Math Problem Solver

\[ \frac{4}{77} - \frac{2}{69} = \frac{122}{5313} = 0.\overline{022962544701675136457745153397327310370788631658196875588179936006} \]

The sum can be computed by rewriting each term over a common denominator, where the least common denominator of \(\frac{4}{77}\) and \(\frac{-2}{69}\) is \(5313\). \[ \begin{aligned} \frac{4}{77} - \frac{2}{69} &= \frac{4 \cdot 69}{77 \cdot 69} + \frac{-2 \cdot 77}{69 \cdot 77} \\ &= \frac{276 + -154}{5313} \\ &= \frac{122}{5313} \end{aligned} \]