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

Visually adding fractions: 5/6+1/4

To add two fractions with different denominators, you need to find the least common multiple of the denominators. You can then rewrite both fractions with this common denominator, which will allow you to add the numerators together. In the example given, 5/6 and 1/4 are rewritten as 10/12 and 3/12, respectively, resulting in a sum of 13/12.

Want to join the conversation?

  • purple pi purple style avatar for user May
    So you basically change both of the fraction's denominators and change them to something like 3/8+4/6 the denominator would be 24?
    (69 votes)
    Default Khan Academy avatar avatar for user
    • aqualine ultimate style avatar for user Andrew Zhu
      Yes, because if you think of 8*? = 24 and 6*? = 24 then they can both be divisible by 24 and have no remainder. We can use division to help. 24 divided by 8 is 3, right? 24 divided by 6 is 4. This is called simplifying or it can also be called common denominators. Or LCM which stands for Least common multiple.
      (40 votes)
  • hopper cool style avatar for user Denis Zhang
    At , why didn't the denominator change? Why didn't it stack up to 24 when 10 and 13 stacked up? I thought that what you do to the top, you must do the same to the bottom. So when you add the numerator, then shouldn't the denominator be changed as well?
    (27 votes)
    Default Khan Academy avatar avatar for user
    • duskpin ultimate style avatar for user SkyKlubnik
      OOF indeed. Adding fractions doesn't add the two "divided by"s, or the denominators, simply the numerators. The denominators do stack up, however, just only in cases like (3/12)/12. Then that would be 3/24. Hope that helped, have a yeet-erific day :D
      (27 votes)
  • piceratops seed style avatar for user GalaxyQueen735
    how do i convert a fraction?
    (22 votes)
    Default Khan Academy avatar avatar for user
  • starky sapling style avatar for user Ezri1
    I want 10 votes plez
    (29 votes)
    Default Khan Academy avatar avatar for user
  • marcimus purple style avatar for user Chloe Kovac
    How can you add 1/4 3/5 3/10?
    (17 votes)
    Default Khan Academy avatar avatar for user
    • starky ultimate style avatar for user DewMcStew
      The first thing you would have to do is to change all of the denominators to a common denominator. To do this, find the lowest number that is divisible by all of your denominators. In this case, that number would be 100.

      Then look at the numerator. To make sure that the fractions are still the same value, we need to change the numerator by the same amount we changed the denominator. So:

      4 goes into 100 25 times. That means we need to also multiply the numerator by 25. That means that we now have 25/100 instead of 1/4. That means that 1/4 and 25/100 are the same value. We now do this for the other fractions.

      5 goes into 100 20 times. So in this case we multiply the numerator by 20. 20 multiplied by 3 is 60. So instead of 3/5 we now have 60/100.

      Finally, you need to do the last fraction. 10 goes into 100 10 times. So we need to do 3 multiplied by 10. Then we would get 30/100.

      The last thing you have to do is add the numerators back together. Our denominators are now the same, so the new problem is this:

      25/100 + 60/100 +30/100

      Then we add the numerators, so we do 25+60+30. This comes out to be 115.

      So our answer would be 115/100. But this is an improper fraction, so we could also change it into 1 and 15/100, because 100/100 is equal to one.

      To simplify it, then we change it to 3/20 by dividing both 15 and 100 by 5.

      Our final answer would be 1 and 3/20. Hope this helped!
      (20 votes)
  • mr pants teal style avatar for user Tennis Queen🎾✌🏻
    Why do we need to simplify ?
    (18 votes)
    Default Khan Academy avatar avatar for user
  • blobby green style avatar for user Tykeasia.Duke
    how do i do this
    (7 votes)
    Default Khan Academy avatar avatar for user
  • aqualine ultimate style avatar for user Draganclash123
    can 1 have 50 votes please.
    (19 votes)
    Default Khan Academy avatar avatar for user
  • piceratops ultimate style avatar for user E
    Easy way to do it:

    Let's say the problem is... you know what, 5/6 + 1/4.

    So. Step one is to find the common denominator, which, in this case, is 12.

    next, we see how many times 6 goes into 12, which is 2. now we take the top number, 5, and times it by 2, because if we are multiplying the denominator we have to multiply the numerator as well. so- 5x2 is ten. our new fraction is 10/12.
    repeat this with the next fraction!
    (13 votes)
    Default Khan Academy avatar avatar for user
  • starky tree style avatar for user ajkolar14
    how are they both equal
    (5 votes)
    Default Khan Academy avatar avatar for user
    • female robot grace style avatar for user kferguson
      Example: 3/4 is equal to 6/8. They are equal because 3 x 2=6 and 4 x 2=8. Another Example: 2/4 is equal to 1/2 because 2 divided by 2 =1 and 4 divided by 2 =2. as long as you multiply or divide both numbers by the same thing, they are equal. The same applies for mixed numbers and improper fractions. Hope that was helpful!
      (15 votes)

Video transcript

- [Voiceover] Let's see if we can calculate what 5/6 plus 1/4 is, and to help us, I have a visual representation of 5/6, and a visual representation of 1/4. Notice I have this whole whole, I guess you could say, broken up into one, two, three, four, five, six sections, and we've shaded in five of them, so this is 5/6, and then down here, we have another whole, and we have one out of the four equal sections shaded in so this is 1/4, and I want to add them, and I encourage you at any point, pause the video, and see if you could figure it out on your own. Well, whenever we're adding fractions, we like to think in terms of fractions that have the same denominator, and these clearly don't have the same denominator, but in order to rewrite them, with a common denominator, we just have to think of a common multiple of six and four, and ideally, the smallest common multiple of six and four, and the way that I like to do that is I like to take the larger of the two, which is six, and then think about its multiples. So I could first think about six itself. Six is clearly divisible by six, but it's not perfectly divisible by four, so now, let's multiply by two, so then we get to 12. 12 is divisible by both six and four. So 12 is a good common denominator here. It's the least common multiple of six and four. So we can rewrite both of these fractions as something over 12. So, something over 12 plus something, plus something over 12 is equal to. Now, there's a bunch of ways to tackle it, but what I want to do is I just want to visualize it here on this drawing. So, if I go, if I were to go from, if I were to go from six equal sections to 12 equal sections, which is what I'm doing if I'm going from six in the denominator to 12 in the denominator. I'm essentially multiplying each of these sections by, or, I'm essentially multiplying the number of sections I have by two, or I'm taking each of these existing sections and I'm turning them into two sections, so let's do that. Let's do that. Let me see if I can do it pretty neatly, so, I can do it a little bit neater than that. So, it'll look like that. And, whoops. Let me do this one. I want to divide them fairly close to evenly. I'm doing it by eye so it's not going to be perfect. So, and you have that one. And then last not, last but not least, you have that one there, and then notice, I had six sections, but now I've doubled the number of sections. I've turned the six sections into 12 sections by turning each of the original six into two, so now I have one, two, three, four, five, six, seven, eight, nine, 10, 11, 12 sections. So if I have 12 sections now, how many of those 12 are now shaded in? Instead of having five of the six, I now have 10 of the 12 that are shaded in. So I now have 10/12. 5/6 is the same thing as 10/12. Another way you could have thought about that, to go from six to 12, I had to multiply by two, so then I have to do the same thing in the numerator. Five times two is 10. But hopefully you see that those two fractions are equivalent, that I didn't change how much is shaded in, I just took each of the original six and I turned it into two, or I multiplied the total number of sections by two to get 12, and then instead of having 5/6, I now have 10/12 shaded in. Now let's do the same thing with the four, with the 1/4. Right here, I've depicted 1/4, but I want to turn this into something over 12. So to turn it into something over 12, each section has to be turned into three sections. So let's do that. Let's turn each section into three sections. So, that's one, two, and three. So then I have one, two, and three. I have, I think you can see where this is going. One, two and three. I have one, two, and three. And so notice, all I did is I multiplied, before I had four equal sections. Now I turned each of those four sections into three sections, so now I have 12 equal sections. And I did that, essentially, by multiplying the number of sections I had by three. So now what fraction is shaded in? Well, now, this original that was one out of the four, we can now see is three out of the 12 equal sections. It's now three out of the 12 equal sections, and so what is this going to be? Well, if I have 10/12, and I'm adding it to 3/12, well how many twelfths do I have? I'm going to have 13/12. And you could see it visually over here as well. Up here in green, I have 10/12 shaded in. Each of these boxes are a twelfth. Let me write that down. Each of these boxes are 1/12. That's 1/12. This is 1/12. So how many twelfths do I have shaded in? I have the 10 that are shaded in in green, and then I have an 11/12, a 12/12 and then finally, the 13/12 is one way to think about it.