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Quotitive Division and Invert and Multiply Algorithm for Fraction Division  

Yim, Jaehoon (경인교육대학교)
Publication Information
Journal of Elementary Mathematics Education in Korea / v.20, no.4, 2016 , pp. 521-539 More about this Journal
Abstract
The structures of partitive and quotitive division of fractions are dealt with differently, and this led to using partitive division context for helping develop invert-multiply algorithm and quotitive division for common denominator algorithm. This approach is unlikely to provide children with an opportunity to develop an understanding of common structure involved in solving different types of division. In this study, I propose two approaches, measurement approach and isomorphism approach, to develop a unifying understanding of fraction division. From each of two approaches of solving quotitive division based on proportional reasoning, I discuss an idea of constructing a measure space, unit of which is a quantity of divisor, and another idea of constructing an isomorphic relationship between the measure spaces of dividend and divisor. These ideas support invert-multiply algorithm for quotitive as well as partitive division and bring proportional reasoning into the context of fraction division. I also discuss some curriculum issues regarding fraction division and proportion in order to promote the proposed unifying understanding of partitive and quotitive division of fractions.
Keywords
fraction division; proportional reasoning; quotitive division; partitive division; invert and multiply algorithm;
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