Approximation and quick calculation: Evaluate 6.39 × 128.948 + (5.215 ÷ 12.189) + 25.056 and select the closest option.

Introduction / Context:The expression is dominated by the product 6.39*128.948. The division term is small (≈0.43), and the constant is modest. A careful product estimate plus the small add-ons will point clearly to the nearest option.

Given Data / Assumptions:

• Main term: 6.39 * 128.948
• Small term: 5.215 / 12.189
• Constant: 25.056

Concept / Approach:Approximate 128.948 ≈ 129; 6.39*129 = 6.39*(130 − 1) = 830.7 − 6.39 = 824.31. Add the small division (~0.43) and the constant 25.056 to reach the final estimate near 850.

Step-by-Step Solution:

Verification / Alternative check:Exact computation gives about 849.46, still nearest to 850 compared with 800, 900, or 950.

Why Other Options Are Wrong:800 is too low by ~49; 900 and 950 are too high. 850 is closest.

Common Pitfalls:Ignoring the constant 25.056 or over-rounding 128.948 to 130 without subtracting the 6.39 correction.

Final Answer:850