Math Problem Solver

\[ \frac{2}{19} + \frac{31}{38} + \frac{11}{19} + \frac{5}{19} = \frac{67}{38} = 1.7\overline{631578947368421052} \]

The sum can be computed by rewriting each term over a common denominator, where the least common denominator of \(\frac{2}{19}\), \(\frac{31}{38}\), \(\frac{11}{19}\), and \(\frac{5}{19}\) is \(38\). \[ \begin{aligned} \frac{2}{19} + \frac{31}{38} + \frac{11}{19} + \frac{5}{19} &= \frac{2 \cdot 2}{19 \cdot 2} + \frac{31 \cdot 1}{38 \cdot 1} + \frac{11 \cdot 2}{19 \cdot 2} + \frac{5 \cdot 2}{19 \cdot 2} \\ &= \frac{4 + 31 + 22 + 10}{38} \\ &= \frac{67}{38} \end{aligned} \]