Math Problem Solver

$$\frac{1}{10} + \frac{2}{30} + \frac{5}{90} = \frac{2}{9} = 0.\overline{2}$$

The sum can be computed by rewriting each term over a common denominator, where the least common denominator of $\frac{1}{10}$, $\frac{2}{30}$, and $\frac{5}{90}$ is $90$. $$\begin{aligned} \frac{1}{10} + \frac{2}{30} + \frac{5}{90} &= \frac{1 \cdot 9}{10 \cdot 9} + \frac{2 \cdot 3}{30 \cdot 3} + \frac{5 \cdot 1}{90 \cdot 1} \\ &= \frac{9 + 6 + 5}{90} \\ &= \frac{20}{90} \\&= \frac{2}{9} \end{aligned}$$