Which Arithmetical Data Types Admit Fracterm Flattening?

The formal theory of division in arithmetical algebras reconstructs fractions as syntactic objects called fracterms. Basic to calculation is the simplification of fracterms to fracterms with one division opera- tor, a process called fracterm flattening. We consider the equational axioms of a calculus for calculating with fracterms to determine what is necessary and sufficient for the fracterm calculus to allow fracterm flattening. For computation, arithmetical algebras require operators to be total for which there are several semantical methods. It is shown under what constraints up to isomorphism, the unique total and min- imal enlargement of a field Q(÷) of rational numbers equipped with a partial division operator ÷ has fracterm flattening.