$a)$  

$1\frac{2}{3}:2\frac{1}{2}+9\cdot 1\frac{1}{6}=$   $\frac{5}{3}:\frac{5}{2}+{\sout{9}}^3\cdot \frac{7}{{\sout{6}}^2}=$   $\frac{{\sout{5}}^1}{3}\cdot \frac{2}{{\sout{5}}^1}+3\cdot \frac{7}{2}=$   $\frac{1}{3}\cdot \frac{2}{1}+\frac{21}{2}=$   $\frac{2}{3}+10\frac{1}{2}=\frac{4}{6}+10\frac{3}{6}=10\frac{7}{6}=10+1\frac{1}{6}=11\frac{1}{6}$  

 

$b)$  

${\left(1\frac{1}{2}\right)}^2-1\frac{3}{5}:2\frac{2}{3}={\left(\frac{3}{2}\right)}^2-\frac{8}{5}:\frac{8}{3}=$   $\frac{3}{2}\cdot \frac{3}{2}-\frac{{\sout{8}}^1}{5}\cdot \frac{3}{{\sout{8}}^1}=$   $\frac{9}{4}-\frac{1}{5}\cdot \frac{3}{1}=$   $2\frac{1}{4}-\frac{3}{5}=2\frac{5}{20}-\frac{12}{20}=1\frac{25}{20}-\frac{12}{20}=1\frac{13}{20}$  

 

$c)$  

$3\frac{1}{4}:\left[\left(2\frac{5}{8}-1\frac{1}{6}\right):2\frac{1}{2}\right]=$   $\frac{13}{4}:\left[\left(2\frac{15}{24}-1\frac{4}{24}\right):\frac{5}{2}\right]=$   $\frac{13}{4}:\left[1\frac{11}{24}\cdot \frac{2}{5}\right]=$   $\frac{13}{4}:\left[\frac{{\sout{35}}^7}{{\sout{24}}^{12}}\cdot \frac{{\sout{2}}^1}{{\sout{5}}^1}\right]=$   $\frac{13}{4}:\left[\frac{7}{12}\cdot \frac{1}{1}\right]=\frac{13}{4}:\frac{7}{12}=\frac{13}{{\sout{4}}^1}\cdot \frac{{\sout{12}}^3}{7}=$   $\frac{13}{1}\cdot \frac{3}{7}=\frac{39}{7}=5\frac{4}{7}$