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Watch 1st

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Video transcript

let's think about what it means to take 8/3 and divide it by one-third so let me draw a number line here so there is my number line this is 0 this is 1 and this is 2 maybe this is 3 right over here and let me plot 8/3 so to do that I just need to break up my each each hole into thirds so let's see it's one-third two-thirds three-thirds 4/3 5/3 6 thirds 7/3 8/3 so right over here and then of course 9/3 would get us to 3 so this right over here is 8/3 8/3 now one way to think about 8/3 divided by 3 is what if we take this length and we say how many jumps would it take to get there if we're doing it in jumps of 1/3 or essentially we're breaking this up if we were to break up 8/3 into sections of 1/3 how many sections would I have or how many jumps what I have well let's think about that if we're trying to take jumps of 1/3 we're gonna have to go 1 2 3 4 5 6 7 8 jumps so we could view this as we could you let me do this in a different color in this orange so we took these 8 jumps right over here so we could view 8/3 divided by 1/3 as being equal to 8 now why is this actually make sense well when you're dividing things in 2/3 for every hole you're now going to have 3 jumps so whatever value you're trying to get to you're going to have that number times 3 jumps so another way of thinking about it is that 8/3 8/3 divided by divided by 1/3 is the same thing as 8/3 8/3 times 3 now we could either write it like this we could write x 3 like that or if we want to write 3 as a fraction we know that 3 is the same thing three over one and when we already know how to multiply fractions a multiply the numerators eight times three so you have eight let me do that that same color you have eight times three in the numerator now eight times three and then you have three times 1 in the denominator three times three times one in the denominator which would give you 24 thirds which is the same thing as 24 divided by three which once again is equal is equal to is equal to is equal to eight now let's see if this still makes sense instead of dividing by one-third if we were divided by two-thirds so let's think about what 8/3 divided by two-thirds is divided by two-thirds well once again this is like asking the question if we wanted to break up this section from zero to 8/3 into sections of 2/3 or jumps of two-thirds how many sections or how many jumps would I have to make well let's think about it one jump just in a different color we could make one jump that's the same color as my 8/3 we could do one jump my computer is doing something strange we could do one jump two jumps three jumps and four jumps so we see 8/3 divided by 2/3 is equal is equal to four now does this make sense in this world right over here well if we take 8/3 and we do the same thing saying hey look dividing by a fraction is the same thing as multiplying by a reciprocal well let's multiply by three halves let's multiply by the reciprocal of 2/3 so we swap the numerator and the denominator so we multiply it times three halves and then what do we get in the numerator once again we get eight times three which is 24 and in the denominator we get 3 times 2 which is 6 so now we get 24 divided by 6 is equal to four now does it make sense that we got half the answer if you think about the difference between what we did here and what we did here these are almost the same except here we really just didn't divide or you could say you divided by one while here you / - well does that make sense well sure because here you jumped twice as far you jumped twice as far so you had to take half the number of steps and so in the first example you saw why it makes sense to multiply by 3 when you divide by a fraction for every hole you're making 3 jumps so that's why when you divide by this fraction you multiply or when you divide whatever's in the denominator you multiply by it and now when the numerator is greater than 1 every jump you're going twice as far as you did in this first one right over here and so you would have to do half as many jumps hopefully that makes sense it's easy to think about just mechanically how to divide fractions dividing 8/3 divided by 1/3 is the same thing as 8/3 times 3 over 1 or 8/3 divided by 2/3 is the same thing as 8/3 times 3 over 2 but hopefully this this video gives you a little bit more of an intuition of why this is the case

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Understanding division of fractions (video) | Khan Academy

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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. To log in and use all the features of Khan Academy, please enable JavaScript in your browser.

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Dividing fractions: 3/5 ÷ 1/2 (video) | Khan Academy

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Dividing two fractions is the same as multiplying the first fraction by the reciprocal of the second fraction. The first step to dividing fractions is to find the reciprocal (reverse the numerator and denominator) of the second fraction. Next, multiply the two numerators. Then, multiply the two deno…

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Word Problem

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Dividing whole numbers by fractions: word problem

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Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere.

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Multiplying and Dividing Fractions - BrainPOP

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Tim and Moby show you how to multiply and divide fractions in this BrainPOP movie! Dividing can actually make a number bigger?!

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Multiply 1 and 3/4 times 7 and 1/5. Simplify your answer and write it as a mixed fraction. So the first thing we want to do is rewrite each of these mixed numbers as improper fractions. It's very difficult, or at least it's not easy for me, to directly multiply mixed numbers. One can do it, but it's much easier if you just make them improper fractions. So let's convert each of them. So 1 and 3/4 is equal to-- it's still going to be over 4, so you're still going to have the same denominator, but your numerator as an improper fraction is going to be 4 times 1 plus 3. And the reason why this makes sense is 1 is 4/4, or 1 is 4 times 1 fourths, right? 1 is the same thing as 4/4, and then you have three more fourths, so 4/4 plus 3/4 will give you 7/4. So that's the same thing as 1 and 3/4. Now, let's do 7 and 1/5. Same exact process. We're going to still be talking in terms of fifths. That's going to be the denominator. You take 5 times 7, because think about it. 7 is the same thing as 35/5. So you take 5 times 7 plus this numerator right here. So 7 is 35/5, then you have one more fifth, so you're going to have 35 plus 1, which is equal to 36/5. So this product is the exact same thing as taking the product of 7/4 times 36/5. And we could multiply it out right now. Take the 7 times 36 as our new numerator, 4 times 5 as our new denominator, but that'll give us large numbers. I can't multiply 7 and 36 in my head, or I can't do it too easily. So let's see if we can simplify this first. Both our numerator and our denominator have numbers that are divisible by 4, so let's divide both the numerator and the denominator by 4. So in the numerator, we can divide the 36 by 4 and get 9. If you divide something in the numerator by 4, you need to divide something in the denominator by 4, and the 4 is the obvious guy, so 4 divided by 4 is 1. So now this becomes 7 times 9, and what's the 7 times 9? It's 63, over 1 times 5. So now we have our answer as an improper fraction, but they want it as a mixed number or as a mixed fraction. So what are 63/5? So to figure that out-- let me pick a nice color here-- we take 5 into 63. 5 goes into 6 one time. 1 times 5 is 5. You subtract. 6 minus 5 is 1. Bring down the 3. 5 goes into 13 two times. And you could have immediately said 5 goes into 63 twelve times, but this way, at least to me, it's a little bit more obvious. And then 2 times 5 is 12, and then we have sorry! 2 times 5 is 10. That tells you not to switch gears in the middle of a math problem. 2 times 5 is 10, and then you subtract, and you have a remainder of 3. So 63/5 is the same thing as 12 wholes and 3 left over, or 3/5 left over. And if you wanted to go back from this to that, just think: 12 is the same thing as 60 fifths, or 60/5. 60/5 plus 3/5 is 63/5, so these two things are the same thing. These two things are equivalent. This is as an improper fraction. This is as a mixed number or a mixed fraction. But this is our answer right there: 12 and 3/5.

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Multiplying mixed numbers (video) | Khan Academy

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Multiply 1 and 3/4 times 7 and 1/5. Simplify your answer and write it as a mixed fraction. So the first thing we want to do is rewrite each of these mixed numbers as improper fractions. It's very difficult, or at least it's not easy for me, to directly multiply mixed numbers.

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We're asked to multiply 5/6 times 2/3 and then simplify our answer. So let's just multiply these two numbers. So we have 5/6 times 2/3. Now when you're multiplying fractions, it's actually a pretty straightforward process. The new numerator, or the numerator of the product, is just the product of the two numerators, or your new top number is a product of the other two top numbers. So the numerator in our product is just 5 times 2. So it's equal to 5 times 2 over 6 times 3, which is equal to-- 5 times 2 is 10 and 6 times 3 is 18, so it's equal to 10/18. And you could view this as either 2/3 of 5/6 or 5/6 of 2/3, depending on how you want to think about it. And this is the right answer. It is 10/18, but when you look at these two numbers, you immediately or you might immediately see that they share some common factors. They're both divisible by 2, so if we want it in lowest terms, we want to divide them both by 2. So divide 10 by 2, divide 18 by 2, and you get 10 divided by 2 is 5, 18 divided by 2 is 9. Now, you could have essentially done this step earlier on. You could've done it actually before we did the multiplication. You could've done it over here. You could've said, well, I have a 2 in the numerator and I have something divisible by 2 into the denominator, so let me divide the numerator by 2, and this becomes a 1. Let me divide the denominator by 2, and this becomes a 3. And then you have 5 times 1 is 5, and 3 times 3 is 9. So it's really the same thing we did right here. We just did it before we actually took the product. You could actually do it right here. So if you did it right over here, you'd say, well, look, 6 times 3 is eventually going to be the denominator. 5 times 2 is eventually going to be the numerator. So let's divide the numerator by 2, so this will become a 1. Let's divide the denominator by 2. This is divisible by 2, so that'll become a 3. And it'll become 5 times 1 is 5 and 3 times 3 is 9. So either way you do it, it'll work. If you do it this way, you get to see the things factored out a little bit more, so it's usually easier to recognize what's divisible by what, or you could do it at the end and put things in lowest terms.

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Multiplying 2 fractions: 5/6 x 2/3 (video) | Khan Academy

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How to multiply fractions? The first step when multiplying fractions is to multiply the two numerators. The second step is to multiply the two denominators. Finally, simplify the new fractions. The fractions can also be simplified before multiplying by factoring out common factors in the numerator and denominator.

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Multiplying unit fractions and whole numbers

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Sal multiplies 1/2 x 5 using repeated addition and fraction models.

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Funny :)

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KEEP CHANGE FLIP

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Flocabulary - Dividing Fractions - Keep, Change, Flip

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See the full lyrics and lesson plan at http://www.flocabulary.com/divide-fractions/ This educational hip-hop song uses the 'Keep, Change, Flip' mnemonic to teach students how to divide fractions.