$\text{a)}\frac{5}{9}:\frac{2}{3}=\frac{5}{{\sout{9}}^3}\cdot \frac{{\sout{3}}^1}{2}=\frac{5}{6}$  

$\frac{7}{8}:\frac{3}{4}=\frac{7}{{\sout{8}}^2}\cdot \frac{{\sout{4}}^1}{3}=\frac{7}{6}=1\frac{1}{6}$ $\frac{7}{8}:\frac{3}{4}=\frac{7}{{\sout{8}}^2}\cdot \frac{{\sout{4}}^1}{3}=\frac{7}{6}=1\frac{1}{6}$   

 

$\text{b)}\frac{9}{10}:\frac{3}{8}=\frac{{\sout{9}}^3}{{\sout{10}}^5}\cdot \frac{{\sout{8}}^4}{{\sout{3}}^1}=\frac{12}{5}=2\frac{2}{5}$   

$3\frac{1}{2}:\frac{5}{8}=\frac{7}{2}:\frac{5}{8}=\frac{7}{{\sout{2}}^1}\cdot \frac{{\sout{8}}^4}{5}=\frac{28}{5}=5\frac{3}{5}$        

 

$\text{c)}1\frac{3}{4}:1\frac{1}{2}=\frac{7}{4}:\frac{3}{2}=\frac{7}{{\sout{4}}^2}\cdot \frac{{\sout{2}}^1}{3}=\frac{7}{6}=1\frac{1}{6}$  

$\frac{5}{9}:3\frac{1}{3}=\frac{5}{9}:\frac{10}{3}=\frac{{\sout{5}}^1}{{\sout{9}}^3}\cdot \frac{{\sout{3}}^1}{{\sout{10}}^2}=\frac{1}{6}$