1A.
\(a.-\dfrac{3}{4}\cdot31\dfrac{11}{23}-\dfrac{3}{4}\cdot8\dfrac{12}{23}\\
=-\dfrac{3}{4}\cdot\left(31\dfrac{11}{23}+8\dfrac{12}{23}\right)\\
=-\dfrac{3}{4}\cdot\left(31+\dfrac{11}{23}+8+\dfrac{12}{23}\right)\\
=-\dfrac{3}{4}\cdot\left(39+1\right)\\
=-\dfrac{3}{4}\cdot40\\
=-30\\
b.4\dfrac{5}{9}:\left(\dfrac{-5}{7}\right)+5\dfrac{4}{9}:\left(\dfrac{-5}{7}\right)\\
=4\dfrac{5}{9}\cdot\left(\dfrac{-7}{5}\right)+5\dfrac{4}{9}\cdot\left(\dfrac{-7}{5}\right)\\
=\left(\dfrac{-7}{5}\right)\left(4\dfrac{5}{9}+5\dfrac{4}{9}\right)\\
=\left(\dfrac{-7}{5}\right)\left(4+\dfrac{5}{9}+5+\dfrac{4}{9}\right)\\
=\left(\dfrac{-7}{5}\right)\cdot\left(9+1\right)\\
=\left(\dfrac{-7}{5}\right)\cdot10\\
=-14\)
1B:
a: \(4+375\left(\dfrac{9}{16}:\dfrac{125}{64}:\dfrac{-27}{8}\right)\)
\(=4+375\cdot\left(\dfrac{9}{16}\cdot\dfrac{64}{125}\cdot\dfrac{-8}{27}\right)\)
\(=4+375\cdot\left(\dfrac{9}{27}\cdot\dfrac{-8}{16}\cdot\dfrac{64}{125}\right)\)
\(=4+375\cdot\left(\dfrac{1}{3}\cdot\dfrac{-1}{2}\cdot\dfrac{64}{125}\right)\)
\(=4+375\cdot\dfrac{-64}{750}=4-32=-28\)
b: \(\dfrac{2}{3}-4\left(\dfrac{1}{2}+\dfrac{3}{4}\right)\)
\(=\dfrac{2}{3}-4\cdot\left(\dfrac{2}{4}+\dfrac{3}{4}\right)\)
\(=\dfrac{2}{3}-4\cdot\dfrac{5}{4}=\dfrac{2}{3}-5=-\dfrac{13}{3}\)
c: \(\left(\dfrac{12}{35}-\dfrac{6}{7}+\dfrac{18}{14}\right):\dfrac{6}{-7}-\dfrac{-2}{5}\)
\(=\left(\dfrac{12}{35}-\dfrac{6}{7}+\dfrac{9}{7}\right)\cdot\dfrac{-7}{6}+\dfrac{2}{5}\)
\(=\left(\dfrac{12}{35}+\dfrac{15}{35}\right)\cdot\dfrac{-7}{6}+\dfrac{2}{5}\)
\(=\dfrac{27}{35}\cdot\dfrac{-7}{6}+\dfrac{2}{5}=\dfrac{9}{2}\cdot\dfrac{-1}{5}+\dfrac{2}{5}=-\dfrac{9}{10}+\dfrac{2}{5}\)
\(=-\dfrac{9}{10}+\dfrac{4}{10}=-\dfrac{5}{10}=-\dfrac{1}{2}\)
d: \(\left[-\dfrac{54}{64}-\left(\dfrac{1}{9}:\dfrac{8}{27}\right):\dfrac{-1}{3}\right]:\dfrac{-81}{128}\)
\(=\left(-\dfrac{27}{32}-\dfrac{1}{9}\cdot\dfrac{27}{8}\cdot\left(-3\right)\right)\cdot\dfrac{128}{-81}\)
\(=\left(-\dfrac{27}{32}+\dfrac{9}{8}\right)\cdot\dfrac{-128}{81}=\dfrac{9}{32}\cdot\dfrac{-128}{81}=\dfrac{-4}{9}\)
