$400 \div 0.1 \times 0.2 = x$

### Concept & Logic When multiplication and division appear consecutively in an expression without brackets, they have the same precedence and must be evaluated strictly from left to right. ### Step-by-Step Solution * **Given:** $$ 400 \div 0.1 \times 0.2 = x $$ * **Calculation:** Perform the division first since it is the leftmost operation. $$ \frac{400}{0.1} = 4000 $$ * Now multiply that quotient by the remaining factor. $$ 4000 \times 0.2 $$ $$ 4000 \times \frac{2}{10} = 800 $$ * Check the provided options. The value $800$ is not among (a), (b), (c), or (d). ### Exam Strategy & Shortcut Dividing any number by $0.1$ is mathematically identical to multiplying it by $10$. Thus, $400 \div 0.1$ instantly becomes $4000$. Multiplying by $0.2$ is the same as finding $20\%$ of a number, or dividing it by $5$. $4000 \div 5 = 800$. Using these conceptual translations makes the math immediate and entirely mental. ### Common Pitfall The most common mistake is executing the multiplication first because it "looks cleaner." Students mistakenly calculate $0.1 \times 0.2 = 0.02$, and then divide $400 \div 0.02 = 20000$. Remember that division and multiplication are lateral peers; left-to-right rule always applies. ### Final Answer **Therefore, the correct answer is None of these (800).**