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Intro to multiplying 2 fractions

Sal introduces multiplying 2 fractions.  Created by Sal Khan.

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  • duskpin tree style avatar for user KhanAcademy User
    Is there another way to put answers in simplest form another way then the ones shown in the video?
    (19 votes)
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    • leafers ultimate style avatar for user INFNTY
      I personally think it is easier to simplify a fraction by dividing the numerator and the denominator by their lowest common factor, eg.

      4/8

      LCM = 4

      4 divide 4 = 1
      8 divide 4 = 2

      = 1/2

      Or...

      6/8

      LCM = 2

      6 divide 2 = 3
      8 divide 2 = 4

      = 3/4

      Hope that helps.
      (21 votes)
  • blobby green style avatar for user leah wojnowiak
    1/20 x 2 11/20=
    (7 votes)
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  • boggle yellow style avatar for user andy
    Hello!
    I don't really understand why we are splitting 2/3 into 4/5th. I thought splitting things is considered division?
    Thank-you!
    - Andy An
    (5 votes)
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    • orange juice squid orange style avatar for user Hunter Rowlee
      Fractions can be confusing.That step is division, but the equation is not.When you multiply with whole numbers, you take one number and make it grow, but since fractions are less than one,they have strange properties that basically switch the function of multiplication and division.If you didn't understand this and/or this didn't help you, rewatch the video and pay close attention.
      (7 votes)
  • blobby green style avatar for user Kim Smith-Vison
    So 5/8 x 4/10 would be 1/4
    (3 votes)
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  • stelly blue style avatar for user Atiqa8946
    Aren't we supposed to multiply both the denominators till they have an equivalent value? Or is it supposed to be until they have a common denominator?
    (3 votes)
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  • aqualine ultimate style avatar for user Sam Ecclesia
    I understand how you do it and I can follow the instructions to get the desired result.

    However, can someone explain why when we multiply the 2 fractions together we are 'taking 2/3 of 4/5'? I've never thought of multiplication in this way before.

    2/3 x 4/5 = 8/15
    but
    2/3 & 4/5, when changed using the LCM, would be 10/15 & 12/15. Larger fractions than the 8/15. I always thought that multiplication would increase our final result, but this is not the case?

    So in terms of multiplication with fractions, I should view it as taking a portion? Example - 2/3 OF 4/5?

    Thanks to anyone that answers me :)
    (5 votes)
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  • blobby green style avatar for user Madison
    When we multiplying fractions, why do we multiply the numerators and the denominator?
    (3 votes)
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  • leaf red style avatar for user thomas fentaw
    how do you simifly farctions
    (2 votes)
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  • duskpin tree style avatar for user Catherine R. Wang
    Do you always need to simplify?
    (2 votes)
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  • blobby green style avatar for user J. Reel
    When you make the statement, "If you have 12 of something and want to take 2/3 of it, you are going to take 8," you have done two WRONG things. First, you stop looking at the problem from the visual viewpoint. Second, you throw out a mathematical statement with no evidence, no explanation of how you got to the fact of that statement. I am left totally clueless from either perspective. I cannot do these types of problems. Where do you explain any of it from the beginning and consistently?
    (2 votes)
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    • starky ultimate style avatar for user Batuhan #BringBackBackgrounds
      So, let's say that you have twelve of something, right?
      Part 1:
      If you want to take 2/3's of 12,
      we should find 1/3 of 12 first so that we can multiply 1/3 of 12 and 2 which will get us 2/3's of 12,
      because 2/3 is 1/3 times 2.
      It works the same way for other fractions:
      2/7 times 2 is 4/7
      3/8 times two is 6/8
      To find 1/3 of 12, simply multiply 12 by the numerator of 1/3(which is 1), and divide 12 by the denominator(which is 3).
      Part 2:
      Doing the operations I stated in the last sentence:
      Multiply 12 by the numerator(which is 1): 1 times 12 = 12
      Divide the number we got by the denominator(which is 3): 12 / 3 = 4
      4 is 1/3 of 12. So, to find 2/3 of 12, we multiply 4 by 2
      Part 3:
      4 * 2 = 8
      8 is 2/3 of 12!
      (2 votes)

Video transcript

Let's think about what it means to multiply 2 over 3, or 2/3, times 4/5. In a previous video, we've already seen how we can actually compute this. This is going to be equal to-- in the numerator, we just multiply the numerators. So it's going to be 2 times 4. And in the denominator, we just multiply the denominator. So it's going to be 3 times 5. And so the numerator is going to be 8, and the denominator is going to be 15. And this is about as simple as we can make it. 8 and 15 don't have any factors common to each other, than 1, so this is what it is. It's 8/15. But how, why does that actually makes sense? And to think about it, we'll think of two ways of visualizing it. So let's draw 2/3. I'll draw it relatively big. So I'm going to draw 2/3, and I'm going to take 4/5 of it. So 2/3, and I'm going to make it pretty big. Just like this. So this is 1/3. And then this would be 2/3. Which I could do a little bit better job making those equal, or at least closer to looking equal. So there you go. I have thirds. Let me do it one more time. So here I have drawn thirds. 2/3 represents 2 of them. It represents 2 of them. One way to think about this is 2/3 times 4/5 is 4/5 of this 2/3. So how do we divide this 2/3 into fifths? Well, what if we divided each of these sections into 5. So let's do that. So let's divide each into 5. 1, 2, 3, 4, 5. 1, 2, 3, 4, 5. And I could even divide this into 5 if I want. 1, 2, 3, 4, 5. And we want to take 4/5 of this section here. So how many fifths do we have here? We have 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. And we've got to be careful. These really aren't fifths. These are actually 15ths, because the whole is this thing over here. So I should really say how many 15ths do we have? And that's where we get this number from. But you see if 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15. Where did that come from? I had 3, I had thirds. And then I took each of those thirds, and I split them into fifths. So then I have five times as many sections. 3 times 5 is 15. But now we want 4/5 of this right over here. This is 10/15 right over here. Notice it's the same thing as 2/3. Now if we want to take 4/5 of that, if you have 10 of something, that's going to be 8 of them. So we're going to take 8 of them. So 1, 2, 3, 4, 5, 6, 7, 8. We took 8 of the 15, so that is 8/15. You could have thought about it the other way around. You could have started with fifths. So let me draw it that way. So let me draw a whole. So this is a whole. Let me cut it into five equal pieces, or as close as I can draw five equal pieces. 1, 2, 3, 4, 5. 4/5, we're going to shade in 4 of them. 4 of the 5 equal pieces. 3, 4. And now we want to take 2/3 of that. Well, how can we do that? Well, let's split each of these 5 into 3 pieces. So now we have essentially 15ths again. So 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15. We want to take 2/3 of this yellow area. We're not taking 2/3 of the whole section. We're taking 2/3 of the 4/5. So how many 15ths do we have here? We have 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12. So if you have 12 of something, and you want to take 2/3 of that, you're going to be taking 8 of it. So you're going to be taking 1, 2, 3, 4, 5, 6, 7, 8 or 8 of the fifteenths now. So either way, you get to the same result. One way, you're thinking of taking 4/5 of 2/3. Another way you could think of it as you're taking 2/3 of 4/5.