Let a = 11/13, b = 13/14 and c = 15/17 be three fractions. Which of the…

Concept: To compare two positive fractions p/q and r/s, cross-multiply: p/q is less than r/s exactly when p × s is less than r × q (since q, s > 0, this avoids finding a common denominator). Chaining pairwise comparisons this way places any set of fractions in strict order.

Application:

1. Let a = 11/13, b = 13/14 and c = 15/17.

2. Compare a and c: 11 × 17 = 187 and 13 × 15 = 195. Since 187 < 195, a < c, i.e. 11/13 < 15/17.

3. Compare c and b: 15 × 14 = 210 and 17 × 13 = 221. Since 210 < 221, c < b, i.e. 15/17 < 13/14.

4. Chain the two results together: a < c < b, i.e. 11/13 < 15/17 < 13/14.

Cross-check: Converting each fraction to a decimal gives an independent confirmation — 11/13 ≈ 0.846, 15/17 ≈ 0.882, and 13/14 ≈ 0.929. Since 0.846 < 0.882 < 0.929, the same order holds.

So the true ordering is 11/13 < 15/17 < 13/14.