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Multiplying 2 fractions: number line

Sal uses a number line to multiply fractions. Created by Sal Khan.

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  • hopper jumping style avatar for user Amanuel Ayalew
    At , doesn't Sal mean the two halves?
    (46 votes)
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  • blobby green style avatar for user Ivanna Morales
    Why does he make this more confuseing than it needs to be?
    (14 votes)
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  • starky tree style avatar for user Scout Askar
    I do not understand this. Could you make more simpimler? Please?
    (14 votes)
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  • 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?
    (5 votes)
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    • 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.
      (8 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 ?
    (5 votes)
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    • 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.)
      (5 votes)
  • duskpin ultimate style avatar for user Jon
    When i'm adding fractions do I need to add the numerator
    (6 votes)
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  • winston default style avatar for user ConnorTheBoi
    i lik tis epizode it relly halped
    (4 votes)
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  • blobby green style avatar for user Patty Bilberry
    can you do the same with division?
    (0 votes)
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    • sneak peak green style avatar for user Isabelle Thurmond
      In some cases, yes! It might be really easy to use division for this sort of thing, when you have a nice whole number, (like 6) and a nice and clean, simple fraction, (like 1/2) and you know that 1/2 of 6 is the same as dividing 6 by 2. However, with numbers that are impossible to apply this method to, (like 13/89 of 24.12) multiplication must be used instead. I hope that answers your question. :)

      Edit: With the numbers I gave ( 13/89 of 24.12) , the problem might also look something like this: 13/89 -Divided by- 1/24.12 Because any number (x) multiplied by and other number (y) is the same as dividing x by the reciprocal of y.
      In this case, It's not "impossible" to find the answer this way like I said before, but multiplying would be far easier to dividing by the reciprocal, Hope that helps. :)
      (14 votes)
  • starky tree style avatar for user Jadyn
    I know that the person is trying their best but, i still don't understand the number line. Could somebody help me understand it? or could somebody put it by part so i could understand it a little bit better?
    (3 votes)
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  • aqualine ultimate style avatar for user KingKevin
    If you multiply or divide the top and bottom of any fraction by the same number, you do not change the value of the fraction. If you modify only top or only bottom you are changing the value of the fraction.
    Here are examples.
    Let's say I have a fraction of 1/2. That's half.
    I can multiply top and bottom by 2. (1*2)/(2*2) = 2/4. Now I made 2 quarters. Guess what? 2 quarters is one half. 1/2=2/4. These two fractions look different, but they represent the same value.

    Take a pizza, divide it into 12 equal slices, take 3 slices. How much pizza did you get? 3/12. I can divide top and bottom by 3. (3/3)/(12/3) = 1/4. Take a look at the 3 slices you got. You have a quarter of a pizza. So 3/12 = 1/4

    In the video the fraction was (5 * 2) / (6 * 3). We can divide top and bottom by 2 and the value will not change. (5 * 2 / 2) / (6 * 3 / 2). 2 / 2 = 1 and 6 / 2 = 3. You'll get (5 * 1) / (3 * 3). That is what you've seen in the video.
    Let's compare (5 * 2) / (6 * 3) = 10/18. Divide top and bottom by 2 you'll get 5/9. (5 * 1) / (3 * 3) = 5/9. The same!! If you take 2 pizzas and divide one into 18 equal slices and then take 10 slices, the other divide into 9 slices and take 5 of them, you'll get the same amount of pizza.
    Let's take original fraction (5 * 2) / (6 * 3) and try to divide only the bottom part (5 * 2) / (6 / 3 * 3 / 3) = (5 * 2) / (3 * 1) = 10/3 That is totally different value. That fraction means 3 whole pizzas and one third of fourth pizza. This does not equal to our original fraction.
    Lengthy explanation, but I hope it is helpful.
    (3 votes)
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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.