Order and select: second-smallest value among 4/7, 5/13, 6/11, 3/5, and 2/3 Rank the fractions and identify the second smallest.

Introduction / Context:
Here you must identify the second-smallest fraction from a set. This type of question checks your ability to compare fractions efficiently using estimation or cross-multiplication.

Given Data / Assumptions:

• Candidates: 4/7, 5/13, 6/11, 3/5, 2/3.
• We seek the second-smallest (the next value after the minimum).

Concept / Approach:
Estimate each value: 5/13 is clearly below 0.4; 6/11 is a bit below 0.55; 4/7 is about 0.57; 3/5 equals 0.6; 2/3 is about 0.6667. Order them by size from smallest to largest.

Step-by-Step Solution:
Approximations: 5/13 ≈ 0.3846 (smallest); 6/11 ≈ 0.5455; 4/7 ≈ 0.5714; 3/5 = 0.6; 2/3 ≈ 0.6667.Ascending order: 5/13, 6/11, 4/7, 3/5, 2/3.Thus, the second-smallest is 6/11.

Verification / Alternative check:
Cross-multiply 6/11 and 4/7: 6*7 = 42 vs. 4*11 = 44; since 42 < 44, 6/11 < 4/7, consistent with the ordering above.

Why Other Options Are Wrong:
5/13 is the smallest, not the second; 4/7, 3/5, and 2/3 are all larger than 6/11 and hence not the second-smallest.

Common Pitfalls:
Judging only by numerators or denominators; forgetting that 3/5 equals 0.6 exactly, which helps anchor the ordering.

Final Answer:
6/11