[tex]a)\\\\\frac{8}{1\frac{2}{3}}=8:1\frac{2}{3}=8: \frac{5}{3}=8*\frac{3}{5}=\frac{24}{5}=4\frac{4}{5}\\\\b)\\\\ \frac{\frac{1}{2}*\frac{5}{6}}{5}=\frac{\frac{5}{12}}{5}=\frac{5}{12}:5=\frac{\not{5}^1}{12}*\frac{1}{\not{5}^1}= \frac{1}{12} \\\\c)\\\\\frac{\frac{1}{3}}{1\frac{4}{9}}=\frac{1}{3}:1\frac{4}{9}=\frac{1}{3}: \frac{13}{9}=\frac{1}{\not{3}^1}*\frac{\not{9}^3}{13}= \frac{3}{13}[/tex]
[tex]d)\\\\ \frac{13}{2\frac{1}{6}*\frac{3}{4}}= \frac{13}{ \frac{13}{\not{6}^2}*\frac{\not{3}^1}{4}}=\frac{13}{\frac{13}{8}}=13:\frac{13}{8}=\not{13}^1*\frac{8}{\not{13}^1}=8\\\\e)\\\\\ \frac{1}{3} *\frac{1\frac{1}{2}}{\frac{2}{3}}=\frac{1}{3} *\frac{ \frac{3}{2}}{\frac{2}{3}}= \frac{1}{3}*\frac{3}{2}:\frac{2}{3}= \frac{1}{\not{3}^1}*\frac{\not{3}^1}{2}*\frac{3}{2}=\frac{3}{4}\\\\f)\\\\\frac{2}{7}:\frac{\frac{1}{7}}{3}=\frac{2}{7}:(\frac{1}{7}:3)=\frac{2}{7}:(\frac{1}{7} *\frac{1}{3})= \frac{2}{7}:\frac{1}{21}=\frac{2}{\not{7}^1}*\frac{\not{21}^3}{1}=6[/tex]
