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Multiplying fractions word problem: bike

Sal solves a word problem by multiplying a fraction by a mixed number. Created by Sal Khan.

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  • leaf green style avatar for user Divij Kodi
    isn't 3 1/3's improper fraction supposed to be 10/3
    (1 vote)
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  • duskpin seed style avatar for user kamari.j
    Is there a quicker way and easier way ?
    (7 votes)
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  • starky seedling style avatar for user Isabel V. Lomeli
    If I'm being honest the way he explains things is very confusing. I couldn't understand the lesson.
    (4 votes)
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  • duskpin seed style avatar for user 149005298Diego
    not gonna lie I din't understand most of that
    (2 votes)
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  • starky sapling style avatar for user Eli White
    Isn't 3 times 3 plus 1 10/3? Why'd he right 9/3 + 1/3?
    (2 votes)
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  • hopper happy style avatar for user Lachlan
    There is a much easier way and less complicated way. You don’t have to do all the complex steps that sal has shown. He is just showing different ways to do it so hopefully you might get it. Start with 1/5 x 3 1/3. 3 1/3 can be changed to 10/3 * 1/5 =10/15. Then you can simplify to 2/3 which gives you the answer. Hope this helps!
    (2 votes)
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  • aqualine tree style avatar for user Esmeralda L.
    How do u guys know all of these stuff without making mistakes in the video?
    (0 votes)
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  • starky ultimate style avatar for user Jacob Harrison
    umm, why did he not simplify the 10 and the 5 before multiplying them? that would have make things much easier
    (0 votes)
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  • female robot grace style avatar for user 👹🥭TheNewTellyTubbie🧋🐧
    You can ride your bike 1/5 of a mile per minute. If it takes you 3 and 1/3 minutes to get to your friend's house, how many miles away does your friend live? And this here is pictures of these guys on bicycles. It's pretty clear they're not riding to work, or some of these guys aren't even riding a bicycle. But let's focus on the question. So you can ride your bike 1/5 of a mile per minute. And you're going to do this for 3 and 1/3 minutes-- times 3 and 1/3. So we really have to figure out, how do we multiply 1/5 times 3 and 1/3? So there's a couple of ways to think about it. You could literally view a 3 and 1/3 as this is the same thing as 1/5 times 3 plus 1/3. That's exactly what 3 and 1/3 is. And then we can just apply the distributive property. This would be 1/5 times 3-- I'm going to keep the colors the same-- plus 1/5 times 1/3. And this is going to be equal to-- well, we could rewrite 1/5 times 3 as 1/5 times 3/1. That's what 3 really is if we wrote it as a fraction. And then, of course, we're going to have plus 1/5 times 1/3. And let's just think about what each of these evaluate to. Here you multiplied the numerators, and you multiplied the denominators. So this is going to be equal to 1 times 3 over 5 times 1. And this business right over here is going to be-- and remember, order of operations. We want to do our multiplication first. So this is going to be 1 times 1 over 5 times 3. And so that's going to be equal to 3/5 plus 1/15. And now we have different denominators here. But lucky for us, 3/5, if we multiplied the numerator and the denominator by 3, we're going to get a denominator of 15. And so that's equal to 9/15 plus 1/15, which equals 10/15. And if you divide the numerator and the denominator both by 5, you're going to get 2/3. So your friend lives 2/3 miles away from your house. Well, that's kind of interesting. And this was kind of a long way to do it. Let's think about if there's a simpler way to do it. So this is the same thing as 1/5 times-- and I'm just going to write 3 and 1/3 as a mixed number. So it's 1/5 times 3 and 1/3 can be rewritten as 9/3-- sorry, I'm going to rewrite 3 and 1/3 as an improper fraction. So this is the same thing as 9/3-- that's 3-- plus 1/3, which is the same thing as 1/5-- well, I switched colors arbitrarily-- which is the same thing-- I'm still on the same color-- as 1/5 times 9/3 plus 1/3 is 10/3. And now we can just multiply the numerator and multiply the denominator-- or multiply the numerators. So this is 1 times 10-- I'm trying to stay good with the color coding-- over 5 times 3, which is exactly equal to what we just got. 1 times 10 is equal to 10. 5 times 3 is 15. 10/15, we already established, is the same thing as 2/3. So your friend lives 2/3 of a mile away from you.
    (1 vote)
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  • blobby green style avatar for user Angelina
    Can I find one with a whole number. I've only been getting the single fraction?
    (1 vote)
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Video transcript

You can ride your bike 1/5 of a mile per minute. If it takes you 3 and 1/3 minutes to get to your friend's house, how many miles away does your friend live? And this here is pictures of these guys on bicycles. It's pretty clear they're not riding to work, or some of these guys aren't even riding a bicycle. But let's focus on the question. So you can ride your bike 1/5 of a mile per minute. And you're going to do this for 3 and 1/3 minutes-- times 3 and 1/3. So we really have to figure out, how do we multiply 1/5 times 3 and 1/3? So there's a couple of ways to think about it. You could literally view a 3 and 1/3 as this is the same thing as 1/5 times 3 plus 1/3. That's exactly what 3 and 1/3 is. And then we can just apply the distributive property. This would be 1/5 times 3-- I'm going to keep the colors the same-- plus 1/5 times 1/3. And this is going to be equal to-- well, we could rewrite 1/5 times 3 as 1/5 times 3/1. That's what 3 really is if we wrote it as a fraction. And then, of course, we're going to have plus 1/5 times 1/3. And let's just think about what each of these evaluate to. Here you multiplied the numerators, and you multiplied the denominators. So this is going to be equal to 1 times 3 over 5 times 1. And this business right over here is going to be-- and remember, order of operations. We want to do our multiplication first. So this is going to be 1 times 1 over 5 times 3. And so that's going to be equal to 3/5 plus 1/15. And now we have different denominators here. But lucky for us, 3/5, if we multiplied the numerator and the denominator by 3, we're going to get a denominator of 15. And so that's equal to 9/15 plus 1/15, which equals 10/15. And if you divide the numerator and the denominator both by 5, you're going to get 2/3. So your friend lives 2/3 miles away from your house. Well, that's kind of interesting. And this was kind of a long way to do it. Let's think about if there's a simpler way to do it. So this is the same thing as 1/5 times-- and I'm just going to write 3 and 1/3 as a mixed number. So it's 1/5 times 3 and 1/3 can be rewritten as 9/3-- sorry, I'm going to rewrite 3 and 1/3 as an improper fraction. So this is the same thing as 9/3-- that's 3-- plus 1/3, which is the same thing as 1/5-- well, I switched colors arbitrarily-- which is the same thing-- I'm still on the same color-- as 1/5 times 9/3 plus 1/3 is 10/3. And now we can just multiply the numerator and multiply the denominator-- or multiply the numerators. So this is 1 times 10-- I'm trying to stay good with the color coding-- over 5 times 3, which is exactly equal to what we just got. 1 times 10 is equal to 10. 5 times 3 is 15. 10/15, we already established, is the same thing as 2/3. So your friend lives 2/3 of a mile away from you.