a: \(-\dfrac{1}{24}-\left[\dfrac{1}{4}-\left(\dfrac{1}{2}-\dfrac{7}{8}\right)\right]\)
\(=\dfrac{-1}{24}-\dfrac{1}{4}+\dfrac{1}{2}-\dfrac{7}{8}\)
\(=\dfrac{-1-6+12-21}{24}=\dfrac{-16}{24}=\dfrac{-2}{3}\)
b: \(\left(\dfrac{5}{7}-\dfrac{7}{5}\right)-\left[\dfrac{1}{2}-\left(-\dfrac{2}{7}-\dfrac{1}{10}\right)\right]\)
\(=\dfrac{5}{7}-\dfrac{7}{5}-\dfrac{1}{2}+\dfrac{-2}{7}-\dfrac{1}{10}\)
\(=\left(\dfrac{5}{7}-\dfrac{2}{7}\right)+\left(-\dfrac{7}{5}-\dfrac{1}{2}-\dfrac{1}{10}\right)\)
\(=\dfrac{3}{7}+\dfrac{-14-5-1}{10}=\dfrac{3}{7}-2=-\dfrac{11}{7}\)
c: \(11\dfrac{1}{4}-\left(2\dfrac{5}{7}+5\dfrac{1}{4}\right)\)
\(=11+\dfrac{1}{4}-2-\dfrac{5}{7}-5-\dfrac{1}{4}\)
\(=4-\dfrac{5}{7}=\dfrac{23}{7}\)
d: \(\left(3-\dfrac{1}{4}+\dfrac{2}{3}\right)-\left(5-\dfrac{1}{3}-\dfrac{6}{5}\right)-\left(6-\dfrac{7}{4}+\dfrac{3}{2}\right)\)
\(=3-\dfrac{1}{4}+\dfrac{2}{3}-5+\dfrac{1}{3}+\dfrac{6}{5}-6+\dfrac{7}{4}-\dfrac{3}{2}\)
\(=\left(3-5-6\right)+\left(-\dfrac{1}{4}+\dfrac{7}{4}\right)+\left(\dfrac{2}{3}+\dfrac{1}{3}\right)+\dfrac{6}{5}-\dfrac{3}{2}\)
\(=-8+\dfrac{3}{2}+1+\dfrac{6}{5}-\dfrac{3}{2}\)
\(=-7+\dfrac{6}{5}=\dfrac{-29}{5}\)
e: \(\dfrac{1}{3}-\dfrac{3}{4}-\left(-\dfrac{3}{5}\right)+\dfrac{1}{64}-\dfrac{2}{9}-\dfrac{1}{36}+\dfrac{1}{15}\)
\(=\left(\dfrac{1}{3}+\dfrac{3}{5}+\dfrac{1}{15}\right)+\left(-\dfrac{3}{4}-\dfrac{2}{9}-\dfrac{1}{36}\right)+\dfrac{1}{64}\)
\(=\dfrac{5+9+1}{15}+\dfrac{-27-8-1}{36}+\dfrac{1}{64}=\dfrac{1}{64}\)
f: \(\dfrac{3}{5}:\left(-\dfrac{1}{15}-\dfrac{1}{6}\right)+\dfrac{3}{5}:\left(-\dfrac{1}{3}-1\dfrac{1}{15}\right)\)
\(=\dfrac{3}{5}:\dfrac{-2-5}{30}+\dfrac{3}{5}:\left(-\dfrac{1}{3}-\dfrac{16}{15}\right)\)
\(=\dfrac{3}{5}\cdot\dfrac{30}{-7}+\dfrac{3}{5}:\dfrac{-5-16}{15}\)
\(=\dfrac{3}{5}\cdot\dfrac{30}{-7}+\dfrac{3}{5}\cdot\dfrac{-15}{21}\)
\(=\dfrac{3}{5}\left(-\dfrac{30}{7}-\dfrac{5}{7}\right)=\dfrac{3}{5}\cdot\left(-5\right)=-3\)
