Compare fractions to find the smallest value: Among 11/13, 9/11, 3/4, and 5/7, determine which fraction is the smallest.

Introduction / Context:
Comparing fractions appears frequently in aptitude tests. Efficient techniques include converting to decimals mentally, using cross-multiplication for pairs, or bringing them to a common denominator. Here we identify the smallest among four familiar ratios.

Given Data / Assumptions:

• Candidates: 11/13, 9/11, 3/4, 5/7
• All are proper fractions between 0 and 1.

Concept / Approach:
Two quick approaches: approximate decimal values or cross-multiply pairwise against a benchmark. Noting that denominators near numerators give fractions close to 1; larger gaps yield smaller values. Compute or estimate to rank them reliably.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• 11/13, 9/11, 3/4: Each has a value greater than 5/7 when compared by cross-multiplication or decimal conversion.

Common Pitfalls:

• Assuming larger denominators always imply smaller values without considering numerators.
• Rounding errors when estimating decimals too coarsely.

Final Answer: