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Dividing fractions and whole number word problems

This video uses tape diagrams to visually represent division with fractions. It shows how to divide a fraction or a whole number into equal parts. Tape diagrams help us see the process in a clear, simple way.

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  • aqualine ultimate style avatar for user lokyl000
    Could you just do 1/4 divided by 2 much simpler? I think you can
    (23 votes)
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  • piceratops ultimate style avatar for user E
    Also, why are they called "tape diagrams"?
    (8 votes)
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  • aqualine tree style avatar for user danand30
    There is no single division problem that is the hardest one in the world. When working division problems by hand, some people find one kind of problem harder than others, but everyone would not agree on which problem is hardest. When using a computer or calculator, all division problem have essentially equal difficulty.

    There is no definitive answer to that, as difficulty will differ from person to person. One could argue that there are degrees of difficulty in different types of division problems. For instance:

    1 / 1 might be one of the easiest possible ones.
    2 / 1 could arguably be a little more difficult
    4 / 2 may perhaps be a little more difficult than that
    7 / 2 a bit harder
    3 / 7 harder still
    pi / 7 again perhaps harder
    pi / √2 may be even more so
    These are very subjective statements. This order may make sense some, but to others, it may be easier to divide seven by two than four by two. This is akin to asking whose face is the prettiest. You could get a billion different answers and all of them correct from the point of view of those giving the answer.

    Another point to made here is that it may not be possible to define a "hardest" division problem, as one could argue that it's always possible to take an existing problem and make it more difficult. This would be comparable to asking what the highest number is.
    (11 votes)
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  • leaf red style avatar for user Zachariah S.
    For questions like this, you can just multiply the whole number times the denominator. For example, if you had 5 divided by 2/3, you would multiply 5 times 3 and you will get 15.
    (7 votes)
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  • mr pants teal style avatar for user rporter967
    it's 4 x 2 = 8 then make it a fraction make 8 denominators and make 1 numerator
    (4 votes)
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  • duskpin seed style avatar for user Thomas Tapia
    wait.. Why do we have to divide the fourth Square by 2.?
    (3 votes)
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  • blobby green style avatar for user oliverosborn
    you can divide by 2 in the frst 1.
    (3 votes)
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  • blobby green style avatar for user Maia DePriest
    A simple question of mine is who invented math? Whoever did severally deserves much praise
    (0 votes)
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    • blobby green style avatar for user Darryn Asher
      I recently heard someone say that math wasn't an invention by humans but a discovery made by humans. Math explains how our universe works, it's a universal language of a sort. If anybody disagrees let me know, but I thought it was a nifty perspective :)
      (9 votes)
  • blobby green style avatar for user binjal.ali
    can't you you share it by a 1/2 half?
    (2 votes)
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  • blobby green style avatar for user 2029bmcdowell
    uhh is this a Question spot like this if it is?
    (2 votes)
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Video transcript

- [Instructor] We are told that Billy has 1/4 of a pound of trail mix. He wants to share it equally between himself and his brother. How much trail mix would they each get? So pause this video and try to figure that out. All right, now let's work through this together. So Billy starts with 1/4 of a pound of trail mix. So how can we represent 1/4? Well, if this is a whole pound, let's just imagine this rectangle is a whole pound, I could divide it into four equal sections. So let's see, this would be roughly two equal sections, and then if I were to divide each of those into two, now I have four equal sections. So Billy is starting with 1/4 of a pound. Draw a little bit, try to make it a little bit more equal. Billy is starting with 1/4 of a pound, so let's say that is that 1/4 of a pound that he starts with. He's starting with 1/4 of a pound, and he wants to share it equally between himself and his brother. So he wants to share it equally between two people right over here. So what we wanna do is essentially say, let's start with our total amount of trail mix, and then we're going to divide it into two equal shares. So when they ask us how much trail mix would they each get, we're really trying to figure out what is this 1/4 divided by two? So what would that be? Well, what if we were to take all of these four equal sections and divide them into two? So I'll divide that one into two. I will divide this one into two. I will divide this one into two, and then I would divide this one into two. And now what are each of these sections? Well, each of these are now 1/8. That's a 1/8 right over there, the whole is divided into eight equal sections. And so you can see, that when you start with that 1/4, and you divide it into two equal sections, so one section and two equal sections right over there, each of these is equal to 1/8. So 1/4 divided by two is equal to 1/8. Let's do another example. So we are told Matt is filling containers of rice. Each container holds 1/4 of a kilogram of rice. And then they tell us if Matt has three kilograms of rice, how many containers can he fill? So like always, pause this video, and see if you can figure that out. All right, so let's think about what's going on. We're starting with a total amount, three kilograms of rice, and we're trying to divide it into equal sections. In this case we're trying to divide it into equal sections of 1/4 of a kilogram. So we are trying to figure out what three divided by 1/4 is going to be equal to. Now to imagine that, let's imagine three wholes, this would be three whole kilograms. So that is one whole, this is two wholes, trying to make them all the same, but it's hand-drawn, so it's not as exact as I would like. So that's three whole kilograms here. And he wants to divide it into sections of 1/4. So if you divide it into fourths, how many fourths are you going to have? Well, let's do that. So let's see, if we were to divide it into halves, it would look like this. If you divide these three wholes into halves. But then if you want to divide it into fourths, it would look like this, I'm trying to get it as close to equal sections. They should be exactly equal sections. So I am almost there. So there you have it. So I've just taken three wholes and I've divided it into fourths. So how many fourths are there? Well, there are one, two, three, four, five, six, seven, eight, nine, 10, 11, 12 fourths. So three divided by 1/4 is equal to 12. And I encourage you to really think about why this is the case, that if we take a whole number like three and you divide it by 1/4, we're getting a value larger than three. And we're getting a value that is four times three. Think about why that is the case.