Math Problem Solver

$$2\frac{3}{4} + 2\frac{5}{9} = \frac{191}{36} = 5.30\overline{5}$$

The sum can be computed by rewriting each term over a common denominator, where the least common denominator of $\frac{2}{1}$, $\frac{3}{4}$, $\frac{2}{1}$, and $\frac{5}{9}$ is $36$. $$\begin{aligned} 2\frac{3}{4} + 2\frac{5}{9} &= \frac{2 \cdot 36}{1 \cdot 36} + \frac{3 \cdot 9}{4 \cdot 9} + \frac{2 \cdot 36}{1 \cdot 36} + \frac{5 \cdot 4}{9 \cdot 4} \\ &= \frac{72 + 27 + 72 + 20}{36} \\ &= \frac{191}{36} \end{aligned}$$