1: \(-\dfrac{4}{3}+\dfrac{1}{3}:\left(-1,5\right)\)
\(=-\dfrac{4}{3}+\dfrac{1}{3}:\dfrac{-3}{2}\)
\(=-\dfrac{4}{3}+\dfrac{-2}{9}=\dfrac{-12}{9}-\dfrac{2}{9}=-\dfrac{14}{9}\)
2: \(-\dfrac{5}{3}+\dfrac{2}{3}:\left(-1,5\right)\)
\(=-\dfrac{5}{3}+\dfrac{2}{3}:\dfrac{-3}{2}\)
\(=-\dfrac{5}{3}+\dfrac{2}{3}\cdot\dfrac{-2}{3}=-\dfrac{5}{3}-\dfrac{4}{9}=\dfrac{-15}{9}-\dfrac{4}{9}=-\dfrac{19}{9}\)
3: \(\sqrt{\dfrac{4}{9}}-\dfrac{1}{2}:\left|-\dfrac{2}{3}\right|\)
\(=\dfrac{2}{3}-\dfrac{1}{2}:\dfrac{2}{3}\)
\(=\dfrac{2}{3}-\dfrac{1}{2}\cdot\dfrac{3}{2}=\dfrac{2}{3}-\dfrac{3}{4}=\dfrac{8}{12}-\dfrac{9}{12}=-\dfrac{1}{12}\)
4: \(\left(40\%-1\dfrac{2}{3}\right):\dfrac{-3}{2}+\left(-\dfrac{1}{2}\right)^2\)
\(=\left(\dfrac{2}{5}-\dfrac{5}{3}\right)\cdot\dfrac{-2}{3}+\dfrac{1}{4}\)
\(=\left(\dfrac{6}{15}-\dfrac{25}{15}\right)\cdot\dfrac{-2}{3}+\dfrac{1}{4}\)
\(=\dfrac{-19}{15}\cdot\dfrac{-2}{3}+\dfrac{1}{4}=\dfrac{38}{45}+\dfrac{1}{4}=\dfrac{197}{180}\)
5: \(\dfrac{5}{14}-3,7-\dfrac{19}{14}+\dfrac{8}{9}-6,3\)
\(=\left(\dfrac{5}{14}-\dfrac{19}{14}\right)+\left(-3,7-6,3\right)+\dfrac{8}{9}\)
\(=-\dfrac{14}{14}-10+\dfrac{8}{9}\)
\(=-11+\dfrac{8}{9}=\dfrac{-91}{9}\)
6: \(-3-\dfrac{16}{23}-\sqrt{\dfrac{4}{49}}-\dfrac{7}{23}+\dfrac{\left(-3\right)^2}{7}\)
\(=-3-\left(\dfrac{16}{23}+\dfrac{7}{23}\right)-\dfrac{4}{7}+\dfrac{9}{7}\)
\(=-3-1+\dfrac{5}{7}=-4+\dfrac{5}{7}=\dfrac{-23}{7}\)
7: \(-\left(\dfrac{8}{9}+\dfrac{7}{5}-\dfrac{2}{11}\right)+\left(-\dfrac{2}{5}+\dfrac{17}{9}-\dfrac{13}{11}\right)\)
\(=-\dfrac{8}{9}-\dfrac{7}{5}+\dfrac{2}{11}-\dfrac{2}{5}+\dfrac{17}{9}-\dfrac{13}{11}\)
\(=\left(-\dfrac{8}{9}+\dfrac{17}{9}\right)+\left(-\dfrac{7}{5}-\dfrac{2}{5}\right)+\left(\dfrac{2}{11}-\dfrac{13}{11}\right)\)
\(=\dfrac{9}{9}-\dfrac{9}{5}-\dfrac{11}{11}=-\dfrac{9}{5}\)
8: \(\dfrac{1}{7}\cdot\dfrac{3}{8}+\dfrac{1}{7}\cdot\dfrac{5}{8}+\dfrac{\left(-1\right)^{2019}}{7}\)
\(=\dfrac{1}{7}\left(\dfrac{3}{8}+\dfrac{5}{8}\right)+\dfrac{-1}{7}\)
\(=\dfrac{1}{7}-\dfrac{1}{7}\)
=0
9: \(\dfrac{4}{5}\cdot\dfrac{3}{7}-\dfrac{-4}{7}:\sqrt{\dfrac{25}{16}}-\left|-1\right|\)
\(=\dfrac{4}{7}\cdot\dfrac{3}{5}+\dfrac{4}{7}:\dfrac{5}{4}-1\)
\(=\dfrac{4}{7}\left(\dfrac{3}{5}+\dfrac{4}{5}\right)-1=\dfrac{4}{7}\cdot\dfrac{7}{5}-1=\dfrac{4}{5}-1=-\dfrac{1}{5}\)
10: \(\left|1,37\right|\cdot\dfrac{2}{9}-7,37\cdot\left|-\dfrac{2}{9}\right|\)
\(=1,37\cdot\dfrac{2}{9}-7,37\cdot\dfrac{2}{9}\)
\(=\dfrac{2}{9}\left(1,37-7,37\right)=\dfrac{2}{9}\cdot\left(-6\right)=-\dfrac{12}{9}=-\dfrac{4}{3}\)
11: \(\left(-\dfrac{2}{3}\right)^2\cdot\dfrac{5}{13}-\dfrac{8}{13}:\dfrac{-9}{4}-\dfrac{1}{2}\)
\(=\dfrac{4}{9}\cdot\dfrac{5}{13}+\dfrac{8}{13}\cdot\dfrac{4}{9}-\dfrac{1}{2}\)
\(=\dfrac{4}{9}\left(\dfrac{5}{13}+\dfrac{8}{13}\right)-\dfrac{1}{2}=\dfrac{4}{9}-\dfrac{1}{2}=\dfrac{-1}{18}\)
12: \(\left(\dfrac{4}{9}\right)^{11}\cdot\left(\dfrac{2}{3}\right)^{12}:\left(\dfrac{8}{27}\right)^{10}\)
\(=\left(\dfrac{2}{3}\right)^{22}\cdot\left(\dfrac{2}{3}\right)^{12}:\left(\dfrac{2}{3}\right)^{30}\)
\(=\left(\dfrac{2}{3}\right)^{22+12-30}=\left(\dfrac{2}{3}\right)^4=\dfrac{16}{81}\)
13: \(\left(\dfrac{1}{4}\right)^5\cdot\left(\dfrac{1}{8}\right)^6:\left(\dfrac{1}{2}\right)^{26}\)
\(=\left(\dfrac{1}{2}\right)^{10}\cdot\left(\dfrac{1}{2}\right)^{18}:\left(\dfrac{1}{2}\right)^{26}\)
\(=\left(\dfrac{1}{2}\right)^{10+18-26}=\left(\dfrac{1}{2}\right)^2=\dfrac{1}{4}\)
14: \(\dfrac{\dfrac{2}{7}+\dfrac{2}{5}+\dfrac{2}{17}-\dfrac{2}{25}}{\dfrac{3}{14}+\dfrac{3}{10}+\dfrac{3}{34}-\dfrac{3}{50}}\)
\(=\dfrac{2\left(\dfrac{1}{7}+\dfrac{1}{5}+\dfrac{1}{17}-\dfrac{1}{25}\right)}{\dfrac{3}{2}\left(\dfrac{1}{7}+\dfrac{1}{5}+\dfrac{1}{17}-\dfrac{1}{25}\right)}=2:\dfrac{3}{2}=\dfrac{4}{3}\)
