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The meaning of fractions with integer multiplication is something that is difficult to understand by students. They tend to think that the product it produces a larger number, while the multiplication of fractions with integers, the result can be any number larger or smaller. This study is a research design that aims to develop a local instructional theory to support the students expand their understanding of the meaning of multiplication of fractions with integers. By applying the characteristics of realistic mathematics education (Realistic Mathematics Education), the researchers designed a series of instructional activities related to daily life, such as Indonesia prepares dishes and equitable distribution. Participants of this study were Grade 5 students from an elementary school in Surabaya, along with a mathematics teacher of that class. Some students of the class participated in the first cycle, in order to see how the design of the hypothetical learning trajectory (Hypothetical Learning Trajectory) is running. After going through several revisions, HLT is then implemented in all the other students in grade 5. The results showed that students' prior knowledge affect their learning process. The fractions solve multiplication problems with whole numbers, some students convert the integers to fractions and then use a fraction by a fraction multiplication procedure. The learning process begins with students exploring the contextual situation of fair division, where students extend their understanding that the fraction associated with the division and multiplication. One indicator that the student has broadened his understanding is the more varied representation of the given problem.