$a)5\frac{1}{2}\cdot {\left(1,5\right)}^2-4\frac{5}{7}:1\frac{1}{21}=5\frac{1}{2}\cdot {\left(1\frac{1}{2}\right)}^2-\frac{33}{7}:\frac{22}{21}=5\frac{1}{2}\cdot {\left(\frac{3}{2}\right)}^2-\frac{{\sout{33}}^3}{7}\cdot \frac{21}{{\sout{22}}^2}=$

$=\frac{11}{2}\cdot \frac{9}{4}-\frac{3}{{\sout{7}}^1}\cdot \frac{{\sout{21}}^3}{2}=\frac{99}{8}-\frac{9}{2}=\frac{99}{8}-\frac{36}{8}=\frac{63}{8}=7\frac{7}{8}$

$b)\left(3\frac{3}{4}\cdot \frac{4}{5}-4,5:3,5\right):24=\left(\frac{{\sout{15}}^3}{4}\cdot \frac{4}{{\sout{5}}^1}-45:35\right):24=\left(\frac{12}{4}-\frac{45}{35}\right)\cdot \frac{1}{24}=$ $b)\left(3\frac{3}{4}\cdot \frac{4}{5}-4,5:3,5\right):24=\left(\frac{{\sout{15}}^3}{4}\cdot \frac{4}{{\sout{5}}^1}-45:35\right):24=\left(\frac{12}{4}-\frac{45}{35}\right)\cdot \frac{1}{24}=$

$=\left(3-\frac{9}{7}\right)\cdot \frac{1}{24}=\left(3-1\frac{2}{7}\right)\cdot \frac{1}{24}=1\frac{5}{7}\cdot \frac{1}{24}=\frac{{\sout{12}}^1}{7}\cdot \frac{1}{{\sout{24}}^2}=\frac{1}{14}$

$c)11\frac{1}{4}\cdot \left(1\frac{2}{3}-1\frac{19}{21}\cdot 0,7\right)=\frac{45}{4}\cdot \left(1\frac{2}{3}-\frac{40}{{\sout{21}}^3}\cdot \frac{{\sout{7}}^1}{10}\right)=\frac{45}{4}\cdot \left(\frac{5}{3}-\frac{40}{30}\right)=$

$=\frac{45}{4}\cdot \left(\frac{5}{3}-\frac{4}{3}\right)=\frac{{\sout{45}}^{15}}{4}\cdot \frac{1}{{\sout{3}}^1}=\frac{15}{4}=3\frac{3}{4}$

$d)\left(2\frac{1}{3}-1,6\right):\left(1,25\cdot 0,88\right)=\left(2\frac{1}{3}-1\frac{6}{10}\right):\left(1\frac{25}{100}\cdot \frac{88}{100}\right)=$

$=\left(2\frac{5}{15}-1\frac{3}{5}\right):\left(1\frac{1}{4}\cdot \frac{22}{25}\right)=\left(1\frac{20}{15}-1\frac{9}{15}\right):\left(\frac{{\sout{5}}^1}{4}\cdot \frac{22}{{\sout{25}}^5}\right)=$

$=\frac{11}{15}:\frac{22}{20}=\frac{11}{15}:\frac{11}{10}=\frac{{\sout{11}}^1}{15}\cdot \frac{10}{{\sout{11}}^1}=\frac{10}{15}=\frac{2}{3}$

$e)\frac{3\frac{1}{3}+1,25}{3\frac{1}{3}-1,25}=\frac{3\frac{1}{3}+1\frac{1}{4}}{3\frac{1}{3}-1\frac{1}{4}}=\frac{3\frac{4}{12}+1\frac{3}{12}}{3\frac{4}{12}-1\frac{3}{12}}=\frac{4\frac{7}{12}}{2\frac{1}{12}}=\frac{\frac{55}{12}}{\frac{25}{12}}=\frac{55}{12}:\frac{25}{12}=\frac{55}{{\sout{12}}^1}\cdot \frac{{\sout{12}}^1}{25}=\frac{55}{25}=\frac{11}{5}=2\frac{1}{5}$

$f)1+\frac{4\frac{2}{5}}{2\frac{3}{4}}-\frac{2\frac{3}{4}}{4\frac{2}{5}}=1+\frac{\frac{22}{5}}{\frac{11}{4}}-\frac{\frac{11}{4}}{\frac{22}{5}}=1+\frac{22}{5}:\frac{11}{4}-\frac{11}{4}:\frac{22}{5}=1+\frac{{\sout{22}}^2}{5}\cdot \frac{4}{{\sout{11}}^1}-\frac{{\sout{11}}^1}{4}\cdot \frac{5}{{\sout{22}}^2}=$

$=1+\frac{8}{5}-\frac{5}{8}=1+1\frac{3}{5}-\frac{5}{8}=2\frac{3}{5}-\frac{5}{8}=2\frac{24}{40}-\frac{25}{40}=1\frac{64}{40}-\frac{25}{40}=1\frac{39}{40}$