Math Problem Solver

\[ \frac{10}{9} - \frac{5}{8} = \frac{35}{72} = 0.486\overline{1} \]

The sum can be computed by rewriting each term over a common denominator, where the least common denominator of \(\frac{10}{9}\) and \(\frac{-5}{8}\) is \(72\). \[ \begin{aligned} \frac{10}{9} - \frac{5}{8} &= \frac{10 \cdot 8}{9 \cdot 8} + \frac{-5 \cdot 9}{8 \cdot 9} \\ &= \frac{80 + -45}{72} \\ &= \frac{35}{72} \end{aligned} \]