>>Hi this is Julie Harland and I’m your math gal. Please visit my web site at yourmathgal.com where you can search for any of my videos organized by topic. In this video we do unit conversions involving area and we do the following five problems on this video. This is part three of unit conversions and we’re going to discuss area and converting one kind of area to another kind of area. So, let’s start off with this one. How many square feet are in 1 square yard? Okay, well first of all, what is a square yard means– what does it mean? You’ve got basically a square where it’s 1 yard on one side and 1 yard on the other side. So, we say the whole thing, the area of this is 1 square yard, which you could write as 1 yard squared. Okay that’s all– how we usually write it. Now wonder how many square feet are in there? Well if you break up a yard there’s 3 foot– 3 feet in a yard so, if I broke this up that’s 1 foot, there’s another foot and there’s another foot so that would be a whole yard. And I could do the same thing on the other side. 1 foot, 1 foot and 1 foot and if we go ahead and cross this through inside each of here is each of these little squares is 1 square foot because its 1 foot times 1 foot. So, this is called 1 square foot right here. Think of it as tiles so usually when you buy carpeting it’s by the square yard but when you buy tiles it might be by the square foot. So, if you think of this as 1 big square yard of carpeting and then said you’re gonna put how many tiles that are 1 foot by 1 foot would fit in it. There would be 9 square feet in there. See how there’s 9 of these little squares. So, the answer to this is how many square feet are in 1 square yard by looking at the picture there’s 9 square feet and we would write that as 9 square feet. Now notice that does not mean that the 9 is squared, it means I’ve got some square feet. How many of those? There’s 9 of them all together. Okay, now you don’t want to have to draw a picture each time so, let’s move on. So, we found out that 1 square yard equals 9 square feet. Alright, what’s another way we could have gotten that without actually drawing a picture? You could say well we know 1 yard equals 3 feet right. So we could square both sides because these 2 things are equal and that says 1 square yard equals 9 square feet. So, there’s another way of getting it. Now if you’re trying to convert something from square yards to square feet you might do it this way. You might say well let’s say I’ve got 6 square yards and I wanna know how many square feet it is. So, the way we were doing it before, we’re gonna multiply it by something [Sound effects] that converts yards into feet right. So, we could put– well I know there’s three feet in 1 yard you know. Oops, sorry. The reason I’m putting the yard in the denominators is because I need to get this yard squared, but the problem is notice this is a square yard and this only says 1 yard. So, the way to rectify that is you can square everything inside this fraction like– remember this fraction represents the number 1 so, you could just say 1 squaring it right. But, when you square something really you’re squaring everything inside. So, if you do that you could just write 3 squared, feet squared, 1 squared and yard squared and that’s how you’re gonna get that yard squared to cancel that yard squared. So, I cancelled those yard squares and then what does that give me? Well, in the numerator what do I have? Be careful, it’s 6 times 3 squared. So remember that 6 times 9, which is 54. And then– and then I have the square feet right, which is what I wanted. In the denominator I just have 1 squared, you don’t leave a 1 in the denominator, so 6 square yards is just 54 square feet. Let’s try another one. So, we’re gonna convert 8 square feet to square inches. Okay so, we’re starting out with 8 square feet alright so, then I’ll multiply it by something. So, I wanna see is there a simple way to convert between inches and feet and you know that 12 inches is 1 foot. You want your numerator to have the inches right and you want the denominator to have the feet so it’ll cancel. Alright so, we know that– well how’s it work? 1 foot is the same as 12 inches but, here’s the problem is that would only give you 1 foot it’s not gonna cancel with the square feet so, we’re just gonna square everything here. So, now what cancels? The square feet cancels. And what do I have left in the numerator? I have 8 times 12 squared alright. I’m just gonna write this out, 8 times 12 squared is 144 and you’re gonna have squared inches. In the denominator you just have 1 so you don’t need to write it when it’s just a 1 in the denominator. So, just get out your calculator and do 8 times 144 and that gives you 1152. So, I’m just going to rewrite this 1152 square inches. Now some people like writing that out in words, that’s fine if you wanna write square inches. That means the same thing. Okay here’s another one. How many square yards are in 1 square mile alright? So, what we’re starting off with is 1 square mile and we wanna end up with square yards. So, we don’t have a conversion that goes directly from miles to yards but, we can go from miles to feet and then feet to yards. So, I’m gonna write down here at the bottom what we know. We know that 1 mile– and of course you could look this up if you forget it, 1 mile is 5280 feet and then we know that 1 yard [Sound effects] is 3 feet right. Those are our conversions. So, I need to first get rid of the miles. So I need to multiply by something where the miles are gonna cancel. So, if I put the miles in the denominator, 1 over 1 mile and the numerator would be 5280 feet. [Sound effects] But, I have miles squared so I gotta square everything here. Okay, now that’s gonna get the mile squares to cancel so I’m okay so far. But, I’m gonna have my answer in square feet but, I want my answer what? In square yards. Alright so, I have to do it again. I gotta multiply by another fraction. And I want the feet to cancel right and I wanna get yards and I just have to figure out what this is gonna be. Well, I know that 1 yard is 3 feet correct? But, I want to have square feet, so if I square everything in here I’ve got it. Notice what this is saying is 1 square yard is 9 square feet, which is where we started off on this video. So, then we’ve got the square feet canceling and our answer’s finally going to be just in square yards. Now what do I have in the numerator? I’ve got a 1 times 5280 squared times 1 squared, that’s also 1. So, you’re gonna have to put that in your calculator, 5280 squared divided by your denominator, which is 9. Alright so, that’s what you wanna do on your calculator and all you’re gonna have left is whatever that answer is, square yards. So, try that in your calculator. And I’ve got 3097600 square yards, that’s a lot of square yards. [Laughter] A square mile is huge, think about it. Okay so, 1 mile is only– is 5280 feet. Keep in mind a square mile would be 5280 times 5280 square feet at 10, so this is a big number and yea it should be. So, that’s how many square mile– I’m sorry, how many square yards are in 1 square mile. Here’s another one. Convert 13 square inches to square centimeters using the approximation 1 inch equals 2.54 centimeters. Now square– a square inch is a lot bigger than a square centimeter so we’re gonna get a- a– a lot more than 13 when we figure this out. Try putting the video on pause and trying this on your own first. Okay hopefully you tried it. So, what do we start with? We’re gonna start with 13 [Sound effects] square inches and I wanna multiply it by something that if I can that goes between inches and centimeters, which is right here. So, I want the inches in the denominator. So I put 1 inch is the same thing as 2.54 centimeters but, of course really I want square inches to cancel. So, I square everything alright, and I’m done. Now you don’t have to use this parentheses. If that confuses you, you could leave the parentheses off. I just don’t write the little time sign here because I don’t want you to get confused with a decimal point right there. Okay so, the square inches is going to cancel and what is this, what am I left with? I’m just gonna have 1 in the denominator so it’ll just be a whole number so I have 13 times 2.54 squared. So, you’re gonna have to square this number times 13 and your answer’s going to be in square centimeters. So, go ahead, get out your calculator and try that. Alright, I get 83.8708 [Sound effects] square centimeters, 83 okay. And it should be a lot more because remember there’s 2 and a half centimeters in there. So, just look at the picture again you know here’s a square inch right. The centimeters like 2 and a half of those. It’s like you know 2 plus it’s like a half right. So, if you kind of look at a picture. These– these aren’t exactly whole centimeters but, you know this is 4 plus all this extra space here. So, there’s a lot of square centimeters you know there’s like about 6 if you added this all up it’s close to that, a little bit bigger. There’s 6 square centimeters actually in a square inch, this is just 1 inch. Okay let’s do one more. How many square kilometers are in a square mile? So, it means I start with a square mile and my answers’ gotta be in square kilometers. Now a kilometer is smaller than a mile, so there’s gonna be more square miles than in a square– than in a square [Sound effects] I’m sorry. There are going to be more square kilometers than there are in a square mile. Alright so, we’re gonna start with 1 square mile okay. Alright now we’re going from metric– I’m sorry we’re going from English to metric. So, we’ve got miles and the first thing we need to do is change that to feet because we know remember that 1 mile is 5280 feet okay. But, of course I have square miles so I have to square everything. Now of course you don’t have to put 1 squared because we know 1 squared is the same as 1 but I’m just being consistent here. And our square miles will cancel out. [Sound effects] Alright so, I’m trying to get the kilometers right. So, I’m still not to the metric but, I know this conversion between inches and centimeters, so first let’s get this to inches. So, alright let’s do this because you’ve got square feet now. We know there’s 1 foot in 12 inches and of course we’re gonna square it because we wanna get rid of the square feet. And now the square feet are gonna cancel okay, so I got my square inches okay, hmm. But now I’ve got to move over to my metric and let’s use the– the 2.54 approximation we’ve been using. So, we know that 1 inch is approximately 2.54 centimeters and I’m gonna square everything right. And I’m running out of room here but, so I’m gonna just have to go– I’ll try and make this a little bit smaller. We’re almost there. [Laughter] We just need to get the centimeters to kilometers. So you do have to know your metric system. And so we’re, what we wanna do is get the– the centimeters to cancel out. So, the question is in 1 kilometer how many centimeters are there? Well there’s a 1000 meters but, there’s that many centimeters in a kilometer. So, again we’ve gotta square everything and that will cancel out that and that. And I’m gonna look at all the numerators and all the denominators and what do we have here? We’ve got 5280 squared times 12 squared times 2.54 squared right. That’s gonna be my numerator. Kilometers squared, which is what I’m looking for and the denominator I’m gonna divide by this huge number, which is what is that 100,000 squared, can be pretty big. So, you gotta put all of that in your calculators. Go ahead and put that in your calculator now. This is pretty tricky to enter into your calculator so I’m showing you what I did. 5280 squared is this big number here and then 12 squared is 144. 2.54 squared is 6.4516 and the denominator, this number 100,000 times 100– let’s see did I put 10,000 instead of 100,000? Yes I did. I meant to put 100,000. Okay so, what I’m gonna do is– is just deal with dividing by this 100,000, basically that means move the decimal. If I’m dividing by this I’m gonna move this one up here 5 to the left so 1-2-3-4-5. So, now I’m just gonna take that number just divided that out and then if I want to take the– move this one over for 2 of these 0’s I’m gonna move the– I’m gonna move this decimal over 3 places for 3 of the 0’s, so it actually goes 3 more places. And for these two 0’s I’m gonna move this one in 2 places. So, I’ve done my division so now my calculator I’m gonna put in this number .278784 times 1.44 times 6.4516 and that was kilometers squared. Remember I cancelled the inches squared too and let’s see what we get. Okay what I get is approximately 2.– and I’m gonna round to the nearest tenth, 2.6 square kilometers. Very tricky problem. Man if you could do that you’ve got it down. [ Sound effects and Silence]>>Please visit my website at yourmathgal.com where you can view all of my videos, which are organized by topic.