$$ \frac{1.6 \times 3.2}{0.08} = x $$

### Concept & Formula To clear decimals from a fraction, count the total decimal places in the numerator and the denominator. Multiply both by a power of 10 that eliminates the decimals completely, converting the problem into simple integer arithmetic. ### Step-by-Step Solution **Given:** $$ \frac{1.6 \times 3.2}{0.08} $$ **Calculation:** * Count the decimal places: * Numerator: $1.6$ (1 place) $\times$ $3.2$ (1 place) = $2$ total decimal places. * Denominator: $0.08$ = $2$ total decimal places. * Since the number of decimal places in the numerator perfectly matches the denominator (2 places each), the decimals simply cancel each other out. * Rewrite the expression with whole numbers: $$ \frac{16 \times 32}{8} $$ * Simplify by dividing $32$ by $8$: $$ \frac{32}{8} = 4 $$ * Multiply the remaining terms: $$ 16 \times 4 = 64 $$ ### Exam Strategy & Shortcut **Shift & Cancel Method:** Mental math is faster when you shift the decimal. You can shift the decimal of $0.08$ two places to the right to make it $8$. To balance this, shift the decimal of $1.6$ one place (to $16$) and $3.2$ one place (to $32$). The equation immediately becomes $16 \times 32 / 8$. Recognize that $32 / 8 = 4$. Then $16 \times 4 = 64$. ### Common Pitfall A very common mistake is miscounting the decimal places and incorrectly assuming the expression simplifies to $16 \times 32 / 80$ or similar. Students often see $0.08$ and $1.6 \times 3.2$ and think there are more decimal places in the denominator, leading to an answer off by a factor of 10 (like $6.4$). Always sum the decimal places in the numerator before comparing. ### Final Answer **Therefore, the correct answer is 64.**