— He ﷺ said, “The daughter receives one-half, the son’s daughter one-sixth to complete two-thirds, and whatever remains goes to the sister.” Reported by al-Bukhārī.

The same ruling applies to a granddaughter through a son’s son when she inherits alongside a granddaughter through a son, and so on down the line.

• One-sixth is the fixed share of one or more paternal half-sisters when there is a single full sister present, and this is unanimously agreed upon.

• One-sixth likewise belongs to the father—or to the grandfather if the father is absent—when the deceased is survived by a qualifying descendant.

These, then, are the six prescribed shares mentioned in the Noble Qur’an, together with the heirs entitled to them and the manner in which they take them.

If, after those entitled to the fixed shares have received their portions, anything remains, it passes to the residuary heir (ʿaṣaba). This follows the Almighty’s words: “But if he has no child and his parents inherit from him, then for his mother is one-third” (4:11), the implication being that the rest devolves to his father as an agnatic share; and it is confirmed by the Prophet’s ﷺ statement in the hadith at hand, “Assign the prescribed shares to their rightful recipients; whatever is left goes to the nearest male agnate.” Concerning the inheritance of Saʿd ibn al-Rabīʿ’s brother he ﷺ likewise said, “Whatever remains is yours.”

Residuary heirs fall into successive classes, some nearer to the deceased than others, and they inherit according to their proximity. The classes are: (1) descendants, (2) parents, (3) siblings and their sons, (4) paternal uncles and their sons, and (5) walāʾ—that is, the emancipator and his agnates, the closest first, in the same order as blood relatives.

The nearer class is given precedence, so a son, for example, is preferred to a father. If the heirs belong to the same class, the one closer in degree to the deceased is preferred, as the son is preferred over the grandson. If they share both class and degree, the stronger tie prevails—the full brother over the paternal half-brother, and the same applies to their sons or to paternal uncles and their sons.

Heirs can bar one another from inheritance either totally (disinheritance) or partially (reduction). Reduction may affect all heirs, whereas total disinheritance never applies to the spouses.