Math Problem Solver

\[ 2\frac{5}{9} + 1\frac{1}{3} + \frac{2}{27} = \frac{107}{27} = 3.\overline{962} \]

The sum can be computed by rewriting each term over a common denominator, where the least common denominator of \(\frac{2}{1}\), \(\frac{5}{9}\), \(\frac{1}{1}\), \(\frac{1}{3}\), and \(\frac{2}{27}\) is \(27\). \[ \begin{aligned} 2\frac{5}{9} + 1\frac{1}{3} + \frac{2}{27} &= \frac{2 \cdot 27}{1 \cdot 27} + \frac{5 \cdot 3}{9 \cdot 3} + \frac{1 \cdot 27}{1 \cdot 27} + \frac{1 \cdot 9}{3 \cdot 9} + \frac{2 \cdot 1}{27 \cdot 1} \\ &= \frac{54 + 15 + 27 + 9 + 2}{27} \\ &= \frac{107}{27} \end{aligned} \]