See the working draft Fundamentals
This draft represents an initial attempt to incorporate an idea in a book by Kline, about looking differently than we usually do at ways for handling fractions. He considers the division operation in terms of baseball arithmetic to point out that the way we calculate depends on our local model or field of interest.
[The appendix example there discusses - point 5. - Kline's reasonable alternative view of adding fraction (reference listed in the draft). It is based on the way that baseball batting averages are computed.]