Question

\(\left(6-\dfrac{4}{3}\right)\)\(\cdot\dfrac{9}{7}-\dfrac{19}{5}\):\(\dfrac{2}{3}\)

\(\left(1-\dfrac{1}{5}\right)\cdot\left(\dfrac{-3}{10}+\dfrac{1}{5}\right)\)

1+\(\dfrac{1}{8}+\dfrac{1}{24}+\dfrac{1}{48}+\dfrac{1}{80}+\dfrac{1}{120}\)

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Answer 1

a: \(=\dfrac{14}{3}\cdot\dfrac{9}{7}-\dfrac{19}{5}\cdot\dfrac{3}{2}\)

\(=6-\dfrac{57}{10}=\dfrac{3}{10}\)

b: \(=\dfrac{4}{5}\cdot\dfrac{-3+2}{10}=\dfrac{4}{5}\cdot\dfrac{-1}{10}=\dfrac{-2}{25}\)

c: \(=1+\dfrac{1}{2\cdot4}+\dfrac{1}{4\cdot6}+\dfrac{1}{6\cdot8}+\dfrac{1}{8\cdot10}+\dfrac{1}{10\cdot12}\)

\(=1+\dfrac{1}{2}\left(\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{6}+...+\dfrac{1}{10}-\dfrac{1}{12}\right)\)

\(=1+\dfrac{1}{2}\cdot\dfrac{5}{12}=1+\dfrac{5}{24}=\dfrac{29}{24}\)