Math Problem Solver

$$\frac{1}{7} + \frac{11}{7} + \frac{7}{11} + \frac{7}{1} = \frac{720}{77} = 9.\overline{350649}$$

The sum can be computed by rewriting each term over a common denominator, where the least common denominator of $\frac{1}{7}$, $\frac{11}{7}$, $\frac{7}{11}$, and $\frac{7}{1}$ is $77$. $$\begin{aligned} \frac{1}{7} + \frac{11}{7} + \frac{7}{11} + \frac{7}{1} &= \frac{1 \cdot 11}{7 \cdot 11} + \frac{11 \cdot 11}{7 \cdot 11} + \frac{7 \cdot 7}{11 \cdot 7} + \frac{7 \cdot 77}{1 \cdot 77} \\ &= \frac{11 + 121 + 49 + 539}{77} \\ &= \frac{720}{77} \end{aligned}$$