Bracketed ratio near integers: Evaluate [137 ÷ 17 × 3.99] / [4.02 × 3.98] and choose the nearest option.

Introduction / Context:This expression compares two products of numbers close to integers. By recognizing near-cancellations and rounding sensibly, the result lands close to a small integer. This is typical in approximation questions where factors hover near 4 or 8, and divisions collapse to neat values.

Given Data / Assumptions:

• Numerator: (137/17) × 3.99
• Denominator: 4.02 × 3.98

Concept / Approach:Compute 137/17 exactly: that equals 8 + 1/17 ≈ 8.0588. Multiplying by ~3.99 is close to multiplying by 4 but slightly less. The denominator 4.02 × 3.98 is close to 4 × 4 = 16. The overall ratio should be near (8.06 × 4) / 16 ≈ 2.01, i.e., about 2.

Step-by-Step Solution:

Verification / Alternative check:Exact computation yields about 2.0097, which is nearest to 2 among the listed choices. Thus, 2 is the correct selection.

Why Other Options Are Wrong:

• 2.5, 3.2, 3.5, 2.2: all lie farther from ≈2.01 and would overstate the ratio.

Common Pitfalls:Rounding 3.99 up to 4 while also rounding the denominator down (e.g., 4.02 → 4 and 3.98 → 4) without recognizing the near-compensating effects can skew the estimate.

Final Answer:2