\(\frac{1}{30}+\frac{2}{30}+...+\frac{9}{30}\)
\(=\frac{1+2+...+9}{30}\)
\(=\frac{\left(9+1\right)\cdot9\div2}{30}\)
\(=\frac{45}{30}=\frac{3}{2}\)
\(\frac{1}{30}+\frac{2}{30}+...+\frac{8}{30}+\frac{9}{30}\)
\(\Rightarrow\frac{9\left(\frac{9+1}{2}\right)}{30}\)
\(\Rightarrow\frac{9\cdot5}{30}=\frac{45}{30}\)
\(\Rightarrow\frac{3}{2}\)