12. (6 points) The sum of all simplest proper fractions for 1996 is



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12. (6 points) The sum of all the simplest proper fractions of 1996 is 498.
【Solution】Solution: $1996=2 \times 2 \times 499$,
The sum of all the numerators of the simplest proper fractions of 1996:
$$
\begin{array}{l}
1+3+5+7+\cdots+1993+1995-499-499 \times 3, \\
=(1+1995) \times[(1995-1) \div 2+1] \div 2-1996, \\
=998 \times 998-1996,
\end{array}
$$

So the sum of the simplest proper fractions is: $\frac{998 \times 998-1998}{1996}=498$; hence the answer is: 498.