Add the fifths, then the sevenths. \[ \begin{aligned} & \frac{4}{5}+\frac{2}{7}+1 \frac{1}{5}+\frac{5}{7} \\ = & \left(\frac{4}{5}+1 \frac{1}{5}\right)+\left(\frac{2}{7}+\frac{5}{7}\right) \\ = & \square+\square\end{aligned} \]

To solve the problem, we will first convert the mixed number \(1 \frac{1}{5}\) into an improper fraction and then add the fractions step by step. 1. **Convert the mixed number to an improper fraction:** \[ 1 \frac{1}{5} = 1 + \frac{1}{5} = \frac{5}{5} + \frac{1}{5} = \frac{6}{5} \] 2. **Rewrite the expression:** \[ \frac{4}{5} + \frac{2}{7} + \frac{6}{5} + \frac{5}{7} \] 3. **Group the fractions:** \[ \left(\frac{4}{5} + \frac{6}{5}\right) + \left(\frac{2}{7} + \frac{5}{7}\right) \] 4. **Add the fifths:** \[ \frac{4}{5} + \frac{6}{5} = \frac{4 + 6}{5} = \frac{10}{5} = 2 \] 5. **Add the sevenths:** \[ \frac{2}{7} + \frac{5}{7} = \frac{2 + 5}{7} = \frac{7}{7} = 1 \] 6. **Combine the results:** \[ 2 + 1 = 3 \] Now we can fill in the squares in the original expression: \[ = \left(\frac{4}{5} + 1 \frac{1}{5}\right) + \left(\frac{2}{7} + \frac{5}{7}\right) = 2 + 1 \] Thus, the final answer is: \[ = 3 \]