a)

$\frac{\left(-\frac{1}{2}\right)+\frac{2}{3}\left[\frac{3}{5}-\left(-0,45\right)\right]}{\left[1,35-\left(-1\frac{2}{5}\right)\right]:2\frac{3}{4}}=\frac{\left(-\frac{1}{2}\right)+\frac{2}{3}\cdot (0,6+0,45)}{(1,35+1,4):\frac{11}{4}}=\frac{\left(-\frac{1}{2}\right)+\frac{2}{3}\cdot \frac{105}{100}}{2,75\cdot \frac{4}{11}}=\frac{\left(-\frac{1}{2}\right)+\frac{35}{50}}{\frac{275}{100}\cdot \frac{4}{11}}=\frac{-0,5+0,7}{\frac{{\cancel{275}}^{25}}{{\cancel{100}}^{25}}\cdot \frac{\cancel{4}}{\cancel{11}}}=0,2$

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b)

$\left[\left(-2,25\right)\cdot \left(-6\frac{2}{3}\right)\right]:\left[{\left(-2\right)}^3:1\frac{1}{4}+7\frac{2}{5}+{\left(-\frac{1}{2}\right)}^2\right]=\left[\left(-2\frac{1}{4}\right)\cdot \left(-\frac{20}{3}\right)\right]:\left[\left(-8\right):\frac{5}{4}+\frac{37}{5}+\frac{1}{4}\right]=\left(\left(-\frac{9}{4}\right)\cdot \left(-\frac{20}{3}\right)\right):\left(\left(-8\right)\cdot \frac{4}{5}+\frac{37}{5}+\frac{1}{4}\right)=15:\left(-\frac{32}{5}+\frac{37}{5}+\frac{1}{4}\right)=15:\left(1+\frac{1}{4}\right)=15:\frac{5}{4}=15\cdot \frac{4}{5}=12$

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c)

$\frac{\left(1\frac{3}{4}:\frac{2}{3}-1,75\cdot 1\frac{1}{8}\right):\frac{3}{32}}{1\frac{1}{4}-{\left(-\frac{1}{2}\right)}^2\cdot 3}=\frac{\left(\frac{7}{4}\cdot \frac{3}{2}-\frac{7}{4}\cdot \frac{9}{8}\right)\cdot \frac{32}{3}}{\frac{5}{4}-\frac{1}{4}\cdot 3}=\frac{\left(\frac{21}{8}-\frac{63}{32}\right)\cdot \frac{32}{3}}{\frac{5}{4}-\frac{3}{4}}=\frac{\frac{21}{8}\cdot \frac{32}{3}-\frac{63}{32}\cdot \frac{32}{3}}{\frac{2}{4}}=\frac{\frac{{\cancel{21}}^7}{\cancel{8}}\cdot \frac{{\cancel{32}}^4}{\cancel{3}}-\frac{63}{3}}{\frac{1}{2}}=\frac{7\cdot 4-21}{\frac{1}{2}}=(28-21)\cdot 2=7\cdot 2=14$

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d)

$\frac{{\left(-2\right)}^3:\left[-\frac{2}{3}\cdot {\left(\frac{8}{9}\right)}^{-1}-\frac{3}{8}\cdot \frac{2}{9}\right]}{\frac{5}{4}:2}=\frac{\left(-8\right):\left[-\frac{2}{3}\cdot \frac{9}{8}-\frac{3}{8}\cdot \frac{2}{9}\right]}{\frac{5}{4}\cdot \frac{1}{2}}=\frac{\left(-8\right):\left[-\frac{3}{4}-\frac{1}{12}\right]}{\frac{5}{8}}=\frac{\left(-8\right):\left(-\frac{9}{12}-\frac{1}{12}\right)}{\frac{5}{8}}=\left(\left(-8\right):\left(-\frac{10}{12}\right)\right)\cdot \frac{8}{5}=8\cdot \frac{12}{10}\cdot \frac{8}{5}=\frac{12\cdot 64}{50}=\frac{6\cdot 64}{25}=\frac{384}{25}=15\frac{9}{25}$

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e)

$\frac{\sqrt{5\frac{4}{9}}-{\left(\frac{1}{3}\right)}^{-2}:4,5}{\left(8-3\cdot 2\frac{1}{3}\right)\cdot {\left(\frac{1}{3}\right)}^{-1}}=\frac{\sqrt{\frac{49}{9}}-9\cdot \frac{10}{45}}{\left(8-7\right)\cdot 3}=\frac{\frac{7}{3}-\frac{10}{5}}{3}=\left(\frac{7}{3}-2\right)\cdot \frac{1}{3}=\frac{1}{3}\cdot \frac{1}{3}=\frac{1}{9}$