Math Problem Solver

\[ \frac{32}{243} - \frac{3}{5} = - \frac{569}{1215} = -0.4\overline{683127572016460905349794238} \]

The sum can be computed by rewriting each term over a common denominator, where the least common denominator of \(\frac{32}{243}\) and \(\frac{-3}{5}\) is \(1215\). \[ \begin{aligned} \frac{32}{243} - \frac{3}{5} &= \frac{32 \cdot 5}{243 \cdot 5} + \frac{-3 \cdot 243}{5 \cdot 243} \\ &= \frac{160 + -729}{1215} \\ &= \frac{-569}{1215} \end{aligned} \]