a: \(\left(\dfrac{2}{7}+\dfrac{3}{8}+\dfrac{12}{7}+\dfrac{5}{8}\right)\cdot\dfrac{19}{63}\)
\(=\left(\dfrac{2}{7}+\dfrac{12}{7}+\dfrac{3}{8}+\dfrac{5}{8}\right)\cdot\dfrac{19}{63}\)
\(=\left(\dfrac{14}{7}+\dfrac{8}{8}\right)\cdot\dfrac{19}{63}\)
\(=\left(2+1\right)\cdot\dfrac{19}{63}=\dfrac{19}{63}\cdot3=\dfrac{19}{21}\)
b: \(\left(\dfrac{2}{7}+\dfrac{3}{8}+\dfrac{12}{7}+\dfrac{5}{8}\right)\cdot\dfrac{19}{63}\)
\(=\left(\dfrac{2}{7}+\dfrac{12}{7}+\dfrac{3}{8}+\dfrac{5}{8}\right)\cdot\dfrac{19}{63}\)
\(=\left(\dfrac{14}{7}+\dfrac{8}{8}\right)\cdot\dfrac{19}{63}\)
\(=\left(2+1\right)\cdot\dfrac{19}{63}=3\cdot\dfrac{19}{63}=\dfrac{19}{21}\)
c: \(\dfrac{1}{2}+\dfrac{2}{4}+\dfrac{3}{6}+...+\dfrac{9}{18}+\dfrac{10}{20}\)
\(=\dfrac{1}{2}+\dfrac{1}{2}+...+\dfrac{1}{2}+\dfrac{1}{2}\)
\(=\dfrac{1}{2}\cdot10=\dfrac{10}{2}=5\)
d: \(\left(1-\dfrac{1}{4}\right)\left(1-\dfrac{1}{9}\right)\cdot...\cdot\left(1-\dfrac{1}{100}\right)\)
\(=\left(1-\dfrac{1}{2}\right)\left(1-\dfrac{1}{3}\right)\cdot...\cdot\left(1-\dfrac{1}{10}\right)\left(1+\dfrac{1}{2}\right)\cdot\left(1+\dfrac{1}{3}\right)\cdot...\cdot\left(1+\dfrac{1}{10}\right)\)
\(=\dfrac{1}{2}\cdot\dfrac{2}{3}\cdot...\cdot\dfrac{9}{10}\cdot\dfrac{3}{2}\cdot\dfrac{4}{3}\cdot...\cdot\dfrac{11}{10}\)
\(=\dfrac{1}{10}\cdot\dfrac{11}{2}=\dfrac{11}{20}\)