$$ \frac{3.25 \times 3.20 - 3.20 \times 3.05}{0.064} $$ is equal to

### Concept & Formula This problem tests your ability to apply the distributive property to factor out common terms, simplifying complex arithmetic into basic mental math. $$ ab - ac = a(b - c) $$ ### Step-by-Step Solution * Focus on the numerator: $3.25 \times 3.20 - 3.20 \times 3.05$. * Notice that $3.20$ is a common factor in both multiplication pairs. * Factor out $3.20$ using the distributive property: $$ 3.20 \times (3.25 - 3.05) $$ * Perform the simple subtraction inside the parentheses: $$ 3.25 - 3.05 = 0.20 $$ * Multiply the factored terms: $$ 3.20 \times 0.20 = 0.64 $$ * Reintroduce the denominator to solve the full fraction: $$ \frac{0.64}{0.064} $$ * Shift the decimal point three places to the right on both top and bottom to clear the decimals: $$ \frac{640}{64} = 10 $$ ### Exam Strategy & Shortcut Never multiply out terms if you see a common number repeated in an addition or subtraction string. By factoring out the $3.20$, the calculation drops to evaluating $3.20 \times 0.20$, which instantly yields $0.64$. Comparing $0.64$ to $0.064$ visually confirms a magnitude difference of exactly $10$. ### Common Pitfall Ignoring the common factor and attempting to calculate $3.25 \times 3.20 = 10.4$ and $3.20 \times 3.05 = 9.76$, then subtracting to get $0.64$. While this eventually works, it wastes precious minutes on a question designed to take 10 seconds. ### Final Answer Therefore, the correct answer is 10.