If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Main content

Subtracting mixed numbers: 7 6/9 - 3 2/5

We can subtract two mixed numbers, by converting them to improper fractions. First, multiply the whole number by the denominator and add the numerator to get the improper fraction. Find a common denominator and adjust the numerators accordingly. Subtract the two improper fractions, and simplify the result if possible. Finally, convert the improper fraction back to a mixed number if desired. Created by Sal Khan.

Want to join the conversation?

  • leafers ultimate style avatar for user Ashlynne Donovan
    Why do we need to add and subtract fractions?
    (84 votes)
    Default Khan Academy avatar avatar for user
    • leaf yellow style avatar for user Testing
      Well, suppose your cooking, and you need, say, 2/3 of a cup of sugar. What if your only doing half of a recipe? You need to chop 2/3 in half. Or if your doing 2 times the recipe. You need to double 2/3. This is only one example, there are lots of others.
      (90 votes)
  • blobby green style avatar for user melissa.ebener
    If you have a whole number minus a fraction for example 3 - 2 2/3 how do you do this
    (17 votes)
    Default Khan Academy avatar avatar for user
  • boggle green style avatar for user error
    this is hard I can't do some problems with this even though he explained it 😪😪😪😯😯😥😥 so can someone explain it much more simpilaier or easier to me?
    (11 votes)
    Default Khan Academy avatar avatar for user
    • piceratops ultimate style avatar for user Adrian
      Okay, Error.

      For example:

      12 3/4 - 7 4/5 = ?

      Here, find the LCM of both the denominators.

      4 and 5's LCM is 20, so it should be 12 ?/20 - 7 ?/20.

      Here, multiply both numerators by the number you multiplied the denominator to get to 20.

      Since you multiplied 4 against 5, which is 20, multiply 3 against 5, the answer to which is 12 15/20.

      Since you multiplied 5 against 4, which is 20, multiply 4 against 5, the answer to which is 7 16/20.

      Now, subtract the numbers.

      Here, you need to borrow 1 from 12.

      Borrow it, and add 20/20 to 15. You now have 12 35/20. Subtract 7 16/20 from it.

      12 35/20 - 7 16/20 = 5 19/20.

      Voilá! You're done!

      #QED

      Hope this helps, Error.
      (18 votes)
  • spunky sam blue style avatar for user Waffles the great!
    Why the minus sign for 3-2/5? I still don't get it.
    (14 votes)
    Default Khan Academy avatar avatar for user
  • stelly blue style avatar for user Becca
    why is fractions so important?
    (5 votes)
    Default Khan Academy avatar avatar for user
  • aqualine ultimate style avatar for user Kien Oehlke
    hello i nee lots of help i dont know how to add fractions if anyone noews the answer can someone pleaes3e tell me sporry my kat is walkijg over ny jkeayboard so i cant ytype very well its quite an issue yes. sorry for speaking bad francais i am not familiar with argentina.
    (5 votes)
    Default Khan Academy avatar avatar for user
    • mr pink orange style avatar for user Adyasha_Priyadarsini
      Well first do 1/2+1/2 the denominator stays the same so add the 1+1 that’s 2 so the answer for that is 2/2 also known as a whole aka 1

      1/3+1/5 to find a common denominator multiply the denominator that’s 15 so for 1/3 u multiply 3x5 to be 15 so u do 1x5 for the numerator for 1/5 you do 5x3 to be 15 so do 1x3 for numerator to find that. Add them up and u got your answer.

      I hoped this helped srry if it’s late and long!
      (6 votes)
  • duskpin sapling style avatar for user Iam_Avery
    when do we usually use the add and subtract fraction in real life?
    😕😕😕
    (5 votes)
    Default Khan Academy avatar avatar for user
    • aqualine ultimate style avatar for user Woah
      In the previous lessons, you learned that a fraction is part of a whole. Fractions show how much you have of something, like 1/2 of a tank of gas or 1/3 of a cup of water. In real life, you might need to add or subtract fractions. For example, have you ever walked 1/2 of a mile to work and then walked another 1/2 mile back?
      (5 votes)
  • aqualine ultimate style avatar for user .
    What happens if the first number is negative and you are subtracting them? Do you have to do something different?
    (3 votes)
    Default Khan Academy avatar avatar for user
    • starky tree style avatar for user Ida Fan
      Yes you do. Example: -1/2 - 3/4
      Since the fractions have the same sign, we add (follow me here). 1/2 = 2/4, and what is 2/4 + 3/4? 5/4, or 1 1/4.
      Now, since we started with two negatives, make your answer negative.
      -1/2 - 3/4 = - 1 1/4
      (9 votes)
  • female robot amelia style avatar for user sophias1002543
    why do we need to find the common number and then either add or subtract. Why not divied and multilpy
    (5 votes)
    Default Khan Academy avatar avatar for user
    • hopper happy style avatar for user achowdhury32
      To multiply or divide, you do not need to do that. To multiply two fractions multiply their numerators and denominators. I know that this sounds confusing but it is true. Dividing fractions is harder. It requires taking the reciprocal of the second fraction and then multiplying.
      (0 votes)
  • blobby green style avatar for user penp2k
    Why do you first use plus and than minus?
    (3 votes)
    Default Khan Academy avatar avatar for user

Video transcript

Let's try to evaluate 7 and 6/9 minus 3 and 2/5. So like always, I like to separate out the whole number parts from the fractional parts. This is the same thing as 7 plus 6/9 minus 3 minus 2/5. And the reason why I'm saying minus 3 minus 2/5 is this is the same thing as minus 3 plus 2/5. And so you distribute the negative sign. You're subtracting a 3, and then you're subtracting the 2/5. And so now we can worry about the whole number parts, 7 minus 3. Well, 7 minus 3 is going to give us 4. So that's going to give us 4. And then we're going to have 6/9 minus 2/5. So let me think about what 6/9 minus 2/5 are. 6/9 minus 2/5, well, we're going to have to find a common denominator. So this is going to be the same thing. And I think the least common multiple of 9 and 5 is going to be 45. Literally, you then multiply. They have no common factors. So it's going to be over 45. To go from 9 to 45, I have to multiply by 5. So I'm going to have to multiply the numerator by 5. So 6 times 5 is 30. Then I'm going to subtract. To go from 5 to 45, I had to multiply by 9. So I have to multiply the numerator by 9 if I don't want to change the value. So 2 times 9 is 18. And 30/45 minus 18/45 is going to be something over 45. 30 minus 18 is 12. If I subtract these two fractions right over here, I get 12/45. So it's 4 plus 12/45. Or if we wanted to write it as a mixed number, this is equal to 4 and 12/45. But we're not done yet. We can simplify this further. 12 and 45 have common factors. They're both divisible by 3. Actually, they're both divisible by-- well, I think we can divide more after that. So let's see. If we divide the numerator by 3 and the denominator by 3, we end up with 4. And 12 divided by 3 is 4. And 45 divided by 3 is 15. 4 and 4/15. And actually, we're done. These two can't be simplified anymore. 4 and 4/15.