The aim of this paper is to analyze the logic of the introduction of fractions in the textbooks of arithmetic which were published in the period of textbook authorization system in the Meiji era (1886-1904), focusing on the explanation of the meaning of fractions. Fractions have two aspects. One is the ratio aspect and the other is division aspect. If we explain these aspects simply as two separate meanings of fractions, the explanation is insufficient. Even if we adopt one aspect as the definition of fractions, we must explain the other aspect and show the identity of these two aspects. In the above-mentioned textbooks, we can see that this viewpoint is adopted and is given a concrete shape and that the various methods are taken in the explanation. In the history of mathematics education in Japan, these facts are notable. At present, we should regard these facts as precious materials for the study of the teaching of fractions.