Math Problem Solver

\[ \frac{1}{2} + \frac{2}{3} + \frac{3}{4} = \frac{23}{12} = 1.91\overline{6} \]

The sum can be computed by rewriting each term over a common denominator, where the least common denominator of \(\frac{1}{2}\), \(\frac{2}{3}\), and \(\frac{3}{4}\) is \(12\). \[ \begin{aligned} \frac{1}{2} + \frac{2}{3} + \frac{3}{4} &= \frac{1 \cdot 6}{2 \cdot 6} + \frac{2 \cdot 4}{3 \cdot 4} + \frac{3 \cdot 3}{4 \cdot 3} \\ &= \frac{6 + 8 + 9}{12} \\ &= \frac{23}{12} \end{aligned} \]