Conventions of Composition Rule 4
Rule: A comma should not separate compound subjects, predicates, or objects of a preposition, unless long and involved or joined by but or yet.
Note: A compound sentence element of more than two items would need separation by commas. To punctuate a compound list, follow the comma rules explained in Rule 37.
Wrong: He suddenly jumped to his feet, and began to insult the chair of the committee.
Better: He suddenly jumped to his feet and began to insult the chair of the committee.
Wrong: He paused but went on again.
Better: He paused, but went on again.
Wrong: Both the girl, and her brothers go to the court after school.
Better: Both the girl and her brothers go to the court after school.
Practice deciding if and where these sentences need commas:
They looked under the bed, and the dresser for the wallet.
Sally, and Mary said their vows, and left the mosque.
The boy who won the prize in the Prep Science competition, and the girl who earned the highest mark in English both went on the school's trip to Quebec.
After I finished David Levithan's Every Day, I raced to read the sequel, and to see the movie.
Resources for further explanations of using commas with compound sentence elements:
Purdue OWL's Commas
Laura McKay's Compound Predicates