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

Multiplying 2 fractions: number line

Learn the concept of multiplying fractions by fractions. Watch as the process is visually represented on a number line, helping to understand the 'why' behind the procedure.  Created by Sal Khan.

Want to join the conversation?

  • hopper jumping style avatar for user Amanuel Ayalew
    At , doesn't Sal mean the two halves?
    (64 votes)
    Default Khan Academy avatar avatar for user
  • blobby green style avatar for user Ivanna Morales
    Why does he make this more confuseing than it needs to be?
    (14 votes)
    Default Khan Academy avatar avatar for user
  • starky tree style avatar for user Scout Askar
    I do not understand this. Could you make more simpimler? Please?
    (11 votes)
    Default Khan Academy avatar avatar for user
  • starky ultimate style avatar for user Kyrogou
    The Number Line approach is interesting but its hard to do unless you have a notebook and pencil with you but in the case where you have to quickly solve a question like "If the tax refund (lets say 1200$) is being divided between 4 people, how large of a fraction is each person getting?", and you don't happen to have a pencil and notebook by your side, how could you more easily do a question like that in your head?
    (6 votes)
    Default Khan Academy avatar avatar for user
    • leaf red style avatar for user Cavan P
      If you're dividing 1 whole among 4 people, then each person gets 1/4 of whatever it is you're dividing.

      Something tells me that's not what you meant, though. Because 1200 is a nice multiple of 100, we can simply drop the zeroes and add them back later on. The problem then changes from 1200/4 to 12/4. 12/4 can be simplified to 3 (4 + 4 + 4 = 12), and then tack the zeroes back on - we get a result of $300.
      (10 votes)
  • aqualine seed style avatar for user ender
    is there a different way to do this ?
    (4 votes)
    Default Khan Academy avatar avatar for user
    • aqualine ultimate style avatar for user taarika t.
      Yes, there is. I actually answered a question just like this a couple of minutes ago... :D The way Mr. Khan likes to do it is by explaining it in a way that teaches you the concept so you understand what you're doing. But the simpler way is actually, well.... a lot simpler. For example, if you're multiplying 1/8 by 2/5, first you multiply the numerators by each other (1 x 2) to get an answer of 2. Then you multiply the denominators by each other (8 x 5) to get 40. Finally, you put the 2 as your numerator and the 40 as your denominator to get a product of 2/40, but that isn't your final answer because each number can be simplified -- each divided by 2 -- to get a final product of 1/20. I hope this helped you!
      (11 votes)
  • mr pants teal style avatar for user Tennis Queen🎾✌🏻
    Why did you use a number line when you could do 2/3 x 4/5 which is easier then number line ?
    Why do it the hardier way which is slower, when you could go the easier way which is way faster? You still get the write answer anyway so why not do it the faster way?
    (6 votes)
    Default Khan Academy avatar avatar for user
    • leaf grey style avatar for user Arzal
      It's just to prove the concept that you are going 2/3 to 4/5 or 4/5 to 2/3, you can't just get that from looking at "2/3 x 4/5", you wouldn't know how you got the product from those numbers, yes you did multiplicate the fractions but why do you do that when they are not whole numbers?
      (6 votes)
  • blobby blue style avatar for user hunayya salsabeel
    umm i don't understand how it become 1/8 2/8 3/8 in number line ?
    (1 vote)
    Default Khan Academy avatar avatar for user
    • hopper cool style avatar for user Philip
      On the number line, there is an increase (increment) of 1/8 each time. Each time a 1/8 is added, there will be that increase (e.g. after adding 1/8 to 0, the result is 1/8; after adding a 1/8 to the already present 1/8, the result is 2/8; adding another 1/8 to the 2 one-eighths gives a 3/8; adding yet another 1/8 to the 3 one-eighths gives a 4/8, etc.)
      (6 votes)
  • mr pants purple style avatar for user Ryker
    how it feels to chew five gum... stimulate your senses.
    (3 votes)
    Default Khan Academy avatar avatar for user
  • duskpin ultimate style avatar for user Jon
    When i'm adding fractions do I need to add the numerator
    (3 votes)
    Default Khan Academy avatar avatar for user
  • aqualine ultimate style avatar for user Dusky
    I will never get models. A little more help would be amazing!
    (2 votes)
    Default Khan Academy avatar avatar for user

Video transcript

In a previous video, we saw that we could view 2/3 times 6 as whatever number is 2/3 of the way to 6 on the number line, which we saw is 4. Or another way to think about it is that 4 is 2/3 of 6. 2/3 times 6 can be viewed as-- well, how many do I have if I take 2/3 of 6? Now, what we want to do now is apply that same idea, but to multiply not a fraction times a whole number, but a fraction times a fraction. So let's say that we wanted to take 3/4 and multiply it by 1/2. And we know, of course, the order that we multiply doesn't matter. This is the exact same thing as 1/2 times 3/4. So to imagine where this gets us, let's draw ourselves a number line. And I'll do it pretty large so that we have some space to work in. So that's 0. And then that is 1. And of course, our line could keep on going. And let's first imagine 3/4 times 1/2 as 3/4 of the way to 1/2. So first let's plot 1/2 on our number line. Well, 1/2 is literally halfway between 0 and 1. So that's 1/2 right over there. And how do we think about 3/4 of the way to 1/2? Well, what we could do is think about well, what's 1/4 of 1/2? Well, we could divide this part of the number line into 4 equal sections. So that's 2 equal sections. Now that's 4 equal sections. And while we're at it, let's divide all of the halves into 4 equal sections. So let's divide all of the halves into 4 equal sections. So that's 4 sections. And now let's do this one. I'm trying my best to draw them equal sections. So I've taken each of the halves and I've made them into 4 equal sections. So this point right over here is 1/4 of 1/2. But that's not what we care about. We want to get to 3/4 of 1/2. So we want to get to 1, 2, 3/4 of 1/2. So this point right over here, this is literally 3/4 times 1/2. And this is, of course, 1/2 here. But what number is this? And let me do this in a new color. We can now visualize it on the number line. But what number is this actually? Well, a big clue is that, well, before we had the section between 0 and 1 divided into 2 equal sections when we only had to plot 1/2. But then we took each of those 2 equal sections and then split them into 4 more sections. By doing that, we now essentially have divided the section between 0 and 1 into 8 equal sections. So each of these is actually 1/8. So this point right over here is 1/8. This is 2/8. And then this is 3/8. And that's in line with what we've seen about multiplying fractions before. This should be equal to 3 times 1 over 4 times 2, which is equal to 3/8. And everything that we're talking about, so we don't get confused, this is all referring to this point right over here on the number line. But what if we thought about it the other way around? What if we thought about it as 1/2 of the way to 3/4? So we could divide the space between 0 and 1 into fourths. So let's do that. So that is 1/4, 2/4, 3/4. So this right over here is the number 3/4. And we want to go half of the way to 3/4. Well, what is half of the way to 3/4? Well, we split this section into 2 equal sections. So we could split right over there. And we want to go exactly one of those sections. 1/2 of 3/4 gets us, once again, right over here to this point-- 3/8. So either way you imagine it, whether you're essentially taking 3/4 of 1/2, or saying I'm going to go 3/4 of the way to 1/2, or you say I'm going to go 1/2 of the way to 3/4, either way, hopefully it now makes conceptual sense. You can visualize it, and it makes numeric sense that this is going to be equal to 3/8.