Keep-Change-Flip

 $\frac{3}{1}\ \times\ \frac{6}{1}$  

 $\frac{1}{3}\ \times\ \frac{1}{6}$  

 $\frac{3}{1}\ \div\ \frac{1}{6}$  

 $\frac{27}{1}\ \times\ \frac{3}{1}$  

 $\frac{1}{27}\ \times\ \frac{1}{3}$  

 $\frac{27}{1}\ \div\ \frac{3}{1}$  

 $\frac{1}{75}\ \times\ \frac{1}{8}$  

 $\frac{75}{1}\ \times\ \frac{8}{1}$  

 $\frac{75}{1}\ \div\ \frac{1}{8}$  

 $\frac{1}{121}\ \div\ \frac{1}{6}$  

 $\frac{121}{1}\ \times\ \frac{1}{6}$  

 $\frac{121}{1}\ \times\ \frac{6}{1}$  

 $\frac{1}{42}\ \times\ \frac{9}{1}$  

 $\frac{42}{1}\ \times\ \frac{9}{1}$  

 $\frac{1}{42}\ \div\ \frac{1}{9}$  

 $\frac{3}{1}\ \times\ \frac{8}{1}$  

 $\frac{1}{3}\ \div\ \frac{1}{8}$  

 $\frac{1}{3}\ \times\ \frac{1}{8}$  

 $\frac{1}{5}\ \times\ \frac{1}{3}$  

 $\frac{5}{1}\ \times\ \frac{3}{1}$  

 $\frac{1}{5}\ \div\ \frac{1}{3}$  

 $\frac{7}{1}\ \times\frac{5}{1}$  

 $\frac{1}{7}\ \times\frac{1}{5}$  

 $\frac{1}{7}\ \div\ \frac{5}{1}$  

 $\frac{9}{1}\ \div\ \frac{2}{1}$  

 $\frac{1}{9}\ \times\ \frac{2}{1}$  

 $\frac{1}{9}\ \times\ \frac{1}{2}$  

 $\frac{1}{6}\ \times\ \frac{1}{4}$  

 $\frac{1}{6}\ \div\ \frac{1}{4}$  

 $\frac{6}{1}\ \times\ \frac{4}{1}$