Understanding Division of Fractions: An Alternative View

The purpose of this paper is to offer three alternatives to patterns or visualization used to justify division of fraction "algorithm" invert and multiply". The three main approaches are historical, similar denominators and algebraic, that teachers could use to justify the standard algorithm of division of fraction. The historical approach uses the Babylonia definition of division as the dividend multiplied by the reciprocal of the divisor. The similar denominators approach converts dissimilar denominators to similar ones and proceeds as division of whole numbers. The algebraic approach uses the property of division of numbers, along with a little algebraic manipulation to show how the "invert and multiply" algorithm can be justified. The pedagogical merits of each approach are discussed. The paper concludes that difficulties with fractions, especially, division of fractions can be traced to students' and teachers' personal experience or image. In particular, there is confusion between fractions as mathematical objects and the mathematical operations of fractions.