Math Problem Solver

\[ 1\frac{1}{7} + 2\frac{9}{14} + 3\frac{3}{4} = \frac{211}{28} = 7.53\overline{571428} \]

The sum can be computed by rewriting each term over a common denominator, where the least common denominator of \(\frac{1}{1}\), \(\frac{1}{7}\), \(\frac{2}{1}\), \(\frac{9}{14}\), \(\frac{3}{1}\), and \(\frac{3}{4}\) is \(28\). \[ \begin{aligned} 1\frac{1}{7} + 2\frac{9}{14} + 3\frac{3}{4} &= \frac{1 \cdot 28}{1 \cdot 28} + \frac{1 \cdot 4}{7 \cdot 4} + \frac{2 \cdot 28}{1 \cdot 28} + \frac{9 \cdot 2}{14 \cdot 2} + \frac{3 \cdot 28}{1 \cdot 28} + \frac{3 \cdot 7}{4 \cdot 7} \\ &= \frac{28 + 4 + 56 + 18 + 84 + 21}{28} \\ &= \frac{211}{28} \end{aligned} \]