Here's the breakdown of the oxidation states of oxygen in peroxides and superoxides:

* Peroxides: In peroxides, oxygen has an oxidation state of -1. This is because the peroxide anion (O₂^2-) has a -2 charge, and since there are two oxygen atoms, each oxygen atom carries a -1 charge. A common example is hydrogen peroxide (H₂O₂).

* Superoxides: In superoxides, oxygen has an oxidation state of -1/2. This is because the superoxide anion (O₂^-) has a -1 charge, and since there are two oxygen atoms, each oxygen atom carries a -1/2 charge. A common example is potassium superoxide (KO₂).

Key Concept: The oxidation state of an element represents the hypothetical charge it would have if all its bonds were 100% ionic. This concept helps us understand the electron distribution and reactivity of compounds.