To compare the size of two or more fractions, or to put those fractions in numerical order, we first need to write each fraction with a common denominator, using the idea of equivalent fractions. We can't compare thirds and fifths straight away, because they are different sizes. However, if we convert them into a form with equal sized pieces (such as fifteenths), we can compare them, because each piece is the same size.
Once we have done that, we can decide which fraction is bigger by looking at the numerator of each fraction. 6/15 is bigger than 5/15 because 6/15 is 6 pieces, whereas 5/15 is only 5 pieces.