a: \(-51+24:\left(-4\right)-37\cdot\left(-2\right)^2\)
=-51-6-37*4
=-57-148
=-205
b: \(\dfrac{19}{12}-\dfrac{7}{22}:\dfrac{21}{11}\)
\(=\dfrac{19}{12}-\dfrac{7}{22}\cdot\dfrac{11}{21}\)
\(=\dfrac{19}{12}-\dfrac{1}{6}=\dfrac{19}{12}-\dfrac{2}{12}=\dfrac{17}{12}\)
c: \(\dfrac{1}{5}\cdot\dfrac{11}{16}+\dfrac{1}{5}\cdot\dfrac{5}{16}+\dfrac{4}{5}\)
\(=\dfrac{1}{5}\left(\dfrac{11}{16}+\dfrac{5}{16}\right)+\dfrac{4}{5}\)
\(=\dfrac{1}{5}+\dfrac{4}{5}=1\)
d: \(\dfrac{5}{9}\cdot\dfrac{7}{13}-\dfrac{5}{9}\cdot\dfrac{9}{13}+\dfrac{5}{13}\cdot\dfrac{35}{9}\)
\(=\dfrac{5}{9}\cdot\dfrac{7}{13}-\dfrac{5}{9}\cdot\dfrac{9}{13}+\dfrac{5}{9}\cdot\dfrac{35}{13}\)
\(=\dfrac{5}{9}\left(\dfrac{7}{13}-\dfrac{9}{13}+\dfrac{35}{13}\right)=\dfrac{5}{9}\cdot\dfrac{33}{13}=\dfrac{5\cdot11}{3\cdot13}=\dfrac{55}{39}\)
\(a.-51+24\div\left(-4\right)-37\cdot\left(-2\right)^2\\ =-51-6-37\cdot4\\ =-51-6-148\\ =-57-148\\ =-205\\ b.\dfrac{19}{12}-\dfrac{7}{22}\div\dfrac{21}{11}\\ =\dfrac{19}{12}-\dfrac{1}{6}\\ =\dfrac{19}{12}-\dfrac{2}{12}\\ =\dfrac{17}{12}\\ c.\dfrac{1}{5}\cdot\dfrac{11}{16}+\dfrac{1}{5}\cdot\dfrac{5}{16}+\dfrac{4}{5}\\ =\dfrac{1}{5}\left(\dfrac{11}{16}+\dfrac{5}{16}\right)+\dfrac{4}{5}\\ =\dfrac{1}{5}\cdot1+\dfrac{4}{5}\\ =1\\ d.\dfrac{5}{9}\cdot\dfrac{7}{13}-\dfrac{5}{9}\cdot\dfrac{9}{13}+\dfrac{5}{13}\cdot\dfrac{35}{9}\\ =\dfrac{5}{9}\cdot\dfrac{7}{13}-\dfrac{5}{9}\cdot\dfrac{9}{13}+\dfrac{5}{9}\cdot\dfrac{35}{13}\\ =\dfrac{5}{9}\left(\dfrac{7}{13}-\dfrac{9}{13}+\dfrac{35}{13}\right)\\ =\dfrac{5}{9}\cdot\dfrac{33}{13}\\ =\dfrac{55}{39}\)
