Solve $48.2 \times 2.5 \times 2.2 + x = 270$

Concept & Strategy Group decimal multiplications strategically. Instead of multiplying sequentially from left to right, look for pairs that form whole numbers or simpler decimals to minimize arithmetic errors. Step-by-Step Solution * Given equation: $$48.2 \times 2.5 \times 2.2 + x = 270$$ * First, group the second and third terms to simplify the multiplication: $$2.5 \times 2.2$$ * Break $2.2$ into $2 \times 1.1$ for easier mental math: $$2.5 \times 2 = 5$$ $$5 \times 1.1 = 5.5$$ * Now multiply this result by the first term: $$48.2 \times 5.5$$ * Use the fraction equivalent for $5.5$ (which is $\frac{11}{2}$): $$48.2 \times \frac{11}{2} = 24.1 \times 11$$ $$24.1 \times 11 = 265.1$$ * Substitute this back into the original equation: $$265.1 + x = 270$$ $$x = 270 - 265.1 = 4.9$$ Exam Strategy & Shortcut Always scan for factors of 5 and even numbers. Spotting that $2.5 \times 2.2$ easily collapses into $5.5$ saves a massive amount of manual decimal multiplication. Additionally, converting $5.5$ to $\frac{11}{2}$ allows you to divide by 2 rather than multiply by a decimal, which is vastly faster and safer. Common Pitfall Multiplying sequentially ($48.2 \times 2.5$) creates large intermediate values ($120.5$) that are cumbersome to multiply by $2.2$ in the next step, drastically increasing the chance of calculation mistakes. Final Answer Therefore, the correct answer is **4.9**.