\[\left| - 3\frac{5}{9} \right| - \left| - 1\frac{11}{18} \right| = 3\frac{5^{\backslash 2}}{9} - 1\frac{11}{18} =\]
\[= 3\frac{10}{18} - 1\frac{11}{18} =\]
\[= 2\frac{28}{18} - 1\frac{11}{18} = 1\frac{17}{18}.\]