  other.numerator * self.denominator,
                            self.denominator * other.denominator)
        # float and complex don't have those operations, but we
        # know about those types, so special case them.
        elif isinstance(other, float):
            return float(self) + other
        elif isinstance(other, complex):
            return complex(self) + other
        # Let the other type take over.
        return NotImplemented

    def __radd__(self, other):
        # radd handles more types than add because there's
        # nothing left to fall back to.
        if isinstance(other, numbers.Rational):
            return Fraction(self.numerator * other.denominator +
                            other.numerator * self.denominator,
                            self.denominator * other.denominator)
        elif isinstance(other, Real):
            return float(other) + float(self)
        elif isinstance(other, Complex):
            return complex(other) + complex(self)
        return NotImplemented


There are 5 different cases for a mixed-type addition on
Fraction. I'll refer to all of the above code that doesn't
refer to Fraction, float, or complex as "boilerplate". 'r'
will be an instance of Fraction, which is a subtype of
Rational (r : Fraction <: Rational), and b : B <:
Complex. The first three involve 'r + b':

    1. If B <: Fraction, int, float, or complex, we handle
       that specially, and all is well.
    2. If Fraction falls back to the boilerplate code, and it
       were to return a value from __add__, we'd miss the
       possibility that B defines a more intelligent __radd__,
       so the boilerplate should return NotImplemented from
       __add__. In particular, we don't handle Rational
       here, even though we could get an exact answer, in case
       the other type wants to do something special.
    3. If B <: Fraction, Python tries B.__radd__ before
       Fraction.__add__. This is ok, because it was
       implemented with knowledge of Fraction, so it can
       handle those instances before delegating to Real or
       Complex.

The next two situations describe 'b + r'. We assume that b
didn't know about Fraction in its implementation, and that it
uses similar boilerplate code:

    4. If B <: Rational, then __radd_ converts both to the
       builtin rational type (hey look, that's us) and
       proceeds.
    5. Otherwise, __radd__ tries to find the nearest common
       base ABC, and fall back to its builtin type. Since this
       class doesn't subclass a concrete type, there's no
       implementation to fall back to, so we need to try as
       hard as possible to return an actual value, or the user
       will get a TypeError.

c