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Suppose you wanted to make a list of all the rationals... How might you start?
One approach to listing all the rationals might be to begin with the denominators of the fractions: first, list those with denominator 1 - zero (0/1) and 1 (1/1).

Next, add those with denominator 2: 0, ½, 1.

Add those with denominator 3 (0, ⅓, ½, ⅔, 1) and you are on your way to the Farey Sequence! This last would be referred to as the Farey Sequence of Order 3.

But did you know that fractions grow on trees?

The web page shown explores three fraction trees - the Farey Tree, the Stern-Brocot and the Calf-Wilkins Trees. These provide wonderful explorations linking fractions, kissing circles and continued fractions!

https://compasstech.com.au/gxwfarey/f...

For a more extensive climb around these wonderful trees, visit:

https://compasstech.com.au/gxwfarey/i...

Correction: Please note an error in the definition of Child’s Addition shown at 1:20 and 4:53.

The definition should refer to two given fractions, a/b and c/d (NOT a/c).