$(0.75 \times 4.4 \times 2.4) \div 0.6 = x$

### Concept & Strategy For complex decimal multiplication and division, the most efficient approach is to convert decimals into whole numbers or fractions, and leverage cancellation before performing any actual multiplication. $$ \frac{a \times b \times c}{d} $$ ### Step-by-Step Solution * **Given:** $$ \frac{0.75 \times 4.4 \times 2.4}{0.6} $$ * **Calculation:** Notice that both $2.4$ and $0.6$ have one decimal place. You can immediately divide them as whole numbers. $$ \frac{2.4}{0.6} = \frac{24}{6} = 4 $$ * Substitute this simplified value back into the expression: $$ 0.75 \times 4.4 \times 4 $$ * Use the associative property to multiply $0.75$ and $4$ first, since $0.75$ is $\frac{3}{4}$. $$ 0.75 \times 4 = 3 $$ * Finally, multiply the result by $4.4$: $$ 3 \times 4.4 = 13.2 $$ ### Exam Strategy & Shortcut Never multiply straight across when division is involved. Always look for the easiest cancellation path. Spotting that $2.4 \div 0.6 = 4$ turns a messy decimal calculation into a trivial mental math problem: $75\%$ of $4$ is $3$, and $3 \times 4.4$ is $13.2$. This avoids large intermediate decimals entirely. ### Common Pitfall A common error is multiplying $(0.75 \times 4.4 \times 2.4)$ first. This leads to calculating $3.3 \times 2.4 = 7.92$, and then attempting to divide $7.92$ by $0.6$. This is time-consuming and highly prone to arithmetic mistakes. Always cancel out fractions first. ### Final Answer **Therefore, the correct answer is 13.2.**