How to set up fractions III - canonical forms via the Euclidean Algorithm | FamousMathProbs24c | NJW

In order to deal with fractions smoothly, young students need to learn about canonical forms for fractions --where the numerators and denominators don’t have any common divisors. But actually this involves going back to a fundamental procedure from ancient Greece -- the Euclidean Algorithm. Curiously, this is originally a geometric phenomenon in the context of the ancient Greek “arithmetic with line segments“. But it also has an important more modern arithmetical form.