Wednesday, May 26, 2021

FamousMathProbs: How to set up fractions (English)

The computational challenge

Having a theoretical framework for fractions is well and good, but what are the computational challenges? Arithmetic with fractions is notoriously complicated for most learners, and we need to inquire into why, and how can we address these difficulties. These issues actually also figure prominently in rational trigonometry.

In fact primary school education has to incorporate additional technology just to get students being able to work with fractions. A key ingredient is Euclid's division lemma to set up mixed fractions.

Canonical forms via the Euclidean Algorithm

UPDATE 14-07-2021

Fractions and Equivalence Relations (Addendum)

There was however an important logical point that we skipped over, and one of our kind viewers pointed out that this gap needed to be filled!

The missing piece is a discussion of equivalence relations and how this get involved with our elementary definition of fractions. This points out once again how subtle foundational issues in modern pure mathematics are, and how we really have a lot of work to do.


See also:
The relation between fractions and other number systems.

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