The value of $$0.4\overline 6 + 0.7\overline {23} - 0.3\overline 9 \times 0.\overline 7 $$     is:

$$\eqalign{ & 0.4\overline 6 + 0.7\overline {23} - 0.3\overline 9 \times 0.\overline 7 \cr & = \frac{{46 - 4}}{{90}} + \frac{{723 - 7}}{{990}} - \frac{{39 - 3}}{{90}} \times \frac{7}{9} \cr & = \frac{{42}}{{90}} + \frac{{716}}{{990}} - \frac{{36}}{{90}} \times \frac{7}{9} \cr & = \frac{{42}}{{90}} + \frac{{716}}{{990}} - \frac{{28}}{{90}} \cr & = \frac{{14}}{{90}} + \frac{{716}}{{990}} \cr & = \frac{{154 + 716}}{{990}} \cr & = \frac{{870}}{{990}} \cr & = 0.\overline {87} \cr} $$