The value of $$22.\overline 4 + 11.5\overline {67} - 33.5\overline 9 $$     is:

$$\eqalign{ & 22.\overline 4 + 11.5\overline {67} - 33.5\overline 9 \cr & = 22 + \frac{4}{9} + 11 + \frac{{567 - 5}}{{990}} - 33 - \frac{{59 - 5}}{{90}} \cr & = 33 - 33 + \frac{4}{9} + \frac{{562}}{{990}} - \frac{{54}}{{90}} \cr & = \frac{{40}}{{90}} - \frac{{54}}{{90}} + \frac{{562}}{{990}} \cr & = \frac{{ - 14}}{{90}} + \frac{{562}}{{990}} \cr & = \frac{{ - 154 + 562}}{{990}} \cr & = \frac{{408}}{{990}} \cr & = 0.4\overline {12} \cr} $$