Math Problem Solver

$$2\frac{1}{3} - \frac{2}{3} + 1\frac{4}{5} = \frac{52}{15} = 3.4\overline{6}$$

The sum can be computed by rewriting each term over a common denominator, where the least common denominator of $\frac{2}{1}$, $\frac{1}{3}$, $\frac{-2}{3}$, $\frac{1}{1}$, and $\frac{4}{5}$ is $15$. $$\begin{aligned} 2\frac{1}{3} - \frac{2}{3} + 1\frac{4}{5} &= \frac{2 \cdot 15}{1 \cdot 15} + \frac{1 \cdot 5}{3 \cdot 5} + \frac{-2 \cdot 5}{3 \cdot 5} + \frac{1 \cdot 15}{1 \cdot 15} + \frac{4 \cdot 3}{5 \cdot 3} \\ &= \frac{30 + 5 + -10 + 15 + 12}{15} \\ &= \frac{52}{15} \end{aligned}$$