Comparing Fractions – UGC NET Question

To compare the fractions, we can either convert them to decimal form or cross multiply. The fraction 3/5 equals 0.6, 4/7 is approximately 0.571, 5/9 is approximately 0.556 and 6/13 is approximately 0.462. Among these decimal values, 0.6 is the largest. Therefore, 3/5 represents the greatest fraction in the given list.

Option A:
Option A, 3/5, clearly exceeds the others when converted into decimals or compared via cross multiplication with a common denominator. It corresponds to 0.6, which is larger than the approximate decimal values of the remaining fractions.

Option B:
Option B, 4/7, is slightly less than 0.6 and therefore smaller than 3/5, even though it is greater than the other two fractions listed. It cannot be the greatest overall.

Option C:
Option C, 5/9, falls between 0.55 and 0.56, making it smaller than both 3/5 and 4/7, so it is not the maximum value.

Option D:
Option D, 6/13, is noticeably less than 0.5, making it the smallest among the four fractions rather than the largest.