the reciprocal is pretty much just the same fraction upside-down.
let's first convert the first one from mixed to "improper" and get the reciprocal.
[tex]\bf \stackrel{mixed}{1\frac{1}{11}}\implies \cfrac{1\cdot 11+1}{11}\implies \stackrel{improper}{\cfrac{12}{11}}\qquad reciprocal\implies \cfrac{11}{12}
\\\\\\
\cfrac{11}{12}\qquad reciprocal\implies \cfrac{12}{11}[/tex]
