Per Year Per $1000 & Per $1000 Per Year

KWF

Junior Member
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Feb 19, 2010
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How are the following expressed mathematically as a fraction and why?


1. $35.69 per year per $1000


2. $17.65 per $1000 per year


Is 1. ($35.69/year)/$1000 or $35.69/(year/$1000) and is 2. ($17.65/$1000)/year or $17.95/($1000/year)
 
How are the following expressed mathematically as a fraction and why?


1. $35.69 per year per $1000


2. $17.65 per $1000 per year


Is 1. ($35.69/year)/$1000 or $35.69/(year/$1000) and is 2. ($17.65/$1000)/year or $17.95/($1000/year)
Typically, it is the first of those so that, if you multiply the first one by $2000, you would get $71.38/year or if you multiply it by 2 years and get $71.38/$1000.
 
How are the following expressed mathematically as a fraction and why?


1. $35.69 per year per $1000


2. $17.65 per $1000 per year


Is 1. ($35.69/year)/$1000 or $35.69/(year/$1000) and is 2. ($17.65/$1000)/year or $17.95/($1000/year)
I do not think the words need to come into play other than that per means to divide. You are correct when you say (in around about way) that (a/b)/c is NOT the same as a/(b/c). Now division does not have the associated law (that is what the last sentence says) so a/b/c is simply not a/(b/c). What I am saying is that a per b per c is a/b/c. Ishuda gave a good example of why it should be this way. And in all honesty his example is a great way to test to see whether 1 or 2 is correct but in the end I think it is just a math problem and the words have no influence on how to write it out.
 
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