5 – One-third: This is the mother’s fixed share when two conditions are met: (i) the deceased leaves no qualifying descendant, and (ii) he leaves no group of siblings. Proof of the first condition is the divine statement, “But if he has no child and his parents inherit from him, then for his mother is one-third” (Q. 4:11). Proof of the second is His words, “But if he has brothers and sisters, then for his mother is one-sixth” (Q. 4:11).
The same one-third is the prescribed share of the uterine siblings—male and female alike—when they are two or more, as in the verse: “If a man or a woman leaves no ascendants or descendants but has a brother or a sister, each of them shall receive one-sixth; but if they are more than that, they share one-third” (Q. 4:12).
The scholars unanimously agree that the “brother” and “sister” mentioned here are those born of the same mother. Ibn Masʿūd and Saʿd ibn Abī Waqqāṣ even recited: “and has a brother or a sister from the mother’s side.”
6 – One-sixth: This is the mother’s share when the deceased is survived by a qualifying descendant or by two or more siblings, as in His words: “For his parents, to each of them one-sixth of what he leaves if he has a child,” and further, “But if he has brothers and sisters, then for his mother is one-sixth” (Q. 4:11).
• The one-sixth also belongs to the grandmother—or grandmothers—however remote through the purely maternal line, and likewise to any of them who is linked through an inheriting father. Reports concerning their inheritance have been transmitted. Their entitlement is conditioned upon the absence of the mother; if several grandmothers are of the same degree they share the portion equally, while the nearer excludes the more remote.
• One-sixth is likewise the fixed share of a single uterine sibling, whether male or female, in accordance with the verse just cited, “each of them shall receive one-sixth” (Q. 4:12). This is reinforced by the alternate reading reported from ʿAbd Allāh ibn Masʿūd and Saʿd ibn Abī Waqqāṣ and is unanimously accepted by the scholars.
• One-sixth is further the prescribed portion of a granddaughter through a son—or further issue—when there is a surviving full daughter, as indicated by the hadith of Ibn Masʿūd: when he was asked about a daughter and a son’s daughter he said, “I judge between them according to the ruling of the Messenger of Allah ﷺ.”