Why do I put parentheses ( ) around a variable that the results are different?

[Sukunta Muadthong]

Dear All,
I calculated the willingness to pay by stata 11.0 from 2 equations.
1.

nlcom  ((_b[ba_salary]*15000)+_b[inf7]+_b[log7]+_b[ asc])/(-_b[ ba_salary])

       _nl_1:  ((_b[ba_salary]*15000)+_b[inf7]+_b[log7]+_b[ asc])/(-_b[ ba_salary])

------------------------------------------------------------------------------
      choice |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       _nl_1 |   6551.413   1530.388     4.28   0.000     3551.907    9550.919
------------------------------------------------------------------------------

and
2.

nlcom  (_b[ba_salary]*15000)+_b[inf7]+_b[log7]+_b[ asc]/(-_b[ ba_salary])

       _nl_1:  (_b[ba_salary]*15000)+_b[inf7]+_b[log7]+_b[ asc]/(-_b[ ba_salary])

------------------------------------------------------------------------------
      choice |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       _nl_1 |   16676.88   1497.943    11.13   0.000     13740.97     19612.8
------------------------------------------------------------------------------

why are coef. present a different value?

Thank you very much
Best Wishes
Sukunta Muadthong

[Carole J. Wilson]

The order of operations in math (with no parentheses or within parentheses is 1) exponents 2) multiplication and/ or division 3) addition and/or subtraction

So, the first equation does this first because it is in parentheses

( (_b[ba_salary]*15000)+_b[inf7]+_b[log7]+_b[ asc] )

Then takes that result and divides by

(-_b[ ba_salary])

The second equation does the division before the addition

_b[ asc]/(-_b[ ba_salary])

Then adds that result to

(_b[ba_salary]*15000)+_b[inf7]+_b[log7]

A more simplified example

*divide first then add
10+10+100 /  2
= 10 + 10 + 50
= 70

*add first because in parentheses then divide
(10 + 10 + 100) / 2
= 120 / 2
= 60

[Sukunta Muadthong]

Dear Carole J.Wilson,
OH .. thank you very much for your kindness. that is very clear .

Best Wishes,
Sukunta Muadthong