h. \( \begin{array}{r}7 \frac{3}{5} \\ +\quad 5 \frac{1}{8} \\ \hline\end{array} \)

1. Convert each mixed number into an improper fraction: - For \( 7\frac{3}{5} \): \[ 7\frac{3}{5} = \frac{7 \times 5 + 3}{5} = \frac{35+3}{5} = \frac{38}{5}. \] - For \( 5\frac{1}{8} \): \[ 5\frac{1}{8} = \frac{5 \times 8 + 1}{8} = \frac{40+1}{8} = \frac{41}{8}. \] 2. Find a common denominator for the fractions \(\frac{38}{5}\) and \(\frac{41}{8}\). The least common denominator of \(5\) and \(8\) is \(40\). 3. Convert both fractions to have the denominator \(40\): - For \(\frac{38}{5}\): \[ \frac{38}{5} = \frac{38 \times 8}{5 \times 8} = \frac{304}{40}. \] - For \(\frac{41}{8}\): \[ \frac{41}{8} = \frac{41 \times 5}{8 \times 5} = \frac{205}{40}. \] 4. Add the fractions: \[ \frac{304}{40} + \frac{205}{40} = \frac{304 + 205}{40} = \frac{509}{40}. \] 5. Convert the improper fraction into a mixed number. Divide \(509\) by \(40\): - \(509 \div 40 = 12\) with a remainder of \(509 - 12 \times 40 = 509 - 480 = 29\). So, \[ \frac{509}{40} = 12\frac{29}{40}. \] The final answer is \( 12\frac{29}{40} \).