$ \left(\frac{1}{4}+\frac{5}{6}\right)\left(\frac{5}{13}-\frac{1}{2}\right)$
$=\frac{3+10}{12}\cdot\frac{10-13}{26}=\frac{13}{12}\cdot\left(-\frac{3}{26}\right)=-\frac{39}{312}=-\frac{1}{8} $
$ \frac{\frac{6}{5}}{\frac{7}{6}\cdot 4-4\cdot\frac{5}{12}}$
$=\frac{\frac{6}{5}}{\frac{28}{6}-\frac{20}{12}}=\frac{\frac{6}{5}}{\frac{14}{3}-\frac{5}{3}}=\frac{\frac{6}{5}}{3}=\frac{6}{5}\cdot\frac{1}{3}=\frac{2}{5} $
$ \frac{\frac{5}{2}-\frac{2}{5}}{(-7)^2}$
$=\frac{\frac{25-4}{10}}{49}=\frac{\frac{21}{10}}{49}=\frac{21}{10}\cdot\frac{1}{49}=\frac{3}{70} $
$ \frac{5}{3}\cdot\frac{9}{50}\cdot\left(1-\frac{4}{9}\right)-\frac{2}{3}$
$=\frac{5}{3}\cdot\frac{9}{50}\cdot\frac{5}{9}-\frac{2}{3}=\frac{25}{150}-\frac{2}{3}=\frac{1}{6}-\frac{2}{3}=-\frac{1}{2} $
$ \frac{\frac{1}{4}+\frac{2}{3}}{\left(3-\frac{9}{4}\right)\cdot\frac{8}{3}}$
$=\frac{\frac{3+8}{12}}{\frac{12-9}{4}\cdot\frac{8}{3}}=\frac{\frac{11}{12}}{\frac{3}{4}\cdot\frac{8}{3}}=\frac{\frac{11}{12}}{2}=\frac{11}{24} $
$ 3:\frac{2\cdot 6}{2+6}-\frac{12}{3}\cdot\frac{5}{8}$
$=3:\frac{12}{8}-4\cdot\frac{5}{8}=3:\frac{3}{2}-\frac{20}{8}=3\cdot\frac{2}{3}-\frac{5}{2}=2-\frac{5}{2}=-\frac{1}{2} $
$ (6-4)\cdot\frac{11}{8}+\frac{9}{14}\cdot\frac{7}{6}$
$=2\cdot\frac{11}{8}+\frac{63}{84}=\frac{11}{4}+\frac{3}{4}=\frac{14}{4}=\frac{7}{2} $
$ \frac{\frac{2\cdot 3}{6}-\frac{4}{2\cdot 3}}{\frac{2+3}{6}}$
$=\frac{1-\frac{4}{6}}{\frac{5}{6}}=\frac{\frac{1}{3}}{\frac{5}{6}}=\frac{1}{3}\cdot\frac{6}{5}=\frac{2}{5} $
$ \frac{1-\frac{1}{3}}{-6^{2}}=\frac{\frac{2}{3}}{-36}$
$=\frac{2}{3}\cdot\left(-\frac{1}{36}\right)=-\frac{2}{108}=-\frac{1}{54} $
$ 12\cdot\left(\frac{2}{3}-\frac{1}{2}\right)-\frac{5}{2}+\frac{2}{3}$
$=12\cdot\frac{1}{6}-\frac{5}{2}+\frac{2}{3}=2-\frac{5}{2}+\frac{2}{3}=-\frac{1}{2}+\frac{2}{3}=\frac{1}{6} $
$ 2-2\cdot\frac{2\cdot\frac{9}{10}}{3}$
$=2-2\cdot\frac{9}{5}\cdot\frac{1}{3}=2-\frac{18}{15}=2-\frac{6}{5}=\frac{4}{5} $
$ \frac{3^{2}}{5}-\frac{3}{5^{2}}+\left(-\frac{3}{5}\right)^{2}$
$=\frac{9}{5}-\frac{3}{25}+\frac{9}{25}=\frac{45}{25}+\frac{6}{25}=\frac{51}{25} $
$ \frac{\frac{4}{1+2}-1}{1+2}$
$=\frac{\frac{4}{3}-1}{3}=\frac{\frac{1}{3}}{3}=\frac{1}{9} $
$ \left(2-\frac{7}{8}\right)\cdot\frac{8}{9}:\left(\frac{5}{8}+\frac{5}{6}\right)$
$=\frac{9}{8}\cdot\frac{8}{9}:\frac{35}{24}=1:\frac{35}{24}=\frac{24}{35} $
$ \left(0,5+\frac{2}{5}\right):\left(2-\frac{7}{8}\right)$
$=\left(\frac{1}{2}+\frac{2}{5}\right):\frac{9}{8}=\frac{9}{10}:\frac{9}{8}=\frac{9}{10}\cdot\frac{8}{9}=\frac{4}{5} $
$ \frac{3\cdot\frac{2}{9}-\frac{3}{5}:\frac{6}{15}}{2}$
$=\frac{\frac{2}{3}-\frac{3}{5}\cdot\frac{15}{6}}{2}=\frac{\frac{2}{3}-\frac{3}{2}}{2}=\frac{-\frac{5}{6}}{2}=-\frac{5}{12} $
$ \frac{7}{12}-\frac{5}{8}\cdot 1{,}6$
$=\frac{7}{12}-\frac{5}{8}\cdot\frac{8}{5}=\frac{7}{12}-1=-\frac{5}{12} $
$ \frac{2\frac{2}{3}-1\frac{3}{5}}{2\frac{2}{3}}$
$=\frac{\frac{8}{3}-\frac{8}{5}}{\frac{8}{3}}=\frac{\frac{40-24}{15}}{\frac{8}{3}}=\frac{\frac{16}{15}}{\frac{8}{3}}=\frac{16}{15}\cdot\frac{3}{8}=\frac{2}{5} $
$ 2-\frac{1}{3}-\frac{1}{6}\cdot\frac{16}{3}$
$=2-\frac{1}{3}-\frac{16}{18}=2-\frac{1}{3}-\frac{8}{9}=\frac{6}{3}-\frac{1}{3}-\frac{8}{9}=\frac{5}{3}-\frac{8}{9}=\frac{7}{9} $
$ \frac{\frac{7}{10}-\frac{2}{5}:\frac{1}{10}}{20\cdot\frac{3}{10}}$
$=\frac{\frac{7}{10}-4}{6}=\frac{-\frac{33}{10}}{6}=-\frac{33}{60}=-\frac{11}{20} $
$ 3\cdot\frac{2}{15}+\frac{1}{3}\cdot\frac{2}{15}$
$=\frac{6}{15}+\frac{2}{45}=\frac{18}{45}+\frac{2}{45}=\frac{20}{45}=\frac{4}{9} $
$ \frac{\frac{2}{3}-\frac{5}{6}}{\frac{2}{3}}$
$=\frac{-\frac{1}{6}}{\frac{2}{3}}=-\frac{1}{6}\cdot\frac{3}{2}=-\frac{1}{4} $
$ \frac{2-\frac{3}{5}\cdot\frac{5}{2}}{2}$
$=\frac{2-\frac{3}{2}}{2}=\frac{\frac{1}{2}}{2}=\frac{1}{4} $
$ \frac{3}{4}:\frac{15}{2}-\left(\frac{3}{5}\right)^{2}$
$=\frac{3}{4}\cdot\frac{2}{15}-\frac{9}{25}=\frac{6}{60}-\frac{9}{25}=\frac{1}{10}-\frac{18}{50}=-\frac{13}{50} $
$ \left(\frac{2}{3}\right)^{2}$
$=\frac{2}{3}\cdot\square \;\;\Rightarrow\;\; \square=\frac{2}{3} $
$ \left(\frac{1}{3}\right)^{2}-\sqrt{\frac{4}{9}}$
$=\frac{1}{9}-\frac{2}{3}=-\frac{5}{9} $
$ \left(\frac{2}{4}\right)^{2}+\square$
$=\frac{5}{8}\;\;\Rightarrow\;\;\square=\frac{5}{8}-\frac{1}{4}=\frac{5}{8}-\frac{2}{8}=\frac{3}{8} $
$ \frac{1}{6}+\frac{2}{3}\cdot\frac{9}{8}$
$=\frac{1}{6}+\frac{18}{24}=\frac{1}{6}+\frac{3}{4}=\frac{2}{12}+\frac{9}{12}=\frac{11}{12} $
$ \frac{2}{3}:\frac{5}{2}-\frac{2}{3}$
$=\frac{2}{3}\cdot\frac{2}{5}-\frac{2}{3}=\frac{4}{15}-\frac{10}{15}=-\frac{2}{5} $
$ \frac{\tfrac{\sqrt{25}}{\sqrt{2}\cdot 2}}{\tfrac{3\cdot(3^{2}-2\cdot 2)}{\sqrt{5^{2}-4^{2}}}}$
$=\frac{\tfrac{5}{2\sqrt{2}}}{\tfrac{3\cdot(9-4)}{\sqrt{25-16}}}=\frac{\tfrac{5}{2\sqrt{2}}}{\tfrac{3\cdot 5}{\sqrt{9}}}=\frac{\tfrac{5}{2\sqrt{2}}}{\tfrac{15}{3}}=\frac{\tfrac{5}{2\sqrt{2}}}{5}=\frac{5}{2\sqrt{2}}\cdot\frac{1}{5}=\frac{1}{2\sqrt{2}}=\frac{\sqrt{2}}{4} $