Approximate the value (nearest sensible option): (2 3/5) × (15/26) × 283.75 = ?

Introduction:
Converting mixed numbers to fractions or decimals first simplifies computation. Here, exact simplification yields a simple decimal, making the approximation trivial and precise relative to the listed options.

Given Data / Assumptions:

• 2 3/5 = 13/5 = 2.6
• Expression: (13/5) * (15/26) * 283.75

Concept / Approach:
Simplify (13/5)*(15/26) by canceling 13 with 26 to get (1/5)*(15/2) = 15/10 = 1.5. Then multiply by 283.75 and choose the nearest option.

Step-by-Step Solution:

Verification / Alternative check:
Rounding 283.75 slightly (e.g., to 284) gives 1.5 * 284 = 426, still closest to 425 among options given typical rounding conventions.

Why Other Options Are Wrong:
435 and 440 overshoot; 410 and 420 are too small relative to 425.6 exactness.

Common Pitfalls:
Not simplifying the fraction product first; computing directly with 2.6 * (15/26) is more error-prone than canceling 13/26 immediately.

Final Answer:
425