Rate Conversions 9

>>This is YourMathGal, Julie Harland. Please visit my website at yourmathgal.com where all of my videos are organized by topic. This is example nine of rate conversions. We’re going to do this problem here where we’re converting 8 meters per second to miles per hour. I chose this because I’ve heard from a science teacher, this is a common conversion students need to do in their classes, either going from meters per second to miles per hour, or vice verse from miles per hour to meters per second. Now, we do have to know some conversions. One mile is approximately, and I’m going to use approximately because I don’t think its exactly, its close. Approximately 1.6 kilometers. And you have to know the metric system that a thousand meters is the same as 1 kilometer, okay? Kilo, that means 1,000, by the way. All right, so given now, we’re going to start with 8 meters per second. [ Pause ] And we want to eventually get to miles. Be careful, this is not miles, its meters, right? M for meters, meters per second. So, I don’t have something that goes directly from meters to miles but I could go from meters to kilometers and then from kilometers to miles. So, that’s what I’m going to do. So, let’s see. I want to end up with kilometers in the numerator and the meter is canceling. So, I know that when kilometer is the same as 1,000 meters. Okay? So, I’m using this conversion right here. You know that it’s like the number ’cause 1 kilometer is the same thing as a thousand meters, so I could write that as a fraction, that means 1. Okay. So, when I do that, does anything cancel so far? Well, my meters are canceled. Now, I have my answer in terms of kilometers per second. But I don’t want kilometers, I want miles. So, we need another conversion. So, miles and kilometers are right here. We could use this conversion right here with the kilometers to cancel. So, there’s kilometers in the numerator, so I want to put this 1.6 kilometers in the denominator and one– and I’m going to write up that word ’cause we don’t want to confuse that with meter or minutes or anything else. So, one mile is the same as 1.6 kilometers. Now, that means the kilometers both cancel, so now, I have miles per second. But what I’m going for, miles per hour. Now, here’s where it depends how you– if you need to convert from seconds to minutes first, and then minutes to hours, or can you go directly to it. So, most people can say, well, there’s 60 seconds in a minute, keep in mind. 60 seconds in one minute, right? And then we know there’s 60 minutes in one hour. And notice that means there’s 3600. So, this sort of tells you there’s 3600 seconds in one hour. So, if you know there’s 3600 seconds in one hour, you can go directly to writing with the seconds to cancel. 3600 seconds the same as 1 hour and cancel the seconds. If not, you would actually write both these things up there. You would write 60 seconds over 1 minute times 60 minutes over 1 hour. So, if you already know this, you can skip writing two things there. It’s up to you. But that’s where I got that from. So, what do I have now? I’ve got just miles in the numerator and hours in the denominator, as far as what kind of units I’m discussing. And so, now I want to put this in the calculator. We’ve got 8 times 3600 and then you could divide by 1,000 times 1.6. And you could do some simplifying. First, if you want like– I like doing things like this, I like to cancel out those two zeroes with those two zeroes, it makes it a little bit easier. And then, in my head, or I might write it down, 10 times 1.6 is just 16. That just makes a little bit easier arithmetic. Oh, gosh, I could do this without a calculator. For those of you who have a calculator, you could just put it all in, 8 times 3600 divided by a thousand divided by 1.6. But here’s what I’m noticing. The 16 and the 8, I can cancel, which is 2, I end up with 36 divided by 2. So, I’ve got 18. And that’s exactly the same thing you should get if you did not do all these canceling stuff which I think has been. You should also get 18– what, miles per hour. And how do you write miles hour usually? Usually, they put mph, okay? Miles per hour. But you might have written it first as miles over hour. Okay. Again, certainly, you don’t need to do all this reducing. You could use a calculator. I find it easier sometimes to do this and actually plug all these numbers in a calculator, right? So, I’ve got 18 miles per hour. Right. What if you didn’t get this 3600 seconds over 1 hour, I’m just going to show you how it might look a little bit differently. [ Pause ] So let’s say, you can start it out with 8 meters per second. If you want to change the time first, and let’s say, you want to get rid of the seconds and get everything in minutes, you know that there are 60 seconds in 1 minute, that would cancel out your seconds. And you’re trying to get to hours, so then, you might say, okay, well, my minutes are canceled, there’s 60 minutes in 1 hour, right? And that cancels the minutes, so I’ve got meters per hour but I need to change this meters to kilometers, so you might have to say, well, I’m going to have to say meters cancel. A thousand meters in one kilometer. And lastly, doing my kilometers in miles, make sure miles is different than the meters here. I could write– its here just 1 mile is 1.6 kilometers, so I could do 1 mile is 1.6 kilometers. So, instead of having just four fractions that period, you might have five. And the order of these could be in any order you want, it depends, you know, what you’re converting along the way. But notice you end up with the same thing. You have 8 times 60 times 60 in the numerator. You have a thousand times 1.6 in the denominator. And you see that the kilometers cancel here and the meters cancel here, and you still will end up with miles over hours. And you will still end up with exactly the same answer, 18 miles per hour. This is YourMathGal, Julie Harland. Please visit my website at yourmathgal.com where all of my videos are organized by topic.

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