$\frac{5.4 \div 3 \times 16 \div 2}{18 \div 5 \times 6 \div 3}$

### Concept & Strategy This question evaluates your strict adherence to the BODMAS / PEMDAS rule (Order of Operations). For sequences containing only multiplication and division, you must evaluate the expression strictly from left to right. $$\text{Evaluate } \div \text{ and } \times \text{ strictly from Left to Right}$$ ### Step-by-Step Solution * **Given:** Numerator: $5.4 \div 3 \times 16 \div 2$ Denominator: $18 \div 5 \times 6 \div 3$ * **Calculation / Deduction:** 1. Evaluate the numerator strictly left to right: * Step 1: $5.4 \div 3 = 1.8$ * Step 2: $1.8 \times 16 = 28.8$ * Step 3: $28.8 \div 2 = 14.4$ * Numerator result = $14.4$ 2. Evaluate the denominator strictly left to right: * Step 1: $18 \div 5 = 3.6$ * Step 2: $3.6 \times 6 = 21.6$ * Step 3: $21.6 \div 3 = 7.2$ * Denominator result = $7.2$ 3. Divide the simplified numerator by the simplified denominator: $$\frac{14.4}{7.2} = 2$$ ### Exam Strategy & Shortcut **Fractional Conversion:** Instead of dealing with decimals, convert division signs into multiplication by reciprocals. This allows you to cancel terms efficiently. Numerator: $5.4 \times \frac{1}{3} \times 16 \times \frac{1}{2} = 5.4 \times \frac{16}{6} = 5.4 \times \frac{8}{3} = 1.8 \times 8 = 14.4$ Denominator: $18 \times \frac{1}{5} \times 6 \times \frac{1}{3} = \frac{18 \times 6}{15} = \frac{108}{15} = 7.2$ Result: $\frac{14.4}{7.2} = 2$. ### Common Pitfall The most common mistake is performing multiplication before division regardless of their order. For example, in the denominator $18 \div 5 \times 6 \div 3$, a student might wrongly calculate $5 \times 6 = 30$ first, completely ruining the evaluation sequence and resulting in an incorrect fraction. ### Final Answer **Therefore, the correct answer is $2$.**