a: \(-\dfrac{3}{4}\cdot31\dfrac{11}{23}-0,75\cdot8\dfrac{12}{23}\)
\(=-\dfrac{3}{4}\left(31+\dfrac{11}{23}+8+\dfrac{12}{23}\right)\)
\(=-\dfrac{3}{4}\cdot\left(39+1\right)=-\dfrac{3}{4}\cdot40=-30\)
b: \(\left(2\dfrac{1}{3}+3\dfrac{1}{2}\right):\left(-4\dfrac{1}{6}+3\dfrac{1}{7}\right)+7\dfrac{1}{2}\)
\(=\left(\dfrac{7}{3}+\dfrac{7}{2}\right):\left(-\dfrac{25}{6}+\dfrac{22}{7}\right)+7\dfrac{1}{2}\)
\(=\dfrac{35}{6}:\dfrac{-25\cdot7+22\cdot6}{42}+\dfrac{15}{2}\)
\(=\dfrac{35}{6}\cdot\dfrac{42}{-175+132}+\dfrac{15}{2}\)
\(=\dfrac{35\cdot7}{-43}+\dfrac{15}{2}=\dfrac{155}{86}\)
c: \(4\dfrac{5}{9}:\dfrac{-5}{7}+\left(5\dfrac{4}{9}\right):\dfrac{-5}{7}\)
\(=\dfrac{41}{9}\cdot\dfrac{-7}{5}+\dfrac{49}{9}\cdot\dfrac{-7}{5}\)
\(=-\dfrac{7}{5}\left(\dfrac{41}{9}+\dfrac{49}{9}\right)\)
\(=-\dfrac{7}{5}\cdot10=-14\)
d: \(\dfrac{\left(13\dfrac{1}{4}-2\dfrac{5}{27}-10\dfrac{5}{6}\right)\cdot230\dfrac{1}{25}+46\dfrac{3}{4}}{\left(1\dfrac{3}{7}+\dfrac{10}{3}\right):\left(12\dfrac{1}{3}-14\dfrac{2}{7}\right)}\)
\(=\dfrac{\left(13+\dfrac{1}{4}-2-\dfrac{5}{27}-10-\dfrac{5}{6}\right)\cdot230,04+46,75}{\left(\dfrac{10}{7}+\dfrac{10}{3}\right):\left(12+\dfrac{1}{3}-14-\dfrac{2}{7}\right)}\)
\(=\dfrac{\left(1-\dfrac{83}{108}\right)\cdot230,04+46,75}{\dfrac{100}{21}:\left(-2+\dfrac{7-6}{21}\right)}\)
\(=\dfrac{\dfrac{25}{108}\cdot230,04+46,75}{\dfrac{100}{21}:\dfrac{-42+1}{21}}\)
\(=\dfrac{100}{\dfrac{100}{21}\cdot\dfrac{21}{-41}}=100:\dfrac{100}{-41}=-41\)
