$(0.05 \times 6.25) \div 2.5 = x$

### Concept & Logic The order of operations (BODMAS) states we evaluate terms within brackets first. To streamline decimal division and multiplication, converting terms to whole numbers or simplifying expressions before executing the calculation minimizes errors. ### Step-by-Step Solution * **Given:** $$ (0.05 \times 6.25) \div 2.5 = x $$ * **Calculation:** You can evaluate the bracket first. $$ 0.05 \times 6.25 = 0.3125 $$ * Next, divide the result by $2.5$. To do this easily, shift the decimal point one place to the right for both numbers: $$ \frac{0.3125}{2.5} = \frac{3.125}{25} $$ * Perform the division: $$ 3.125 \div 25 = 0.125 $$ * Check the options. The calculated value $0.125$ is not among (a), (b), (c), or (d). ### Exam Strategy & Shortcut Instead of calculating $0.05 \times 6.25$ first, recognize that $(a \times b) \div c$ is the same as $a \times (b \div c)$. $$ 0.05 \times (6.25 \div 2.5) $$ Mentally calculate $6.25 \div 2.5$. It is exactly $2.5$ (since $25^2 = 625$). Now, just multiply $0.05 \times 2.5$. $5 \times 25 = 125$. Adjusting for three decimal places gives $0.125$. This takes seconds and avoids ugly decimals. ### Common Pitfall Misplacing the decimal point during multiplication (e.g., getting $3.125$ instead of $0.3125$ for the bracket), leading to an incorrect final quotient of $1.25$ (option d). Always count total decimal places carefully. ### Final Answer **Therefore, the correct answer is None of these (0.125).**