How the Sages Counted David's Forty Years of Reign

"When your days are fulfilled, etc." (2 Samuel 7:12). Rabbi Shmuel bar Nachman said: [The Holy One, blessed be He, said to him: David,] full days of days I am counting for you; I am not counting [for you] deficient days. "And the days that David reigned over Israel were forty years" (1 Kings 2:11), and it is written, "In Hebron he reigned over Judah seven years and six months, and in Jerusalem he reigned thirty-three years" (2 Samuel 5:5). These extra ones (here) [that are here], what are they? Rabbi Yitzchak bar Ketzarta in the name of Rabbi Yonah: They were deficient, but the Scriptures show honor to Jerusalem and count them as full ones. Rabbi Yudan said: The larger reckoning swallows up the smaller reckoning. Since it is written, "For six months Yoav remained there, etc." (1 Kings 11:16), those six months did not enter into the count. Rabbi Yudan said: All those six months that David was fleeing from before Avshalom his son did not enter into his count for him, but through a goat he was atoned for like a commoner.