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At first sight, this seems indeed inconsistent, but I've learned to be wary of "obvious" answers when it comes to Sage's arithmetic.

May I suggest to ask this interesting question on sage-support (or possibly sage-devel) ?

At first sight, this seems indeed inconsistent, but I've learned to be wary of "obvious" answers when it comes to Sage's arithmetic.

The type of the objects may be a hint :

sage: type(.45)
<type 'sage.rings.real_mpfr.RealLiteral'>
sage: type(.45/.28)
<type 'sage.rings.real_mpfr.RealNumber'>

So mpfr defines some operator called / (possibly division) of RealNumbers (and, BTW, of RealLiterals), ...

sage: type(.45%.28)
<type 'sage.rings.real_mpfr.RealNumber'>

... as well as something called % (which indeed looks like modulo.

The question is now why mpfrs authors did not define anything called //. And why Sage's developers didn't extend mpfr to define //...

May I suggest to ask this interesting question on sage-support (or possibly sage-devel) ? There might be subtleties I am not aware of.