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用分數進行單位轉換 (英) : 用分數進行單位轉換
- We are asked how many inches are in four and a half yards.
- We can do it in a couple of ways.
- One we could do is to see how many inches are in four yards and
- how many inches are there in half a yard.
- and this is really four plus one half yards.
- Or we could convert this into improper fraction first and then convert.
- But before I even do that, let us just think about how many inches are there in a yard.
- So, if I have one yard,
- We know that there are 3 feet
- for every one yard.
- Why am I multiplying by three?
- And the easiest way to think about is
- you are going to have a larger value over here
- and you are also going to want to have
- these units right over here cancel out.
- So yard is cancelling out with yard.
- So you have one yard is equal to three feet.
- Now how many inches are there in one foot?
- We know that there are twelve inches for every one foot.
- And same logic over here.
- Inches is a smaller unit of measurement.
- So it makes sense to multiply by twelve.
- Three feet is going to be more inches; so we multiply by twelve
- and also these units cancel out.
- Foot in the numerator, foot in the denominator.
- Three times twelve divided by one is thirty six inches
- You might have already known it, but it is nice to have the dimensions cancel out
- like this.
- We now know that one yard is equal to thirty six inches
- Or there are thirty six inches for every one yard.
- And now we can either break this down
- or convert this into an improper fraction.
- First I will break it down into four yards plus one half a yard.
- Four yards is going to be equal to four multiplied by thirty six inches per yard.
- Yard and yard cancel out.
- four times thirty six is a hundred and fourty four inches.
- That is just the four yards.
- And then if we do the half yard
- One half yard times 36 inches per yard
- yards cancel out.
- One half of thirty six is going to be eighteen inches.
- So four and half a yard is the same thing as four yards plus one half yard.
- Which is the same thing as
- One hundred and fourty four inches plus eighteen inches.
- Which is going to give us one hundred and sixty two inches.
- The other way to do this is:
- to convert this into an improper function
- and then multipy.
- If I have four and a half of anything
- Four is the same thing as eight halves.
- Four and a half is the same thing as four plus one half
- Four is the same thing as four over one.
- plus one half
- The common denominator is two
- So, four over one is the same thing as eight over two.
- plus one over two.
- This is equal to nine over two.
- A simple way to do is four times two is eight, and eight plus one is nine.
- So that gives the nine over two.
- So, we have nine half yards that we want to convert to inches.
- Nine half yards times thirty six inches per yard.
- Yard in the numerator, yard in the denominator.
- We are left with nine over two times thirty six over one inches.
- Divide both the numerator and the denominator by two.
- nine times thirty six over two inches.
- dividing gives nine times eighteen.
- Which is one hundred and sixty two inches.
- So, all of this simplifies to one hundred and sixty two inches.
- and we are done!