1: \(C=\dfrac{5}{18}+\dfrac{8}{19}-\dfrac{7}{21}+\left(-\dfrac{10}{36}+\dfrac{11}{19}+\dfrac{1}{3}\right)-\dfrac{5}{8}\)
\(=\dfrac{5}{18}+\dfrac{8}{19}-\dfrac{1}{3}-\dfrac{5}{18}+\dfrac{11}{19}+\dfrac{1}{3}-\dfrac{5}{8}\)
\(=\left(\dfrac{5}{18}-\dfrac{5}{18}\right)+\left(\dfrac{8}{19}+\dfrac{11}{19}\right)+\left(-\dfrac{1}{3}+\dfrac{1}{3}\right)-\dfrac{5}{8}\)
\(=1-\dfrac{5}{8}=\dfrac{3}{8}\)
2: \(E=\dfrac{1}{13}+\left(-\dfrac{5}{18}-\dfrac{1}{13}+\dfrac{12}{17}\right)-\left(\dfrac{12}{17}-\dfrac{5}{18}+\dfrac{7}{5}\right)\)
\(=\dfrac{1}{13}+\dfrac{-5}{18}-\dfrac{1}{13}+\dfrac{12}{17}-\dfrac{12}{17}+\dfrac{5}{18}-\dfrac{7}{5}\)
\(=\left(\dfrac{1}{13}-\dfrac{1}{13}\right)+\left(-\dfrac{5}{18}+\dfrac{5}{18}\right)+\left(\dfrac{12}{17}-\dfrac{12}{17}\right)-\dfrac{7}{5}\)
\(=-\dfrac{7}{5}\)
3: \(F=\dfrac{15}{14}-\left(\dfrac{17}{23}-\dfrac{80}{87}+\dfrac{5}{4}\right)+\left(\dfrac{17}{23}-\dfrac{15}{14}+\dfrac{1}{4}\right)\)
\(=\dfrac{15}{14}-\dfrac{17}{23}+\dfrac{80}{87}-\dfrac{5}{4}+\dfrac{17}{23}-\dfrac{15}{14}+\dfrac{1}{4}\)
\(=\left(\dfrac{15}{14}-\dfrac{15}{14}\right)+\left(-\dfrac{17}{23}+\dfrac{17}{23}\right)+\dfrac{80}{87}-1\)
\(=\dfrac{80}{87}-1=-\dfrac{7}{87}\)
4: \(G=\dfrac{1}{25}-\dfrac{4}{27}+\left(-\dfrac{23}{27}+\dfrac{-1}{25}-\dfrac{5}{43}\right)+\dfrac{5}{43}-\dfrac{4}{7}\)
\(=\dfrac{1}{25}-\dfrac{4}{27}-\dfrac{23}{27}-\dfrac{1}{25}-\dfrac{5}{43}+\dfrac{5}{43}-\dfrac{4}{7}\)
\(=\left(\dfrac{1}{25}-\dfrac{1}{25}\right)+\left(-\dfrac{4}{27}-\dfrac{23}{27}\right)+\left(-\dfrac{5}{43}+\dfrac{5}{43}\right)-\dfrac{4}{7}\)
\(=-1-\dfrac{4}{7}=-\dfrac{11}{7}\)
5: \(H=\dfrac{4}{15}-\dfrac{23}{28}\left(-\dfrac{23}{28}+\dfrac{-11}{15}-\dfrac{29}{27}\right)-\dfrac{2}{27}\)
\(=\dfrac{4}{15}-\dfrac{23}{28}\cdot\left(-\dfrac{23}{28}+\dfrac{-99}{135}-\dfrac{145}{135}\right)-\dfrac{2}{27}\)
\(=\dfrac{4}{15}-\dfrac{2}{27}+\dfrac{23}{28}\cdot\dfrac{23}{28}+\dfrac{23}{28}\cdot\dfrac{244}{135}\)
\(=\dfrac{26}{135}+\dfrac{529}{784}+\dfrac{1403}{945}=\dfrac{1585}{945}+\dfrac{529}{784}\)
\(=\dfrac{317}{189}+\dfrac{529}{784}=\dfrac{317\cdot784+529\cdot189}{189\cdot784}\)
\(=\dfrac{348509}{148176}\)
6: \(K=\dfrac{1}{16}-\dfrac{5}{21}+\left(-\dfrac{1}{16}+\dfrac{-3}{5}-\dfrac{-5}{21}\right)+\dfrac{-2}{5}+\dfrac{3}{4}\)
\(=\dfrac{1}{16}-\dfrac{5}{21}-\dfrac{1}{16}-\dfrac{3}{5}+\dfrac{5}{21}+\dfrac{-2}{5}+\dfrac{3}{4}\)
\(=-\dfrac{3}{5}-\dfrac{2}{5}+\dfrac{3}{4}=-1+\dfrac{3}{4}=-\dfrac{1}{4}\)
