$\left( 16 \frac{2}{5} - 12 \frac{1}{15} \right) \div 3 \frac{4}{81} = x$

### Concept & Formula This problem requires the application of the BODMAS rule and the conversion of mixed fractions into improper fractions before performing arithmetic operations. $$a \frac{b}{c} = \frac{(a \times c) + b}{c}$$ ### Step-by-Step Solution * **Given:** $\left( 16 \frac{2}{5} - 12 \frac{1}{15} \right) \div 3 \frac{4}{81}$ * **Convert mixed fractions:** * $16 \frac{2}{5} = 16 + \frac{6}{15}$ (creating a common denominator) * $12 \frac{1}{15} = 12 + \frac{1}{15}$ * **Solve the bracket:** * $\left( 16 - 12 \right) + \left( \frac{6}{15} - \frac{1}{15} \right)$ * $4 + \frac{5}{15} = 4 + \frac{1}{3} = \frac{13}{3}$ * **Convert the divisor:** * $3 \frac{4}{81} = \frac{(3 \times 81) + 4}{81} = \frac{243 + 4}{81} = \frac{247}{81}$ * **Perform division:** * $\frac{13}{3} \div \frac{247}{81} = \frac{13}{3} \times \frac{81}{247}$ * $\left( \frac{13}{247} \right) \times \left( \frac{81}{3} \right)$ * $\frac{1}{19} \times 27 = \frac{27}{19} = 1 \frac{8}{19}$ ### Exam Strategy & Shortcut Separate the integer part and the fractional part for addition and subtraction. Instead of calculating $(16 \times 5)+2$, calculate $(16-12)$ and $(\frac{2}{5} - \frac{1}{15})$ separately. This saves significant calculation time and reduces large number multiplication errors. ### Common Pitfall Students often convert $16 \frac{2}{5}$ into $\frac{82}{5}$ and $12 \frac{1}{15}$ into $\frac{181}{15}$, leading to $3 \times 82 = 246$ and $246 - 181 = 65$, which takes much longer and increases the chance of arithmetic mistakes under pressure. Always split mixed fractions when subtracting. ### Final Answer **Therefore, the correct answer is None of these.**