$\text{a)}54:\left(4\frac{1}{2}\cdot 1\frac{1}{2}\right)-2\frac{7}{8}=54:\left(\frac{9}{2}\cdot \frac{3}{2}\right)-2\frac{7}{8}=54:\frac{27}{4}-2\frac{7}{8}={\sout{54}}^2\cdot \frac{4}{{\sout{27}}^1}-2\frac{7}{8}=$

$=2\cdot \frac{4}{1}-2\frac{7}{8}=\frac{8}{1}-2\frac{7}{8}=8-2\frac{7}{8}=7\frac{8}{8}-2\frac{7}{8}=5\frac{1}{8}$  

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$\text{b)}\left(8-1\frac{3}{7}\cdot 4\frac{2}{3}\right):1\frac{1}{6}=\left(8-\frac{10}{{\sout{7}}^1}\cdot \frac{{\sout{14}}^2}{3}\right):\frac{7}{6}=\left(8-\frac{10}{1}\cdot \frac{2}{3}\right)\cdot \frac{6}{7}=\left(8-\frac{20}{3}\right)\cdot \frac{6}{7}=$

$=\left(8-6\frac{2}{3}\right)\cdot \frac{6}{7}=\left(7\frac{3}{3}-6\frac{2}{3}\right)\cdot \frac{6}{7}=1\frac{1}{3}\cdot \frac{6}{7}=\frac{4}{{\sout{3}}^1}\cdot \frac{{\sout{6}}^2}{7}=\frac{4}{1}\cdot \frac{2}{7}=\frac{8}{7}=1\frac{1}{7}$