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Understanding fractions as division

Sal shows how a/b and a÷b are equivalent. That is, the fraction bar and the division symbol mean the same thing. Created by Sal Khan.

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  • male robot hal style avatar for user Doug McIntosh
    If you upvote me to 100 I will donate 150$ to khan Academy.
    (27 votes)
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  • hopper happy style avatar for user braxton.mcgeorge
    so we can do division or multiplecarion
    (17 votes)
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  • duskpin tree style avatar for user AUDREYC
    can somebody get this to 10 likes plzzzz
    (16 votes)
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  • cacteye purple style avatar for user Jailah Rushing
    just anotha day of khan making things complicated FOR NO REASON💯🔥🗣🙏
    (14 votes)
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  • aqualine sapling style avatar for user Yes
    If you still don't understand how to divide fractions. I will show you. There are 3 steps.
    So say you were doing 1/3 divided by 6 or 6 divided by a third.
    We will do 1/3 divided by 6 first.
    Step 1: Keep the number 1/3
    Step 2: Switch the division symbol to multiplication
    Step 3: Find the reciprocal of 6. And its 1/6 so 1/3 times 1/6 is 1/18. Sometimes you need to simplify.
    Now 6 divided by 1/3
    Keep 6.
    Turn to muliplication
    Switch 1/3 to 3/1
    its easier as 6/1x3/1 and that's 18/1 which can be reduced to 18
    Hope this helped
    (9 votes)
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  • boggle yellow style avatar for user CaedeusB
    KFC method
    (8 votes)
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  • aqualine ultimate style avatar for user Never gonna give you up
    We're no strangers to love
    You know the rules and so do I (do I)
    A full commitment's what I'm thinking of
    You wouldn't get this from any other guy
    I just wanna tell you how I'm feeling
    Gotta make you understand
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    We've known each other for so long
    Your heart's been aching, but you're too shy to say it (say it)
    Inside, we both know what's been going on (going on)
    We know the game and we're gonna play it
    And if you ask me how I'm feeling
    Don't tell me you're too blind to see
    Never gonna give you up
    Never gonna let you down
    Never gonna run around and desert you
    Never gonna make you cry
    Never gonna say goodbye
    Never gonna tell a lie and hurt you
    Never gonna give you up
    Never gonna let you down
    Never gonna run around and desert you
    Never gonna make you cry
    Never gonna say goodbye
    Never gonna tell a lie and hurt you
    We've known each other for so long
    Your heart's been aching, but you're too shy to say it (to say it)
    Inside, we both know what's been going on (going on)
    We know the game and we're gonna play it
    I just wanna tell you how I'm feeling
    Gotta make you understand
    Never gonna give you up
    Never gonna let you down
    Never gonna run around and desert you
    Never gonna make you cry
    Never gonna say goodbye
    Never gonna tell a lie and hurt you
    Never gonna give you up
    Never gonna let you down
    Never gonna run around and desert you
    Never gonna make you cry
    Never gonna say goodbye
    Never gonna tell a lie and hurt you
    Never gonna give you up
    Never gonna let you down
    Never gonna run around and desert you
    Never gonna make you cry
    Never gonna say goodbye
    Never gonna tell a lie and hurt you
    rick roll dudes are you guys gonna upvote or destory this question XD
    (6 votes)
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  • blobby green style avatar for user ConnorE
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    (5 votes)
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  • starky sapling style avatar for user Yocelynh2010
    Any tips? I would love that please! I still cant do it myself.
    (3 votes)
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    • aqualine ultimate style avatar for user AzhinHacker
      Swap the numerator and the denominator, (the top and bottom numbers in a fraction) on the second fraction. WHATEVER YOU DO, DO NOT DO IT FOR THE FIRST FRACTION. For example, 1/2 x 3/9, so it would be re-written as 1/2 x 9/3, and then you just multiply it, which would be 9/6, and then, you divide the numerator by the denominator, so just think, "how many times can 6 go into 9? And how much is left over?" So, if you were to do that, the answer would be 1 3/9, which, by the way, was you second fraction that you swapped. And, if you know how to, then you would simplify, and your final answer would be 1 1/3. (Oh, and by the way, the word for swapping the numerator and the denominator is called recipricals. So if you ever see that word in a test or a math question, then you know what it is.
      (4 votes)
  • blobby green style avatar for user Kristen Bauer
    when it says 5 millimeter can fit in a bottle of perfume how do you answer it when it says how many 2 millimeters can fit in there it is too R one how do you write that so that i dont get the answer wrong again and again.
    (3 votes)
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    • female robot amelia style avatar for user Johanna
      You’re right that one way we could write the answer to that problem is 2 R 1, but this lesson is focusing on fractions in division. How can we represent the answer with a fraction instead?

      We could use an improper fraction, 5/2. We could also use a mixed number, 2 1/2.

      Does that help?
      (4 votes)

Video transcript

When we were first exposed to multiplication and division, we saw that they had an inverse relationship. Or another way of thinking about it is that they can undo each other. So for example, if I had 2 times 4, one interpretation of this is I could have four groups of 2. So that is one group of 2, two groups of 2, three groups of 2, and four groups of 2. And we learned many, many videos ago that this, of course, is going to be equal to 8. Well, we could express a very similar idea with division. We could start with 8 things. So let's start with one, two, three, four, five, six, seven, eight things. So now we're going to start with the 8. And we could say, well, let's try to divide that into four groups, four equal groups. Well, that's one equal group, two equal groups, three equal groups, and four equal groups. And we see when we start with 8 divide it into four equal groups, each group is going to have 2 objects in it. So you probably see the relationship. 2 times 4 is 8. 8 divided by 4 is 2. And actually, if we did 8 divided by 2, we would get 4. And this is generally true. If I have something times something else is equal to whatever their product is, if you take the product and divide by one of those two numbers, you'll get the other one. And that idea applies to fractions. It actually makes a lot of sense with fractions. So for example, let's say that we started off with 1/3 and we wanted to multiply that times 3. Well, there's a couple of ways we could visualize it. Actually, let me just draw a diagram here. So let's say that this block represents a whole, and let me shade in a 1/3 of it. So that's 1/3. We're going to multiply by 3. So we're going to have 3 of these 1/3's. Or another way of thinking about it, it's going to be 1/3 plus another 1/3 plus another 1/3. That's our first 1/3, our second 1/3, and our third 1/3. And we get the whole. This is 3/3, or 1. So this is going to be equal to 1. So you use the exact same idea. If 1/3 times 3 is equal to 1, then that means that 1 divided by 3 must be equal to 1/3. And this comes straight out of how we first even thought about fractions. The first way that we ever thought about fractions was, well, let's start with a whole. And that whole would be our 1. And let's divide it into 3 equal sections, the same way that we divided this 8 into 4 equal groups. So if you divide this into 3 equal sections, the size of each of those sections is going to be exactly 1/3. Now, this leads to an interesting question that might be popping in your brain. Notice, we have 1 is the numerator, 3 is the denominator, and we just said that this is equal to the numerator divided by the denominator. 1 over 3 is the same thing as 1 divided by 3. Is this always true for a fraction? Well, let's just do the same thought experiment, but let's do it with a different fraction. Let's take 3/4 and multiply it by 4. So multiply it by 4. So once again, let's see if I could draw 1/4 here. Let me do this in a new color. So let's say that this block right over here is a whole. We'll divide it into four equal sections. So now I've divided it into fourths. And let me copy and paste it so I can use it multiple times. So copy. All right. Now, 3/4, that's going to be-- we can assume-- I didn't draw it perfectly. Actually, I could draw it a little bit better than that just to make the four equal sections actually look equal. So that looks like a little bit better of a job. I'm trying to make them four equal sections. Let me copy that one. So let me use it for later. Now, 3/4. This is four equal sections, and 3/4 represents three of them-- one, two, three. But now we're going to multiply it by 4. So we're going to have 3/4 four times. So we're going to need some more wholes here. So let's throw in another whole. So this is one 3/4. Now let me do the next 3/4 in another color. So that's a 1/4, that's a second 1/4, that's a third 1/4. That's another 3/4. And now let's do-- so we've done two 3/4 just now. Let me make it clear. This is the first 3/4, and then this plus this is the second 3/4. Now let's do a third 3/4. And we're going to have to use another whole right over here. And I will do that in this color. So my third 3/4, so here's a 1/4, here's my second 1/4, here's a third 1/4. So in green, I have another 3/4. And now we need four 3/4. So let's do that in a color I have not used yet, maybe white. So that's a 1/4, that's two 1/4, and that is three 1/4. So notice, now I have now I have one 3/4, two 3/4, three 3/4, and four 3/4. And what did I do when I got those four 3/4? Well, it's pretty clear. This is turned into 3 wholes. So this is equal to 3 wholes. Well, if 3/4 times 4 is equal to 3, that means that 3 divided by 4 is equal to 3/4. So the same idea again. 3 over 4 is the same thing as 3 divided by 4. And in general, this is true. The fraction symbol here can be interpreted as division. And looking at this diagram right here, it made complete sense. If you started with 3 wholes, and you want to divide it into 4 equal groups, one group, two groups, three groups, four groups, each group is going to have 3/4 in it.