Math Problem Solver

\[ 2\frac{7}{9} + 1\frac{2}{5} = \frac{188}{45} = 4.1\overline{7} \]

The sum can be computed by rewriting each term over a common denominator, where the least common denominator of \(\frac{2}{1}\), \(\frac{7}{9}\), \(\frac{1}{1}\), and \(\frac{2}{5}\) is \(45\). \[ \begin{aligned} 2\frac{7}{9} + 1\frac{2}{5} &= \frac{2 \cdot 45}{1 \cdot 45} + \frac{7 \cdot 5}{9 \cdot 5} + \frac{1 \cdot 45}{1 \cdot 45} + \frac{2 \cdot 9}{5 \cdot 9} \\ &= \frac{90 + 35 + 45 + 18}{45} \\ &= \frac{188}{45} \end{aligned} \]