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Studying for a test? Prepare with these 12 lessons on Measurement and data.
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We're asked how many inches are in 4 and 1/2 yards? Let me write that down. 4 and 1/2 yards. Now, whenever we're dealing with fractions and we're going to multiply and divide by fractions, it really complicates the issue to have a mixed number. So right from the get go, I want to turn this into an improper fraction. Let me do it over here in the top right. 4 and 1/2 written as an improper fraction is equal to what? We're still going to have 2 as a denominator. So 2 times 4 is 8. So 8/2 is the same thing 4. Let me rewrite this, just as a bit of review. 4 is the same thing as 8/2. That's the same thing as 4. And then you have that plus 1/2. That is going to give you 9/2. The quick way to do it: 2 times 4 is 8, 8 plus 1 is 9. So 4 and 1/2 is the same thing as 9/2. So 4 and 1/2 yards is the same thing as-- let me write it over here-- 9/2. yards. Now, we want to convert this into inches. Just so we can take this in baby steps, maybe we convert this into feet first, and then once we have it in feet, then we can convert it into inches. So to convert it into feet, we just have to remember that there are 3 feet for every 1 yard. So let me write that down. There are 3 feet per yard. And if we were to multiply 9/2 yards times 3 feet, this yard would be in the numerator. It'd be divided by this yard, and they would cancel out, and we'd just be left with feet. So we know we have to multiply by 3. You can say this is 3 feet for every 1 yard, if it makes it simple, or just 3 feet per yard. Another way to think about it is however many yards you have, you're going to have more feet, right? There are 3 feet per yard. So if I have 1 yard, I'm going to have 3 feet. If I'm going to have 2 yards, I'm going to have 6 feet. So you should always think about it in your head, OK,, well, yeah, multiplying by 3. So that also makes sense. So if we multiply by 3 right over here the 9 times 3 is 27/2. Let me write it out. Let me take it step by step, not skipping any steps. So this is equal to 9/2 times 3/1 yards. This yards right here, I'll do it in orange. Yards times feet per yards. The yards cancel out, and you're left with 9 times 3 is equal to 27/2 feet. So we figured out 4 and 1/2 yards is 27/2 feet. And that makes sense because we should have more feet than yards. And actually, this should be three times more, so everything makes sense. 27/2 is 3 times 9/2. So now we have 27/2 feet, and now we want to convert this to inches. And we just have to remember there are 12 inches per yard. And we're going to want to multiply by 12, because however many feet we have, we're going to have 12 times as many inches. If we have 1 foot, we're going to have 12 inches, 2 feet, 24 inches. 27/2 feet, we're going to multiply it by 12 to get the number of inches. Since this is going to be times 12, and we'll make sure the dimensions work out: 12 inches per foot. And the feet and the foot, this is just the plural and the singular of the same word. It's the same dimension. This will cancel out. So this will be-- if we just rearrange the multiplication, view it as everything is getting multiplied, and when you just multiply a bunch of things, order doesn't matter. So this is equal to 27/2 times 12 feet. I'm just swapping the order. Feet times inches divided by feet, or foot, just the singular of the same word. The feet and the foot cancel out, they're the same unit. And you have 27 times 12 divided by 2 inches. And what we could do here is that our final answer is going to be 27 times 12/2 inches. And before we multiply the 27 times 12 and then divide by 2, you immediately see, well, I can just divide 12 by 2, and 2 by 2, and it makes our computation simpler. 12 divided by 2 is 6, 2 divided by 2 is 1. It becomes 27 times 6 inches, and let's figure out what that is. 27 times 6. 7 times 6 is 42. 2 times 6 is 12, plus 4 is 16. This is equal to 162 inches, which makes sense. 4 and 1/2 yards, that gets us to this number right here: 27 divided by 2 is 13 and 1/2 feet. You multiply that by 12, it makes sense. You're going to have a bunch of inches. 162 inches.