$\text{a)}2\frac{1}{4}+3\frac{2}{3}=2\frac{3}{12}+3\frac{8}{12}=5\frac{11}{12}$  

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$\text{b)}3\frac{3}{5}-4\frac{3}{4}=3\frac{12}{20}-3\frac{15}{20}=-1\frac{3}{20}$  

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$\text{c)}2\frac{2}{5}\cdot 4\frac{1}{3}=\frac{{\cancel{12}}^4}{5}\cdot \frac{13}{{\cancel{3}}_1}=\frac{4}{5}\cdot 13=\frac{52}{5}=10\frac{2}{5}$  

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$\text{d)}\left(-3\frac{1}{3}\right):\frac{10}{27}=-\frac{{\cancel{10}}^1}{3}\cdot \frac{27}{{\cancel{10}}_1}=-\frac{27}{3}=-9$