\(A=\frac{6}{5.8}+\frac{22}{8.19}+\frac{24}{19.31}+\frac{140}{31.101}+\frac{198}{101.200}\)
\(A=2.\left(\frac{1}{5}-\frac{1}{8}\right)+2.\left(\frac{1}{8}-\frac{1}{19}\right)+2.\left(\frac{1}{19}-\frac{1}{31}\right)+2.\left(\frac{1}{31}-\frac{1}{101}\right)+2.\left(\frac{1}{101}-\frac{1}{200}\right)\)
\(A=2.\left(\frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{19}+\frac{1}{19}-\frac{1}{31}+\frac{1}{31}-\frac{1}{101}+\frac{1}{101}-\frac{1}{200}\right)\)
\(A=2.\left(\frac{1}{5}-\frac{1}{200}\right)\)
\(A=2.\frac{39}{200}\)
\(\Rightarrow A=\frac{39}{100}\)