Multiplying fractions word problem: bike

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.