Solve $\frac{3}{5}$ of $\frac{4}{7}$ of $\frac{5}{12}$ of $1015 = x$

Concept & Formula The word "of" in mathematical word problems and simplification questions translates directly to multiplication. The strategy is to multiply all the fractions together first and cancel out common terms in the numerators and denominators before multiplying by the large whole number. Step-by-Step Solution * Write out the full equation replacing "of" with multiplication signs: $$x = \frac{3}{5} \times \frac{4}{7} \times \frac{5}{12} \times 1015$$ * Isolate the fraction part to simplify it first: $$\left( \frac{3 \times 4 \times 5}{5 \times 7 \times 12} \right)$$ * Notice that the 5 in the numerator cancels with the 5 in the denominator. * Notice that $3 \times 4 = 12$ in the numerator, which perfectly cancels out the 12 in the denominator. * The entire fraction expression simplifies to: $$\frac{1}{7}$$ * Now multiply this simplified fraction by the whole number: $$x = \frac{1}{7} \times 1015$$ * Perform the final division: $$1015 \div 7 = 145$$ Exam Strategy & Shortcut Never multiply the first fraction by the large number immediately. Always scan the chain of fractions for cross-cancellation. In this problem, visually spotting that $(3 \times 4)$ cancels $12$, and $5$ cancels $5$, reduces the entire problem to a single step: $1015 \div 7$, taking mere seconds. Common Pitfall A common time-wasting mistake is trying to solve the chain sequentially from left to right (e.g., finding $\frac{3}{5}$ of something, then $\frac{4}{7}$ of that result). This creates messy intermediate decimals or large irreducible fractions. Final Answer Therefore, the correct answer is **145**.