(c) \( \frac{\frac{3}{4} \times \frac{2}{5} \div 2 \frac{2}{5}}{\left(5 \frac{1}{6}-2 \frac{4}{9}\right) \times \frac{9}{28}} \)

To evaluate the expression: \[ \frac{\frac{3}{4} \times \frac{2}{5} \div 2\frac{2}{5}}{\left(5\frac{1}{6} - 2\frac{4}{9}\right) \times \frac{9}{28}} \] Let's break it down step by step. ### Step 1: Convert Mixed Numbers to Improper Fractions 1. **Convert \(2\frac{2}{5}\):** \[ 2\frac{2}{5} = \frac{2 \times 5 + 2}{5} = \frac{12}{5} \] 2. **Convert \(5\frac{1}{6}\):** \[ 5\frac{1}{6} = \frac{5 \times 6 + 1}{6} = \frac{31}{6} \] 3. **Convert \(2\frac{4}{9}\):** \[ 2\frac{4}{9} = \frac{2 \times 9 + 4}{9} = \frac{22}{9} \] ### Step 2: Simplify the Numerator The numerator is: \[ \frac{3}{4} \times \frac{2}{5} \div \frac{12}{5} \] This can be rewritten as: \[ \frac{3}{4} \times \frac{2}{5} \times \frac{5}{12} \] Simplify: \[ \frac{3 \times 2 \times 5}{4 \times 5 \times 12} = \frac{30}{240} = \frac{1}{8} \] ### Step 3: Simplify the Denominator The denominator is: \[ \left(\frac{31}{6} - \frac{22}{9}\right) \times \frac{9}{28} \] First, subtract the fractions: \[ \frac{31}{6} - \frac{22}{9} = \frac{93}{18} - \frac{44}{18} = \frac{49}{18} \] Now, multiply by \(\frac{9}{28}\): \[ \frac{49}{18} \times \frac{9}{28} = \frac{49 \times 9}{18 \times 28} = \frac{441}{504} \] Simplify \(\frac{441}{504}\): \[ \frac{441 \div 63}{504 \div 63} = \frac{7}{8} \] ### Step 4: Combine Numerator and Denominator Now, the overall expression is: \[ \frac{\frac{1}{8}}{\frac{7}{8}} = \frac{1}{8} \times \frac{8}{7} = \frac{1}{7} \] ### **Final Answer** \(\boxed{\dfrac{1}{7}}\)