Which is the largest among the following fractions?

To compare fractions with different denominators, convert every fraction to an equivalent fraction over their LCM (a common denominator) — the fraction whose converted numerator is greatest is the largest fraction, since all are now measured on the same scale.

1. The four denominators are 2, 3, 4, and 4; their LCM is 12.

2. 21/2 = (21 × 6)/12 = 126/12

3. 50/3 = (50 × 4)/12 = 200/12

4. 41/4 = (41 × 3)/12 = 123/12

5. 25/4 = (25 × 3)/12 = 75/12

6. Comparing the four equivalent numerators over the same denominator 12 — 126, 200, 123, and 75 — the greatest is 200, so 200/12 is the largest fraction.

As an independent check, the approximate decimal values are 21/2 = 10.5, 50/3 ≈ 16.67, 41/4 = 10.25, and 25/4 = 6.25 — confirming 50/3 is clearly the greatest.

Hence, 50/3 is the largest among the given fractions.