The process knowledge gained by the student who cannot build the definition of the concept in his mind is far from permanent. Learning and teaching of the number concept is a lifelong process starting from preschool ages in terms of both conceptual and operational knowledge. In this context, the aim of the study is to examine the concept definitions of secondary education students about fraction and rational number concepts and to determine how mathematics teachers define these two concepts; It is also to investigate the way teachers handle these two concepts in their teaching processes and what they observe in students. This study is a qualitative research. The participant group of the research consisted of 188 students studying in four different schools in a province located in the Central Anatolia Region in the 9th grade level in 2018-2019 academic year and 24 math teachers working in schools affiliated to the Ministry of Education. As a data collection tool, the concept definition determination form related to fraction and rational number concepts and a semi-structured interview form to be made with participant teachers have been developed to be applied to the participant student group. Descriptive analysis of the collected data was made. The results obtained at the end of the study show that students have false definitions about fraction and rational number concepts, and these definitions are caused by teachers’ inadequacy and misleading knowledge about these two concepts.