The a b/c key

[Joe Horn]

That's correct: The fact that Home toggles between improper fraction display and mixed number display, and CAS only returns improper fractions, does not depend on the decimal-to-fraction algorithms they use. The only reason I even brought all that up was to underscore the most important differences between the way that the [a b/c] key acts in Home and in CAS, one of which is the actual results obtained.

The reason that the [a b/c] key in CAS never returns mixed numbers is simply due to the way it always and only calls the EXACT or APPROX functions, neither of which ever returns mixed numbers. Are you requesting that it call the PROPFRAC function whenever the current result is an improper fraction in CAS? If so, I find that idea compelling. That would make it "feel" more like the way the [a b/c] key behaves in Home.