a: \(\left(-\dfrac{5}{24}+\dfrac{7}{6}\right)+\left(-\dfrac{19}{24}+\dfrac{5}{6}\right)\)
\(=\left(-\dfrac{5}{24}-\dfrac{19}{24}\right)+\left(\dfrac{7}{6}+\dfrac{5}{6}\right)\)
\(=-\dfrac{24}{24}+\dfrac{12}{6}=-1+2=1\)
b: \(\left(0,45+\dfrac{-7}{10}+1,25\right):\dfrac{5}{3}\)
\(=\left(1,7-0,7\right):\dfrac{5}{3}=1\cdot\dfrac{3}{5}=\dfrac{3}{5}\)
c: \(\left(-\dfrac{1}{3}-\dfrac{9}{8}\right)\cdot\dfrac{3}{4}+\dfrac{1}{8}\cdot\dfrac{3}{4}\)
\(=\dfrac{3}{4}\left(-\dfrac{1}{3}-\dfrac{9}{8}+\dfrac{1}{8}\right)\)
\(=\dfrac{3}{4}\left(-\dfrac{1}{3}-1\right)=\dfrac{3}{4}\cdot\dfrac{-4}{3}=-1\)
d: \(\left(1-\dfrac{1}{4}\right)\left(1-\dfrac{1}{9}\right)\left(1-\dfrac{1}{25}\right)\left(1-\dfrac{1}{16}\right)\)
\(=\left(1-\dfrac{1}{2}\right)\left(1-\dfrac{1}{3}\right)\left(1-\dfrac{1}{4}\right)\left(1-\dfrac{1}{5}\right)\left(1+\dfrac{1}{2}\right)\left(1+\dfrac{1}{3}\right)\left(1+\dfrac{1}{4}\right)\left(1+\dfrac{1}{5}\right)\)
\(=\dfrac{1}{2}\cdot\dfrac{2}{3}\cdot\dfrac{3}{4}\cdot\dfrac{4}{5}\cdot\dfrac{3}{2}\cdot\dfrac{4}{3}\cdot\dfrac{5}{4}\cdot\dfrac{6}{5}\)
\(=\dfrac{1}{5}\cdot\dfrac{6}{2}=\dfrac{3}{5}\)
