What is 28% of 36% of $\frac{5}{7}$th of 5000?

### Concept & Strategy Like other chain-percentage problems, the fundamental concept relies on translating the sequence of operations into a single product. The primary strategy is to utilize the commutative property of multiplication to rearrange the terms and cancel out large numbers (like $5000$) with the denominators ($100$) before proceeding to the complex multiplication. ### Step-by-Step Solution **Given:** * Expression: $28\%$ of $36\%$ of $\frac{5}{7}$ of $5000$ **Calculation / Deduction:** * Translate the expression into standard mathematical form: $$\frac{28}{100} \times \frac{36}{100} \times \frac{5}{7} \times 5000$$ * Group the denominators together: $100 \times 100 = 10000$ * Simplify the zeroes by dividing $5000$ by $10000$: $\frac{5000}{10000} = \frac{1}{2}$ * Rewrite the expression with the simplified terms: $$28 \times 36 \times \frac{5}{7} \times \frac{1}{2}$$ * Rearrange to cancel out the denominator $7$ with the $28$ (since $28 \div 7 = 4$): $$4 \times 36 \times 5 \times \frac{1}{2}$$ * Multiply $4 \times 5$ to get $20$: $$20 \times 36 \times \frac{1}{2}$$ * Cancel the $20$ with the $\frac{1}{2}$ to get $10$: $10 \times 36$ * Final calculation: $360$ ### Exam Strategy & Shortcut Look for synergies between the fractions. You have a denominator of $7$. Look at the numerators: $28$ is a multiple of $7$. Cancel them immediately to get $4$. You have two percentage signs meaning division by $10000$. You have a multiplier of $5000$. $5000 \div 10000 = \frac{1}{2}$. Now you are just left with $4 \times 36 \times 5 \times 0.5$. Since $4 \times 5 \times 0.5 = 10$, the answer is instantly $36 \times 10 = 360$. ### Common Pitfall A major time-waster is multiplying the numerators ($28 \times 36$) before simplifying the denominators. Never multiply two-digit numbers if there are still denominators left that can be cancelled. ### Final Answer Therefore, the correct answer is **360**.