$\frac{3}{2} \times \frac{11}{5} \div \left( \frac{25}{44} \times \frac{11}{5} \right) \div \frac{33}{15} = x$

### Concept & Strategy This simplification problem strictly follows the BODMAS rule. Operations inside parentheses (brackets) must be executed first, followed by continuous division from left to right by multiplying with the reciprocal. ### Step-by-Step Solution * **Given:** $\frac{3}{2} \times \frac{11}{5} \div \left( \frac{25}{44} \times \frac{11}{5} \right) \div \frac{33}{15}$ * **Solve the expression inside the bracket:** * $\frac{25}{44} \times \frac{11}{5} = \frac{5 \times 5}{4 \times 11} \times \frac{11}{5} = \frac{5}{4}$ * **Substitute back and convert division to multiplication:** * $\frac{3}{2} \times \frac{11}{5} \div \frac{5}{4} \div \frac{33}{15}$ * Replace division signs with multiplication by inverting the fractions: * $\frac{3}{2} \times \frac{11}{5} \times \frac{4}{5} \times \frac{15}{33}$ * **Simplify the terms:** * Notice that $\frac{3 \times 11}{33} = \frac{33}{33} = 1$, so they cancel out completely. * Remaining terms: $\frac{1}{2} \times \frac{1}{5} \times \frac{4}{5} \times 15$ * $\frac{4 \times 15}{2 \times 25} = \frac{60}{50}$ * $\frac{60}{50} = \frac{6}{5}$ * **Convert to mixed fraction:** * $\frac{6}{5} = 1 \frac{1}{5}$ ### Exam Strategy & Shortcut Convert all division signs to multiplication immediately after solving brackets. Write it as one long chain of multiplication: $\frac{3}{2} \times \frac{11}{5} \times \frac{4}{5} \times \frac{15}{33}$. Cross-cancel aggressively (like $3 \times 11$ and $33$) before doing any actual large multiplication. ### Common Pitfall A frequent error in chained division ($A \div B \div C$) is treating it as $A \div (B \div C)$. Division is left-associative. Always process it left-to-right, or better yet, convert all divisions to multiplication by the reciprocal to avoid ambiguity entirely. ### Final Answer **Therefore, the correct answer is None of these.**