$$ \left(\frac{1.49 \times 14.9 - 0.51 \times 5.1}{14.9 - 5.1}\right) $$ is equal to

### Concept & Formula This problem simplifies decimal arithmetic by converting numbers to a common base to reveal a hidden difference of squares identity. $$a^2 - b^2 = (a - b)(a + b)$$ ### Step-by-Step Solution * Notice the terms in the numerator can be rewritten by factoring out $\frac{1}{10}$ or $0.1$: * $1.49 \times 14.9 = \frac{14.9}{10} \times 14.9 = \frac{(14.9)^2}{10}$ * $0.51 \times 5.1 = \frac{5.1}{10} \times 5.1 = \frac{(5.1)^2}{10}$ * Rewrite the numerator using these common bases: $$ \frac{(14.9)^2 - (5.1)^2}{10} $$ * Apply the difference of squares identity $a^2 - b^2 = (a - b)(a + b)$ to the numerator: $$ (14.9)^2 - (5.1)^2 = (14.9 - 5.1)(14.9 + 5.1) $$ * Substitute this back into the overall fraction: $$ \frac{\frac{(14.9 - 5.1)(14.9 + 5.1)}{10}}{14.9 - 5.1} $$ * The term $(14.9 - 5.1)$ cancels out from both the numerator and denominator: $$ \frac{14.9 + 5.1}{10} $$ * Calculate the final sum and divide: $$ \frac{20}{10} = 2.00 $$ ### Exam Strategy & Shortcut Look at the options and decimal placements. The numerator is roughly $(1.5 \times 15) - (0.5 \times 5) = 22.5 - 2.5 = 20$. The denominator is $14.9 - 5.1 = 9.8$. Thus, the expression values to roughly $\frac{20}{9.8} \approx 2$. This instantly eliminates (a), (c), and (d). ### Common Pitfall Trying to multiply $1.49 \times 14.9$ and $0.51 \times 5.1$ directly. This leads to tedious multi-digit decimal operations that waste valuable time. ### Final Answer Therefore, the correct answer is 2.00.