 In this video I'm going to explain proportion problems type of example, so in a previous video I had talked about percent problems and percent problems had a nice little formula that we used, not really a formula, but anyway we'll call it a formula for now, for lack of a better term. Percent problems had a nice little formula, you plug numbers in, you solve, it's pretty easy to come up with. On the other hand, proportion problems are not that simple. We still use proportions, but it's just a little bit different. So as we go through this problem I'm going to solve this with proportions. Alright, Ryan ran 600 meters and counted 482 strides. How long is Ryan's stride in inches? And then here at the end it tells us that 1 meter is 39.37 inches. So what we have to do is not only do we have to find how long Ryan's stride is, but we have to find it in inches. But at the very beginning Ryan ran 600 meters, so we got to convert everything from meters to inches. So there's a lot of steps that we have to do for this problem. A good example of where these problems are used in the real world. Just recently my wife got a step counter and she had to figure out how long her strides are. So we actually did not exactly this, but something very similar to this. We actually didn't do 600 meters, we only did 400, but anyway. 600 meters, that's a time and a half around a typical high school track. And what you can do is you can figure out how long your strides are now. Why do you need to know how long your stride is? Well, knowing how long your stride is, how much you weigh, your activity level, your body fat percentage, things like that, having those different measurements can actually tell the device, this little step counter, how many calories you burned that day. And it's much, much more accurate because it's using your own body measurements. And so this is a type of problem that you will see in the real world if you want to be one of those healthy individuals, if you ever get a step counter or something like that, my wife actually got it through her work, she's kind of nice, she gets points and all sorts of different stuff like that. But anyway, if you ever get one of those step counters and want to be one of those healthy individuals, this is some type of mathematics that you're going to have to do. Alright, so again, reading through the problem, Ryan ran 600 meters and counted 482 strides. How long is Ryan's stride in inches? Alright, so the first thing we want to do is we want to set up our proportion. So we're going to have a fraction equal to a fraction, there's our proportion. So now in this proportion I have four empty spots, four empty spots and I'm going to fill about three of them, not about, I'm going to feel exactly three of them, okay? So the thing is, as I look through the problem, I have to find three different numbers from this problem. Some of them might be in there that are quite obvious, some of them are not. Okay, the first thing I see is 600 meters, there's a quite obvious number, 482 strides, there's another obvious number, but I don't see another one. This one here at the end, one meter is equal to 39.37 inches, that's a conversion, that's not part of the initial problem. Okay, so as I look at this, I need to find another number, I need three numbers to put in those four spots. Okay, Ryan ran 600 meters and counted 482 strides, how long is Ryan's stride in inches? Okay, now as I read that last sentence, I actually figure out what that last number is. How long is Ryan's stride, as in one stride? So it might not be quite obvious where all the numbers are at, sometimes you kind of have to read the problem and figure it out for yourself what the other number is going to be, okay? So Ryan ran 600 meters and counted 482 strides, how long is one of Ryan's stride in inches? Okay, so now as I, I'm going to take those three numbers, I'm going to plug them into, into these spots, here in my proportion, I've got to figure out where they go. The do they go on top, on bottom, left, right, where, where do they kind of go? Now as we go through this, we've got to realize that actually the labeling at the end of the problem is going to give us a hint on how to set this up. So Ryan ran 600 meters and counted 482 strides, how long is Ryan's stride in inches? We're looking for how long his, his stride is, okay? So when we have a, when we have a percentage like this, this is really nice because the English language actually helps us with this. We want to know the distance per stride, distance per stride. Ryan's distance per one of his stride. Okay, now as I say that over and over again, that actually gives us a hint on what's going to go on top, what's going to go on bottom. Distance per stride, distance per stride, that per word kind of gives us an idea of where the fraction bar is going to be. That tells us that we're going to have distance on top and we're going to have strides on bottom. Distance per stride. And now that's going to work for both the left and the right side here. I'm going to put my distances on top and I'll put my strides on the bottom. Okay, now you've got to make sure that distances and strides, they kind of have to go together. So Ryan ran 600 meters and counted 482 strides. So the 600 and the 482 have to go on the same side. It doesn't matter what side, just as long as they're on the same side. So those ones came first, I'll put them over here on the left, 600 meters and out of 482 strides. Okay, 600 meters over 482 strides, okay? How long is Ryan's one stride? How long is his one stride? That's a one, not a seven. One stride, how long is that stride? Now notice I put meters there, I didn't put inches. We have to do all of our math in meters first and then we have to convert all that to inches. Okay, so Ryan ran 600 meters in 482 strides. How many meters is one of his stride? Now see the logic behind setting this up. 600 meters took him 482 strides. How many meters for one stride? See the logic of setting that up. Okay, now instead of a question mark, I'm actually going to put a variable there. It doesn't really matter what variable we use, let's use capital R, capital R for Ryan. It doesn't really matter what we use as long as we know what R means. In this case, R is going to be the length of Ryan's stride. The length of Ryan's stride. All right, now for the math. This is a proportion problem, so we're going to use cross product to solve this. 600 times one is just 600 equals 482 times R, 482 times R. And then from there, what I'm going to do is I'm going to divide by 482. Divide by 482. It's going to give me about 1.2448. That's approximately what that is. Okay, now if you plug that into your calculator, you get a long repeating decimal. Yeah, I'm only going to round to about four decimal places. It makes it a little bit easier to work with. Okay, now in a problem like this, make sure you round to four, five, six, seven different decimal places. Don't round to one decimal place. That's really not going to help you. That's not going to give you an accurate measurement. Try to round to, I would say four or five decimal places that will give you a pretty accurate description of what we're working with. So again, when we chose what the variable meant, R was the length of Ryan's stride. So R is about 1.2448 meters. So Ryan, when he's running, his stride is about 1.2448 meters. So let's call it 1.2 meters. Now if you have an idea of how long a meter is, a meter in our standard system is about, it's about 39 inches, a little bit more than 39 inches as we see here. Okay, so it's a little bit more than three feet. So his stride, when he's running, is a little bit more than three feet. I would say about 40, maybe like 42 inches, something like that, if I was to guess. Because it's one meter plus a little bit of a fraction, a little bit of a decimal. Okay, well we want to find out exactly what that is. How do we do that? Well what we're going to do is we are going to use, now I call this railroad conversion. This is actually a type of conversion that I learned in my chemistry class. I actually didn't learn this in math class when I was in high school. But this is one way of converting. We know that one meter is 39.37 inches. So what I'm going to do is I'm going to take this answer that I got down here. I'm going to write it as 1.2448 meters over one, just as a normal fraction. That doesn't really change. I mean you can put any number over one, doesn't change it. Now what I'm going to do is I'm going to change it from meters to inches. So I'm going to multiply times something. Now I'm going to think of this meter label. I'm going to think of it kind of almost like a variable. I want to get rid of that meters. Now if I have fractions to get rid of something, it's going to be on the bottom of the fraction. So I'm going to have meters on the bottom here. Now this is the conversion that is going to go right here in this fraction. So I know that one meter is equal to 39.37 inches. One meter is 39.37 inches. It looks backwards. It looks upside down. But the reason that we're doing this is notice what's going to happen is that we have meters on top, meters on bottom. They cancel. And so the only label that I have left is inches. So what I'm doing is I'm converting from meters to inches. And this is how I do it. A lot of time when you're converting numbers back and forth, you don't know whether to multiply or divide by it. Well, in this case, we're going to multiply by 39.37. And this tells us right here, 1.2448 times 39.37. So we know for certain that we're going to multiply this. Now some of you that are really good with conversions, you pick this up very quickly. You know you're supposed to multiply by 39.37. Those of you who don't do conversions very well, this is a handy tool to use. This is the handy strategy to use to figure out whether or not you're supposed to multiply or divide by 39.37. But anyway, now to actually multiply those numbers together, you get about 49.0083, rounding just a little bit. But the thing is that number, 49.0083 inches, that is how long Ryan's stride is. So the thing is, after doing all this math, make sure that you write down the answer. Circling that, that's not what the answer is. You actually have to explain yourself. Ryan's stride is 49 inches long. There we go. OK, now notice the .0083, I didn't use that. I'm not going to use .0083, four inches. That's too small of an inch to really use. So I'm not going to worry about that very much. Anyway, Ryan's stride is 49 inches long. That's how you figure out how long his stride is when he's running 600 meters. All right, that's one way of doing those proportion problems. There are a couple of different ways, but that's just one of them. So the first thing that we did is we set up a proportion. Make sure we have the same label on top. We had meters on top, and we had strides on bottom. We used cross product to solve it. Now once we had Ryan's stride in meters, we had to take meters and convert it to inches, meters to inches. 49 inches is the length of Ryan's stride. OK, so that is one way of solving proportion problems. The biggest thing to remember here is make sure when you've initially set up your proportion, make sure that you have the same label on top and the same label on bottom so that everything is kind of equivalent. It's nice to use proportions because that's how you set up. It's just one label on top, in this case meters on top, and then strides on bottom. So it's very straightforward on how to set up proportion problems. Second thing, make sure that you look through the problem and identify all your numbers. And sometimes your numbers are a little hard to identify. Sometimes you'll have to try to come up with your own numbers that logically work with the problem. Like we had to come up with this one here, which logically works because we want Ryan's stride, which is just one of them. All right, and that is how you solve proportion problems.