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Sharing a comment on understanding the ancient concept of adding fractions.
Posted:
Oct 22, 2012 7:48 PM


In "The Math Connection Group" there is a discussion on teaching the addition of fractions, and here is my comment on it which I thought might be of interest to the Math History List; the link to that discussion is hereunder:
"I do agree with the opinion that the students should understand the "why" of any Math formula, i.e., the firstprincipals that feed its notion. In this regard, in ancient Egyptian mathematics, fractions were observed as parts of the circle, i.e., parts of cake or bread. The socalled Rhind Mathematical Papyrus includes great deal of information on fractions. The subdividingimage(s) is the basic principle behind the concept of the Ancient Egyptian fractions. Assume that 3/3 is the image of subdividing the circle (bread) into three equal parts. The "denominator" is the number of divisions, and the "numerator" is what is taken out or remained from them. 1/3 is one of the three parts, and 2/3 is 2 of the 3 that are either remained, or taken out (i.e. perhaps was eaten). Similarly, 1/5 is part of the subdividingimage 5/5. If I would like to add the parts that each belongs to different subdividingimage, e.g., 1/5 to 1/3, I need to combine their images: 3/3 and 5/5, into a unified one that its part divides both, by multiplying the two images [3/3]*[5/5] and get 15/15. That is 1/15 divides 1/3 into 5 parts and divides 1/5 into 3 parts. That means in case of diverse and not the same subdividingimage, the product of addition or subtraction will always be part(s) of a new combined subdividingimage. If one say adding 1/3 + 1/5 equals (1*5+1*3)/(3*5); It meant also he multiplied each of the two fractions by their combined image before adding them, e.g., [(15/15)*(1/3)] + [(15/15)*(1/5)]. Of course using a formula is the short way; any simple whyexplanation should be narrated as a prelude."
Hossam Aboulfotouh
http://www.benfotouh.com
link: http://www.linkedin.com/groups/FeedbackWantedDoYouThink1872005
Thread title: Feedback Wanted: Do You Think This is a Clear Way to Teach the Concept of Adding Fractions?
Message was edited by: Hossam Aboulfotouh



