The ratio 0/1 is an additive identity, and the ratio 1/1 is a multiplicative identity.
The ratios a/b and -a/b are additive inverses, and a/b and b/a (a, b 0) are multiplicative inverses.
For a given field F, the set F(X) of rational functions in the variable X with coefficients in F is a field; this is defined as the set of quotients of polynomials with coefficients in F.