This developmental study examined an acquisition of the concept of fraction. A total of 164 children were administrated six tests over a period of 3 years. Two principal incorrect strategies were found concerning the magnitude of fractions. The first made Rule S, in which children ordered fractions with a larger numerator as a smaller magnitude for problems with the same denominators. Another one made Rule L, in which children ordered the fractions with larger denominators as a greater magnitude for problems with the same numerators. The cross-sectional and longitudinal analyses on these strategies suggested four processes of acquiring the concept of fraction. The first was the process having informal knowledge on fraction before learning the concept formally. The second was one considering the concept of fraction based on children's existing knowledge. The third was a process judging the concept based on an incorrect concept of fraction. The last process consisted on the acquisition of a correct concept. These processes were discussed in terms of interacting process of the existing knowledge with a new concept.