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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.