Prompt 30: Interesting Fraction Methods

Note: Cell 1 provides interesting methods to show that two fractions are equivalent. The ideas have been known for quite some time, but I came up with them independently quite recently before finding out that they already existed. The more general idea being that any point lying on a straight line provides the entire set of equivalent fractions.

I learnt Cell 2 as the first proof by contradiction presented at University.

I believe that I came across the naive sum in Cell 3 on Richard Perring’s (@LearningMaths) twitter feed.

I’m not sure if, how and when I might insert any of these methods into the curriculum. I’m quite sure that I would develop exploratory tasks, possibly to deepen and stretch the knowledge of higher attaining learners. The prompt acts as a reminder that there are always creative and interesting avenues to solve even the most familiar of problems.

Additional links: for cell 3:

1. Here is a geogebra applet I made to visualise the naive sum.
2. A lovely little proof of the naive sum by Matt Parker (@standupmaths).

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