1: \(\dfrac{1}{6}-\left[\dfrac{1}{6}-\left(\dfrac{1}{4}+\dfrac{9}{12}\right)\right]\)
\(=\dfrac{1}{6}-\dfrac{1}{6}+\left(\dfrac{1}{4}+\dfrac{9}{12}\right)\)
\(=\dfrac{1}{4}+\dfrac{9}{12}=\dfrac{1}{4}+\dfrac{3}{4}=1\)
2: \(\dfrac{2}{3}-\left[-\dfrac{7}{4}-\left(\dfrac{1}{2}+\dfrac{3}{8}\right)\right]\)
\(=\dfrac{2}{3}+\dfrac{7}{4}+\left(\dfrac{1}{2}+\dfrac{3}{8}\right)\)
\(=\dfrac{8+21}{12}+\dfrac{7}{8}=\dfrac{29}{12}+\dfrac{7}{8}=\dfrac{58}{24}+\dfrac{21}{24}=\dfrac{79}{24}\)
3: \(-\dfrac{1}{24}-\left[\dfrac{1}{4}-\left(\dfrac{1}{2}-\dfrac{7}{8}\right)\right]\)
\(=\dfrac{-1}{24}-\dfrac{1}{4}+\left(\dfrac{1}{2}-\dfrac{7}{8}\right)\)
\(=\dfrac{-7}{24}+\dfrac{4}{8}-\dfrac{7}{8}=\dfrac{-7}{24}-\dfrac{3}{8}=\dfrac{-7}{24}-\dfrac{9}{24}=-\dfrac{16}{24}=-\dfrac{2}{3}\)
4: \(\dfrac{3}{2}-\left[-\dfrac{5}{4}-\left(\dfrac{1}{2}+\dfrac{6}{8}\right)\right]\)
\(=\dfrac{3}{2}+\dfrac{5}{4}+\left(\dfrac{1}{2}+\dfrac{3}{4}\right)\)
\(=\dfrac{3}{2}+\dfrac{1}{2}+\dfrac{5}{4}+\dfrac{3}{4}=\dfrac{4}{2}+\dfrac{8}{4}=2+2=4\)
5: \(\dfrac{9}{7}-\left[\dfrac{1}{2}-\left(-\dfrac{2}{7}-\dfrac{1}{10}\right)\right]\)
\(=\dfrac{9}{7}-\dfrac{1}{2}+\left(-\dfrac{2}{7}-\dfrac{1}{10}\right)\)
\(=\dfrac{9}{7}-\dfrac{1}{2}-\dfrac{2}{7}-\dfrac{1}{10}=\left(\dfrac{9}{7}-\dfrac{2}{7}\right)-\left(\dfrac{1}{2}+\dfrac{1}{10}\right)\)
\(=1-\left(\dfrac{1}{2}+\dfrac{1}{10}\right)=1-\dfrac{6}{10}=\dfrac{4}{10}=\dfrac{2}{5}\)
6: \(\dfrac{5}{3}+\left[-\left(\dfrac{7}{12}-\dfrac{2}{3}\right)+\dfrac{1}{3}\right]\)
\(=\dfrac{5}{3}-\dfrac{7}{12}+\dfrac{2}{3}+\dfrac{1}{3}=\left(\dfrac{5}{3}+\dfrac{2}{3}+\dfrac{1}{3}\right)-\dfrac{7}{12}\)
\(=\dfrac{8}{3}-\dfrac{7}{12}=\dfrac{32}{12}-\dfrac{7}{12}=\dfrac{25}{12}\)
