Fifth grade children's (n=16) understandings of simple fractions such as 1/2, 1/3, and 1/4 were investigated. The study identified three alternative conceptions of fractions: (1) 1/"N" is one of "N equal" parts, (2) 1/N is one of "N equal" parts, and (3) parts must fit together to form the whole. In addition, many participants believed that the perimeter measured the area. This conception of area measurement also influenced the participants' problem-solving activities significantly. (Author/MKR)