How to average 2 averages with a constant variable present

Question

For example, formula used is

(A*200,000/B) = C. 

 

Is it better to average C1 and C2 such that:

(1*200000)/366425 = 0.55

(0*200000)/185624 = 0.00

and average these two numbers (0.55+0.00)/2 = 0.275

 

Alternatively, is it better to combine individual components

{[(A1+A2)/200,000]/(B1+B2)} such that:

(1*200000)/552049 = 0.36

 

These are the only two methods I want to compare.  Which is statistically correct?

Answer 1

In your "alternative" you are adding the numerators and the denominators, e.g., a/b + c/d = (a+b)/(c +d).

That is incorrect. To add fractions common denominators must be used.