Comparing Fractions

Lew W. S.
This activity was designed specially to address some students' question as to why they always had to compare, add or subtract two fractions by first making them equivalent fractions with common denominators. Why not common numerators? So here it is below. Two fractions are visually represented as shaded portions of the circular pies divided into equal sized parts. You can choose to have common denominators or numerators by clicking on the respective buttons. The original question is: "Which fraction is larger? " Then we should be asking : How do we compare fractions by (a) making equivalent fractions with common denominators or by (b) having equivalent fractions with common numerators? or (c) simply see visually which of the two fractions of a circular pie is larger? Some pairs of fractions to compare : 1/2 vs 1/3 1/3 vs 2/5 1/4 vs 2/9 2/5 vs 3/7 3/5 vs 5/9 5/8 vs 6/7
In conclusion, is it easier to compare fractions by forming equivalent fractions with common denominators or with common numerators?