Final answer:
The common and expected medication side effect after administering promethazine to a patient with nausea and vomiting is drowsiness.
Step-by-step explanation:
The medication side effect that the nurse would explain as common and expected after administering a dose of promethazine to a patient with nausea and vomiting is Drowsiness. Promethazine is an antihistamine medication that can cause drowsiness as a common side effect. It works by blocking the effects of histamine in the body, which can help relieve symptoms of allergies, nausea, and vomiting.