Albert Barnes Commentary 1 Kings 2:11

"And the days that David reigned over Israel were forty years; seven years reigned he in Hebron, and thirty and three years reigned he in Jerusalem." — 1 Kings 2:11 (ASV)

Forty years — In all, it was forty years and six months (see 2 Samuel 5:5 and 1 Chronicles 3:4). The Jewish writers almost universally omit the fractions of a year.