In Shmuel II, 5:5 it says that he was king in Chevron for seven years and six months. Why does it say here and there that he was king for [only] 40 years?
Radak (Shmuel II, 5:5): The Klal (total number) omits the excess, for it is not a full year. In Melachim I, 2:11, it is omitted even in the Prat (his reign in Chevron alone).
Radak (Shmuel II, 5:5, citing R. Yitzchak in Yerushalmi Rosh Hashanah 1:1): The six months are lacking from the 33 years in Yerushalayim. For the honor of Yerushalayim, the half year there is counted like a full year.
Radak (Shmuel II, 5:5), and Malbim (ibid., 4) citing R. Yudan in Midrash Shmuel 26:5: A large amount swallows a small 1 [remainder. This is why it says only 40 years.]
Radak (Shmuel II, 5:5, citing R. Yudan in Yerushalmi Rosh Hashanah 1:1): For six months, Yo'av and Yisrael fought Edom (based on David's command). Hashem said "Al Tisgaru Vam" (Devarim 2:5)! Therefore, they are not counted towards his reign.
Radak (Shmuel II, 5:5, based on Yerushalmi Rosh Hashanah 1:1): The six months that David fled from Avshalom, if he was Chayav Chatas, he would bring the Korban of a commoner, so they are not counted towards his reign.
Sanhedrin 107b: His total reign does not count six months that David was a Metzora.
Many kings had short reigns, and the Navi does not mention additional months. Did all of them rule complete years with no extra months?! Perhaps since one verse counts David's extra months, we need to explain why elsewhere they are omitted. (PF)


