$(0.05 \times 5 - 0.005 \times 5)$ equals

Concept & Formula This problem requires basic arithmetic operations following the order of operations (BODMAS/PEMDAS). Alternatively, you can use the distributive property of multiplication to factor out common terms and simplify the calculation: $$a \times c - b \times c = c(a - b)$$ Step-by-Step Solution **Method 1: Direct Calculation (BODMAS)** * Perform the multiplications first: $0.05 \times 5 = 0.25$ $0.005 \times 5 = 0.025$ * Subtract the second product from the first: $0.25 - 0.025 = 0.225$ **Method 2: Factoring** * Both terms are multiplied by 5, so factor it out: $$5 \times (0.05 - 0.005)$$ * Perform the subtraction inside the parentheses: $$5 \times 0.045$$ * Multiply by 5: $$0.225$$ Exam Strategy & Shortcut Using direct calculation is usually faster for simple multiples like 5. Think of money or simple fractions: $5 \times 5$ cents is $25$ cents ($0.25$). $5 \times 5$ tenths of a cent is $2.5$ cents ($0.025$). Aligning the decimals mentally: $0.250 - 0.025$ leaves $0.225$. Common Pitfall Misaligning the decimal points during subtraction is the primary error here. Students often calculate $0.25 - 0.025$ in their heads and mistakenly get $0.0225$ or $0.250$, forgetting to append a zero ($0.250$) to align the places properly before subtracting. Final Answer **Therefore, the correct answer is 0.225.**