(8) A fraction whose greatest common divisor of the numerator and denominator is 1 is called a reduced fraction. The sum of all positive reduced proper fractions with a denominator of 100 is ( ).
(A) 20
(B) 30
(C) 35
(D) 45
$8 \mathrm{~A}$ Hint: Since $100=2^{2} 5^{2}$, let
$$
\begin{array}{l}
A=\left\{n|2| n, n \leqslant 100, n \in \mathbf{N}^{*}\right\}, \\
B=\left\{n|5| n, n \leqslant 100, n \in \mathbf{N}^{*}\right\},
\end{array}
$$

then
$$
|A \cup B|=|A|+|B|-|A \cap B|=50+20-10=60 .
$$

Therefore, there are 40 proper fractions that meet the conditions.
If a positive number $i$ is coprime with 100, then $100-i$ is also coprime with 100. Therefore, if $\frac{i}{100}$ is a positive reduced proper fraction, then $\frac{100-i}{100}$ is also a positive reduced proper fraction, and $\frac{100-i}{100}+ \frac{i}{100}=1$. Therefore, the sum of all proper fractions is 20.