It is very difficult to tell whether 3/14 is greater or less than 4/21 just by looking at the two fractions. Here's where writing them with a common denominator comes in handy. We know that 3/14 = 9/42 and that 4/21 = 8/42. Since 9 is greater than 8, 9/42 is greater than 8/42. Thus 3/14 is greater than 4/21.
To determine which of two fractions is greater, write them as fractions with the same denominator. Then see which new fraction has the larger numerator. This is the greater fraction.