This study analyzes and compares Swedish and Japanese mathematics textbooks through the whole compulsory schools in respect of rational numbers and proportion. The purpose is to give an insight of what important differences there are between the textbooks in order to offer pupils opportunities to acquire better conceptual understanding, and to give some suggestions for the improved conceptual understanding in the mathematics education. Various differences are found in how the textbooks treat an object between Sweden and Japan. In the Swedish textbooks, concepts of an object are presented and summarized in the beginning of a chapter, and tasks in the books play an important role in students’ conceptual understanding. In Japan an object is introduced with a problem, and discussions of the solutions are interwoven with definitions of the concepts. Generalization of the concepts and making connections are essential elements in the Japanese textbooks.