(4) \( \frac{10 \frac{2}{8} \frac{2}{8}}{5 \frac{3}{9} \frac{4}{8}} \)

To tackle this fraction, let’s first convert the mixed numbers to improper fractions. For the numerator: \(10 \frac{2}{8} = \frac{10 \times 8 + 2}{8} = \frac{80 + 2}{8} = \frac{82}{8}\). For the denominator: \(5 \frac{3}{9} = \frac{5 \times 9 + 3}{9} = \frac{45 + 3}{9} = \frac{48}{9}\) and \( \frac{4}{8} = \frac{1}{2}\). Now, we can express the entire denominator: \(\frac{48}{9} \times \frac{1}{2} = \frac{48 \times 1}{9 \times 2} = \frac{48}{18} = \frac{8}{3}\) (after simplifying). Now we can rewrite the original expression: \[ \frac{10 \frac{2}{8} \frac{2}{8}}{5 \frac{3}{9} \frac{4}{8}} = \frac{\frac{82}{8} \cdot \frac{2}{8}}{\frac{8}{3}}. \] Calculating the numerator: \(\frac{82 \cdot 2}{8 \cdot 8} = \frac{164}{64}\). Now, we have: \[ \frac{\frac{164}{64}}{\frac{8}{3}} = \frac{164}{64} \cdot \frac{3}{8}. \] Multiply the numerators and denominators: \[ \frac{164 \cdot 3}{64 \cdot 8} = \frac{492}{512}. \] Now let’s simplify \(\frac{492}{512}\): Both 492 and 512 can be divided by 4: \[ \frac{123}{128}. \] Thus, the final result is: \[ \frac{123}{128}. \]