Calculate : \( \quad 2 \frac{3}{4} \times 4 \frac{2}{5} \)

To calculate \( 2 \frac{3}{4} \times 4 \frac{2}{5} \), first convert the mixed numbers to improper fractions. For \( 2 \frac{3}{4} \): \[ 2 \frac{3}{4} = \frac{2 \times 4 + 3}{4} = \frac{8 + 3}{4} = \frac{11}{4} \] For \( 4 \frac{2}{5} \): \[ 4 \frac{2}{5} = \frac{4 \times 5 + 2}{5} = \frac{20 + 2}{5} = \frac{22}{5} \] Now we multiply the two improper fractions: \[ \frac{11}{4} \times \frac{22}{5} = \frac{11 \times 22}{4 \times 5} = \frac{242}{20} \] Next, simplify \( \frac{242}{20} \): \[ \frac{242 \div 2}{20 \div 2} = \frac{121}{10} \] To convert back to a mixed number, divide 121 by 10: \[ 121 \div 10 = 12 \text{ remainder } 1 \] Thus, \[ 12 \frac{1}{10} \] So, the answer is \( 12 \frac{1}{10} \).