$a)1\frac{3}{4}:\frac{1}{7}=\frac{7}{4}\cdot \frac{7}{1}=\frac{49}{4}=12\frac{1}{4}$  

$b)2\frac{2}{3}:\frac{4}{9}=\frac{8}{3}\cdot \frac{9}{4}=$   $\frac{2}{3}\cdot \frac{9}{1}=\frac{2}{1}\cdot \frac{3}{1}=6$  

$c)\frac{7}{8}:1\frac{1}{2}=\frac{7}{8}:\frac{3}{2}=\frac{7}{8}\cdot \frac{2}{3}=$   $\frac{7}{4}\cdot \frac{1}{3}=\frac{7}{12}$  

$d)1\frac{3}{7}:1\frac{3}{4}=\frac{10}{7}:\frac{7}{4}=\frac{10}{7}\cdot \frac{4}{7}$   $=\frac{40}{49}$  

$e)3\frac{3}{8}:1\frac{3}{4}=\frac{27}{8}:\frac{7}{4}=$   $\frac{27}{8}\cdot \frac{4}{7}=$   $\frac{27}{2}\cdot \frac{1}{7}=\frac{27}{14}=1\frac{13}{14}$  

$f)1\frac{1}{12}:5\frac{1}{6}=\frac{13}{12}:\frac{31}{6}=$   $\frac{13}{12}\cdot \frac{6}{31}=$   $\frac{13}{2}\cdot \frac{1}{31}=\frac{13}{62}$