$\frac{4}{3}$ of 25% of $\frac{18}{19}$ of 57 = $x$

### Concept & Strategy This problem tests the continuous multiplication of fractions and percentages. The strategy is to immediately convert all percentages to their simplest fractional forms and cancel out numerators and denominators cross-wise before doing any actual multiplication. ### Step-by-Step Solution * **Given**: $\frac{4}{3} \text{ of } 25\% \text{ of } \frac{18}{19} \text{ of } 57 = x$ * **Calculation**: 1. Convert the percentage to a fraction: $25\% = \frac{1}{4}$ 2. Replace all "of" operators with multiplication signs: $$x = \frac{4}{3} \times \frac{1}{4} \times \frac{18}{19} \times 57$$ 3. Cancel out the $4$ in the numerator and denominator: $$x = \frac{1}{3} \times \frac{18}{19} \times 57$$ 4. Simplify the fraction by dividing $18$ by $3$: $$x = 6 \times \frac{57}{19}$$ 5. Recognize that $19 \times 3 = 57$, so cancel the $19$: $$x = 6 \times 3$$ 6. Final multiplication: $$x = 18$$ ### Exam Strategy & Shortcut Scan the equation for natural multiples. You can spot immediately that $19$ goes perfectly into $57$ exactly $3$ times. You can also spot that the $4$ in $\frac{4}{3}$ and the $4$ in the denominator of $25\%$ ($\frac{1}{4}$) will cancel each other out. This reduces the entire intimidating string to just $\frac{18}{3} \times 3$, which simplifies instantly to $18$ without lifting a pen. ### Common Pitfall A common mistake is multiplying all the numerators together and all the denominators together first to get a massive fraction (e.g., trying to calculate $4 \times 25 \times 18 \times 57$), which consumes time and leads to arithmetic errors. Always simplify and cancel factors first. ### Final Answer **Therefore, the correct answer is 18.**