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In order to implement biological computer, arithmetic operations are the foundational in all of computing models.However,the research on arithmetic operations in membrane system is remained in integer field,and the research on it in rational field haven’t implemented so far.The research propose of this paper is want to implement multiplication and division operations in rational field.Based on Biological cell-like model,this paper introduces the basic knowledge and principles of the membrane computing and presents fraction arithmetic P systems for performing multiplication and division respectively in rational field through designing the rules with priority, then gives corresponding instances to illustrate how to implement multiplication and division respectively in fraction arithmetic P systems;at the same time,we simulates multiplication and division respectively based on the the rules with priority designed.According to the experimental simulation results,it can obtained that the idea proposed that fraction arithmetic P systems for performing multiplication and division respectively in rational field and the rules designed are correct.