\(\hbox{between } \frac{1}{6}=\frac{2}{12} \hbox{ and } \frac{1}{12} \\ \\
\frac{2}{12}>\frac{x}{12}>\frac{1}{12} \\
2>x>1 \\ \\
\hbox{x can be 1.01, 1.2, 1.55, etc.} \\
\hbox{the rational numbers are:} \\
\frac{1.01}{12}=\boxed{\frac{101}{1200}} \\
\frac{1.2}{12}=\frac{12}{120}=\boxed{\frac{1}{10}} \\
\frac{1.55}{12}=\frac{155}{1200}=\boxed{\frac{31}{240}} \\ \hbox{etc.}\)
