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# Advanced Math/Per Year Per \$1000 & Per \$1000 Per Year

Question
Hello:

How are the following expressed mathematically?

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)

Hi Kenneth,
The expressions mean the same for both cases. I mean that, for instance, the first statement simply means \$35.69 for every year for every \$1000 which is the same as saying \$35.69 for every \$1000 for every year.
Mathematically,
(A/B)/C = A/(BC)
which is the same as
(A/C)/B = A/(BC)

But,
A/(B/C) = (AC)/B

So, \$35.69/(year/\$1000) would be incorrect and so would \$17.95/(\$1000/year). The positions of the bracket signs are important, algebraically.

I hope this helps you, let me know otherwise.

Regards
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