  We examine the consequences of having a total division operation
$\frac{x}{y}$ on commutative rings. We consider two forms of binary division,
one derived from a unary inverse, the other defined directly as a general
operation; each are made total by setting $1/0$ equal to an error value $\bot$,
which is added to the ring. Such totalised divisions we call common divisions.
In a field the two forms are equivalent and we have a finite equational
axiomatisation $E$ that is complete for the equational theory of fields
equipped with common division, called common meadows. These equational axioms
$E$ turn out to be true of commutative rings with common division but only when
defined via inverses. We explore these axioms $E$ and their role in seeking a
completeness theorem for the conditional equational theory of common meadows.
We prove they are complete for the conditional equational theory of commutative
rings with inverse based common division. By adding a new proof rule, we can
prove a completeness theorem for the conditional equational theory of common
meadows. Although, the equational axioms $E$ fail with common division defined
directly, we observe that the direct division does satisfies the equations in
$E$ under a new congruence for partial terms called eager equality.
