(52) \( \frac{1}{5}\left(\frac{1}{4}-\frac{1}{8}\right)+2 \frac{7}{8} \)

To simplify \( \frac{1}{5}\left(\frac{1}{4}-\frac{1}{8}\right)+2 \frac{7}{8} \), we'll break it down step by step. First, solve the inside of the parentheses: \[ \frac{1}{4} - \frac{1}{8} \] To perform this subtraction, find a common denominator, which is 8: \[ \frac{1}{4} = \frac{2}{8} \] Now subtract: \[ \frac{2}{8} - \frac{1}{8} = \frac{1}{8} \] Now, multiply this result by \( \frac{1}{5} \): \[ \frac{1}{5} \cdot \frac{1}{8} = \frac{1}{40} \] Next, convert \( 2 \frac{7}{8} \) to an improper fraction: \[ 2 \frac{7}{8} = \frac{16}{8} + \frac{7}{8} = \frac{23}{8} \] Now, add \( \frac{1}{40} \) to \( \frac{23}{8} \). To do this, we need a common denominator, which is 40: Convert \( \frac{23}{8} \): \[ \frac{23}{8} = \frac{23 \times 5}{8 \times 5} = \frac{115}{40} \] Now add the two fractions: \[ \frac{1}{40} + \frac{115}{40} = \frac{1 + 115}{40} = \frac{116}{40} \] Finally, simplify \( \frac{116}{40} \): \[ \frac{116 \div 4}{40 \div 4} = \frac{29}{10} = 2 \frac{9}{10} \] So, the final answer is: \[ 2 \frac{9}{10} \]