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  • female robot grace style avatar for user rama
    but the negative + negative = positive .. why you put it as -29 ?
    (19 votes)
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    • duskpin ultimate style avatar for user astra1
      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)
  • spunky sam blue style avatar for user Jyotika
    From to , 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.
    (19 votes)
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    • purple pi purple style avatar for user StarryNight
      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.
      (9 votes)
  • blobby green style avatar for user annaaldridge
    Is the numerator the only number in the fraction to be negative?
    (8 votes)
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    • purple pi purple style avatar for user StarryNight
      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.
      (7 votes)
  • sneak peak green style avatar for user Cynthia Paz
    Get this comment to 150 votes please!
    (10 votes)
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  • leaf yellow style avatar for user Branden Potter
    Can the denominator of a fraction be negative, or is that a nono?
    (6 votes)
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  • aqualine ultimate style avatar for user thoyebayahia
    At -, why would you add -3/4 to -7-3/6? I don't get that.
    (4 votes)
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    • starky ultimate style avatar for user Nichole
      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.
      (4 votes)
  • marcimus purple style avatar for user sophie
    I still don't get why you change it into a positive.
    (3 votes)
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    • leaf orange style avatar for user Alistair McCallum
      Unfortunately this is wrong, -2+(-3) would equal -5.
      Two negative numbers result in a positive movement only when one is subtracted from another eg: -2-(-3) = 1
      So you start with -2 and to add -3 you would go three steps <--- to subtract -3 you must go three steps --->
      The best way to visualise this is to look at a number line. Watch Sal's videos on adding and subtracting negative numbers again and try drawing your own number lines. Best of luck!
      (8 votes)
  • piceratops ultimate style avatar for user A G
    Hi. Can anyone explain why -29/12 is the most simplified form? It's possible to simplify this fraction more to -2 5/12.
    (4 votes)
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  • blobby green style avatar for user denise sullivan
    7 1/2 - 2 7/10 = ? I keep getting 5 4/10 is this correct?
    (2 votes)
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  • starky seed style avatar for user Noah
    What does this equal to? 10/6 = -7/6 ?
    (4 votes)
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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.