This study examined the use of the set, area, and linear models of representation to enhance elementary students’ conceptual understanding of operating addition and subtraction of fractions. Students’ preferences regarding to the set, area, and linear models of fractions during independent work was also investigated. This study took place in grade 5, section A and the class consisting of 51(26F &25M) students out of 147 students of all sections of this grade at Biruh Tesfa primary and full cycle school in Debre markos. The section was selected by simple random sampling technique and used quasi-experimental design-based research approach, i.e., the groups of the students was given a treatment for 13 days. Students participated in classroom activities which required them to use manipulative to represent fractions using the set, area, and linear models. Students also had experiences using the models to investigate equivalent fractions, compare fractions, and perform operations (addition and subtraction). Student’s maintained exercises throughout the study, completed pre and post assessment, participated in class discussions, and participated in individual and group assignments concerning their fraction model preferences. The data collected through quantitative method was analyzed by paired samples t-test. The qualitative data was analyzed through narration on the basis of themes formed in line with the basic questions of this study. Analysis of the data revealed that the group of students after the treatment developed better conceptual understanding of operating addition and subtraction of fractions, when they taught by the three models (area, linear & set) of representations. The data concerning student mix use of models (preferences) were consistent, students’ choice and prefer to operate addition and subtraction of fractions by using both area and linear models during independent work and it was also reflect the preferences indicated in the observation. Basing on these findings the researcher recommend that The REB(Regional Educational bureau) and MOE(Ministry of Education) focused on new methods of mathematics education and prepared guided manuals, train the teachers and monitoring its implementation ,Universities’ colleges of education give community services and support department of mathematics education in the school and enhance the quality of education based on research and Teacher should train themselves and update their profession using CPD (continuous professional development) and invent new methods to address the concept of fraction for their students.