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a, 1. \(\dfrac{2}{17}\)
2. \(22\)
3. 4
b,
1. \(\dfrac{8}{5}\)
2. \(\dfrac{176}{5}\)
3. \(\dfrac{28}{5}\)
4. \(\dfrac{3}{10}\)
5. \(\dfrac{163}{5}\)
6. \(\dfrac{9}{20}\)
a) \(\dfrac{12}{17}:6=\dfrac{12}{17}\cdot\dfrac{1}{6}=\dfrac{2}{17}\)
\(A=1\dfrac{1}{2}\times1\dfrac{1}{3}\times1\dfrac{1}{4}\times....\times1\dfrac{1}{2020}\times1\dfrac{1}{2021}\\ =\dfrac{3}{2}\times\dfrac{4}{3}\times\dfrac{5}{4}\times\dfrac{6}{5}\times....\times\dfrac{2022}{2021}\\ =\dfrac{3\times4\times5\times6\times.....\times2022}{2\times3\times4\times5\times....\times2021}\\ =\dfrac{2022}{2}=1011\)
\(\dfrac{5}{3}\times\dfrac{15}{8}-\dfrac{9}{8}\times\dfrac{5}{8}-\dfrac{5}{3}\)
\(=\dfrac{5}{3}\times\left(\dfrac{15}{8}-\dfrac{9}{8}-1\right)\)
\(=\dfrac{5}{3}\times\left(\dfrac{15}{8}-\dfrac{9}{8}-\dfrac{8}{8}\right)\)
\(=\dfrac{5}{3}\times\dfrac{-1}{4}\)
\(=-\dfrac{5}{12}\)