$48 \div 75 \times 84.5 \div 20 = x$

## Concept & Strategy According to the BODMAS/PEMDAS rule, division and multiplication have the same precedence and are evaluated from left to right. Converting divisions into multiplication by fractions simplifies the process. $$ a \div b \times c \div d = a \times \frac{1}{b} \times c \times \frac{1}{d} $$ ## Step-by-Step Solution * **Calculation:** Convert the expression into fractions for easier cancellation: $x = 48 \times \frac{1}{75} \times 84.5 \times \frac{1}{20}$ Group the terms: $x = \frac{48}{75} \times \frac{84.5}{20}$ Simplify $\frac{48}{75}$ by dividing numerator and denominator by 3: $\frac{16}{25}$ Now substitute it back: $x = \frac{16}{25} \times \frac{84.5}{20}$ Simplify further by dividing 16 and 20 by 4: $x = \frac{4}{25} \times \frac{84.5}{5}$ Multiply the numerators and denominators: $x = \frac{338}{125}$ To easily divide by 125, multiply numerator and denominator by 8: $x = \frac{338 \times 8}{1000}$ $x = \frac{2704}{1000}$ $x = 2.704$ ## Exam Strategy & Shortcut Approximation is key for verification. $\frac{48}{75}$ is roughly $\frac{2}{3}$ (or $0.64$). $\frac{84.5}{20}$ is roughly $4.2$. $0.64 \times 4.2$ is approximately $2.68$. Looking at the options, $2.704$ is the only close answer, instantly eliminating the others without rigorous final calculations. ## Common Pitfall Applying multiplication before division incorrectly (e.g., multiplying 75 by 84.5 first) because of misinterpreting the left-to-right rule. Always treat division as multiplying by the reciprocal to avoid order-of-operations errors. ## Final Answer **Therefore, the correct answer is 2.704.**