Question

Answer 1

a: \(=\dfrac{5}{9}\left(7+\dfrac{1}{2}-6-\dfrac{1}{3}\right)\)

\(=\dfrac{5}{9}\cdot\left(1+\dfrac{1}{6}\right)=\dfrac{5}{9}\cdot\dfrac{7}{6}=\dfrac{35}{54}\)

b: \(=\dfrac{4}{7}\cdot\dfrac{3}{4}-1:\dfrac{5}{2}=\dfrac{3}{7}-\dfrac{2}{5}=\dfrac{15-14}{35}=\dfrac{1}{35}\)

c: \(=\dfrac{1}{2}\left(\dfrac{2}{1\cdot3}+\dfrac{2}{3\cdot5}+...+\dfrac{2}{99\cdot101}\right)\)

\(=\dfrac{1}{2}\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{99}-\dfrac{1}{101}\right)\)

\(=\dfrac{1}{2}\cdot\dfrac{100}{101}=\dfrac{50}{101}\)