a: \(\dfrac{5}{23}\cdot\dfrac{17}{26}+\dfrac{5}{23}\cdot\dfrac{9}{26}\)
\(=\dfrac{5}{23}\left(\dfrac{17}{26}+\dfrac{9}{26}\right)\)
\(=\dfrac{5}{23}\cdot\dfrac{26}{26}=\dfrac{5}{23}\)
b: \(\left(\dfrac{3}{29}-\dfrac{1}{5}\right)\cdot\dfrac{29}{3}\)
\(=\dfrac{3}{29}\cdot\dfrac{29}{3}-\dfrac{1}{5}\cdot\dfrac{29}{3}\)
\(=1-\dfrac{29}{15}=-\dfrac{14}{15}\)
c: \(\dfrac{5}{8}\cdot\left(-56\right)\cdot\dfrac{5}{7}\cdot\left(-4\right)\)
\(=56\cdot\dfrac{5}{8}\cdot\dfrac{5}{7}\cdot4\)
\(=25\cdot4=100\)
d: \(\dfrac{1}{3}\cdot\dfrac{2}{5}+\dfrac{-2}{6}\cdot\dfrac{2}{5}+\dfrac{-3}{9}\cdot\dfrac{2}{5}\)
\(=\dfrac{1}{3}\cdot\dfrac{2}{5}-\dfrac{1}{3}\cdot\dfrac{2}{5}-\dfrac{1}{3}\cdot\dfrac{2}{5}\)
\(=-\dfrac{1}{3}\cdot\dfrac{2}{5}=-\dfrac{2}{15}\)
e: \(\dfrac{-1}{3}\cdot\dfrac{141}{17}-\dfrac{39}{3}\cdot\dfrac{-1}{17}\)
\(=\dfrac{-1}{17}\cdot\dfrac{141}{3}-13\cdot\dfrac{-1}{17}\)
\(=\dfrac{-1}{7}\left(\dfrac{141}{3}-13\right)\)
\(=-\dfrac{1}{7}\cdot\left(47-13\right)=\dfrac{-34}{7}\)
e: \(\dfrac{1}{7}\cdot\dfrac{5}{12}+\dfrac{1}{7}\cdot\dfrac{5}{3}+\dfrac{1}{7}\cdot\dfrac{2}{12}-\dfrac{-2}{3}\cdot\dfrac{1}{7}\)
\(=\dfrac{1}{7}\left(\dfrac{5}{12}+\dfrac{5}{3}+\dfrac{2}{12}+\dfrac{2}{3}\right)\)
\(=\dfrac{1}{7}\cdot\left(\dfrac{7}{12}+\dfrac{7}{3}\right)\)
\(=\dfrac{1}{12}+\dfrac{1}{3}=\dfrac{5}{12}\)
