Choose the greatest fraction among the following options Compare 2/5, 5/6, 11/12, and 7/8 and identify which fraction has the largest value.

Introduction / Context:
Comparing fractions is a frequent aptitude skill. Here you must determine which of 2/5, 5/6, 11/12, and 7/8 is the greatest without relying on a calculator. We use quick estimation and cross-multiplication to rank them correctly.

Given Data / Assumptions:

• Candidates: 2/5, 5/6, 11/12, 7/8.
• All are positive proper fractions.
• Goal: find the maximum value.

Concept / Approach:
Two reliable approaches exist: (1) convert to approximate decimals, or (2) compare in pairs using cross-multiplication (this avoids computing decimals). For a/b and c/d, compare a*d with c*b. The larger cross-product corresponds to the larger fraction.

Step-by-Step Solution:
Estimate: 2/5 = 0.4; 5/6 ≈ 0.8333; 7/8 = 0.875; 11/12 ≈ 0.9167.Ordering by size from largest to smallest: 11/12, 7/8, 5/6, 2/5.Therefore, the greatest fraction is 11/12.

Verification / Alternative check:
Compare 11/12 with 7/8 using cross-multiplication: 11*8 = 88 vs. 7*12 = 84. Since 88 > 84, 11/12 > 7/8. Similarly, 7/8 > 5/6 because 7*6 = 42 vs. 8*5 = 40.

Why Other Options Are Wrong:
7/8 (0.875) and 5/6 (≈0.8333) are both less than 11/12 (≈0.9167); 2/5 equals 0.4, far smaller. A distractor like 13/16 (0.8125) is also less than 11/12.

Common Pitfalls:
Comparing only numerators or denominators; assuming the fraction with the largest denominator is smallest, which is not always true across sets; rounding too coarsely.

Final Answer:
11/12