Math Problem Solver

\[ \frac{1}{9} + \frac{1}{10} + \frac{1}{30} = \frac{11}{45} = 0.2\overline{4} \]

The sum can be computed by rewriting each term over a common denominator, where the least common denominator of \(\frac{1}{9}\), \(\frac{1}{10}\), and \(\frac{1}{30}\) is \(90\). \[ \begin{aligned} \frac{1}{9} + \frac{1}{10} + \frac{1}{30} &= \frac{1 \cdot 10}{9 \cdot 10} + \frac{1 \cdot 9}{10 \cdot 9} + \frac{1 \cdot 3}{30 \cdot 3} \\ &= \frac{10 + 9 + 3}{90} \\ &= \frac{22}{90} \\&= \frac{11}{45} \end{aligned} \]