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

Dividing fractions: 3/5 ÷ 1/2

Dividing two fractions is the same as multiplying the first fraction by the reciprocal of the second fraction. The first step to dividing fractions is to find the reciprocal (reverse the numerator and denominator) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. Finally, simplify the fractions if needed. Created by Sal Khan and Monterey Institute for Technology and Education.

Want to join the conversation?

  • mr pants teal style avatar for user ageorge
    when you are dividing with mixed numbers do you turn them into improper fractions like when you are multiplying with mixed numbers?
    (291 votes)
    Default Khan Academy avatar avatar for user
  • blobby green style avatar for user Cary Blix
    How do you divide fractions that include whole numbers with fractions?
    (34 votes)
    Default Khan Academy avatar avatar for user
  • marcimus pink style avatar for user 12jwhite
    How do you divide a positive by a negative?
    I hope you can help please do.
    (26 votes)
    Default Khan Academy avatar avatar for user
    • female robot grace style avatar for user Brayden Hascup
      It's the same as multiplying and dividing whole numbers. Ignore the positive or negative sign until you have your answer and then follow the rules: +*+=+; -*-=+; +*-=-; -*+=-; same for divide.
      eg
      -3/4*-1/2=3/8 (-*-=+).
      3/4*-1/2=-3/8 (+*-=-).
      -3/4*1/2=-3/8 (-*+=-).
      3/4*1/2=-3/8 (+*+=+).
      Hope that helps and I haven't confused you even more.
      (32 votes)
  • piceratops sapling style avatar for user Rbowater29
    how if its 1/3 divided by 4
    (9 votes)
    Default Khan Academy avatar avatar for user
  • duskpin ultimate style avatar for user 💝💖❤️DuskpinSavior❤️💖💝
    Will you only and always just use the reciprocal of the second fraction?? Please help...Have a test on this soon!! ( If you need me to clarify pls let me know!!) Thanks!!☺️
    (8 votes)
    Default Khan Academy avatar avatar for user
  • duskpin ultimate style avatar for user Mr. Penguin
    I don't understand -. why do you need the multiplication sign when you can put that there in the first place and what is a reciprocal in mixed numbers, example you are solving 1 2/3 divided by 1 3/4 (IF! because I don't understand this) what is the reciprocal of 1 3/4?? please explain this to me!!
    (8 votes)
    Default Khan Academy avatar avatar for user
    • female robot grace style avatar for user loumast17
      I'm not sure what you mean by "when you can put that there in the first place" but I think i can explain mixed numbers.

      There's no easy way to get a reciprocal with mixed numbers as far as I'm aware. So you want to turn any mixed numbers into impoper fractions. In fact, as you get into higher math you use mixed numbers less and less and improper fractions more and more, to the point I just automatically turn all mixed numbers into improper fractions most of the time.

      Anyway, as a quick demonstration I'll turn the two numbers you gave into improper fractions and give their reciprocal.

      1 2/3 = 3/3 + 2/3 = 5/3 so the reciprocal is 3/5

      1 3/4 = 4/4 + 3/4 = 7/4 so the reciprocal is 4/7

      If you wanna work through your other question I'd be happy to, otherwise hope that helps.
      (3 votes)
  • piceratops seed style avatar for user 4804180716
    when dividing fractions how do you do it with a whole number
    (4 votes)
    Default Khan Academy avatar avatar for user
  • old spice man blue style avatar for user Questionnaire
    This is a bit unrelated, but it applies to a certain facet of a problem. Does a fraction need to be simplified before you add/subtract/multiply/divide it with another fraction?
    For example, 3/8 x 2 - 1/4. Using the PEMDAS method, we multiply 3/8 x 2 first.This equals 6/8. Now, does this 6/8 need to be simplified before we subtract it by 1/4?
    (4 votes)
    Default Khan Academy avatar avatar for user
    • hopper cool style avatar for user Philip
      The fractions don't have to be simplified before doing addition or subtraction; we are just converting the fraction(s) into forms which they have common denominators. When fractions have common denominators, you add/subtract the numerators to get the "new numerator's value", and keep the value of the denominator.
      Also, sometimes it is better to not simplify fractions so common denominators can be kept.
      For the 6/8 minus 1/4, simplifying the 6/8 to 3/4 will give it the same denominator as 1/4, and the only calculation that needs to be done is 3 minus 1 (we "copy and paste" the 4 into the denominator). You can also multiply the 1/4 by 2/2, which gives 2/8, and you can subtract 6/8 by 2/8. However, if the problem requires you to write answer in the simplest form, simplifying fractions in advance may make things easier (e.g. you won't have to divide both the numerator and denominator by a very large value.)
      (7 votes)
  • piceratops tree style avatar for user Hugo Pfeffer
    This question is probably on the wrong section but how can I solve a fraction within a fraction on it's denominator?
    Like 10/4/x for example.
    (3 votes)
    Default Khan Academy avatar avatar for user
  • leafers seed style avatar for user bluejay2004
    Prove me wrong:
    24/6 = 4
    6*4 = 24
    0/0 = x
    x*0 = 0
    x = any #
    Yet he claims 0/0 = undefined in the link below. Please vote my question if you are puzzled as I am.
    https://www.khanacademy.org/math/algebra/introduction-to-algebra/division-by-zero/v/why-zero-divided-by-zero-is-undefined-indeterminate
    (4 votes)
    Default Khan Academy avatar avatar for user
    • aqualine ultimate style avatar for user Johnathan
      I think a lot of people are as puzzled as you are. What happens is that even though x*0 = 0 is true and so are the first 2 statements; by definition, 0/0 has infinite values. If x could be any number, then 0/0 could be any number. So if you were to answer a question with the denominator as a 0, what would your answer be? Would it be 1, 2, or 3? And that's why 0/0 is undefined because there is no defined answer for that problem.

      Comment if you would like some examples. :-)
      (4 votes)

Video transcript

Divide and write the answer as a mixed number. And we have 3/5 divided by 1/2. Now, whenever you're dividing any fractions, you just have to remember that dividing by a fraction is the same thing as multiplying by its reciprocal. So this thing right here is the same thing as 3/5 times-- so this is our 3/5 right here, and instead of a division sign, you want a multiplication sign, and instead of a 1/2, you want to take the reciprocal of 1/2, which would be 2/1-- so times 2/1. So dividing by 1/2 is the exact same thing as multiplying by 2/1. And we just do this as a straightforward multiplication problem now. 3 times 2 is 6, so our new numerator is 6. 5 times 1 is 5. So 3/5 divided by 1/2 as an improper fraction is 6/5. Now, they want us to write it as at mixed number. So we divide the 5 into the 6, figure out how many times it goes. That'll be the whole number part of the mixed number. And then whatever's left over will be the remaining numerator over 5. So what we'll do is take 5 into 6. 5 goes into 6 one time. 1 times 5 is 5. Subtract. You have a remainder of 1. So 6/5 is equal to one whole, or 5/5, and 1/5. This 1 comes from whatever is left over. And now we're done! 3/5 divided by 1/2 is 1 and 1/5. Now, the one thing that's not obvious is why did this work? Why is dividing by 1/2 the same thing as multiplying essentially by 2. 2/1 is the same thing as 2. And to do that, I'll do a little side-- fairly simple-- example, but hopefully, it gets the point across. Let me take four objects. So we have four objects: one, two, three, four. So I have four objects, and if I were to divide into groups of two, so I want to divide it into groups of two. So that is one group of two and then that is another group of two, how many groups do I have? Well, 4 divided by 2, I have two groups of two, so that is equal to 2. Now, what if I took those same four objects: one, two, three, four. So I'm taking those same four objects. Instead of dividing them into groups of two, I want to divide them into groups of 1/2, which means each group will have half of an object in it. So let's say that would be one group right there. That is a second group. That is a third group. I think you see each group has half of a circle in it. That is the fourth. That's the fifth. That's the sixth. That's the seventh, and then that's the eighth. You have eight groups of 1/2, so this is equal to 8. And notice, now each of the objects became two groups. So you could say how many groups do you have? Well, you have four objects and each of them became two groups. I'm looking for a different color. Each of them became two groups, and so you also have eight. So dividing by 1/2 is the same thing as multiplying by 2. And you could think about it with other numbers, but hopefully, that gives you a little bit of an intuition.