Qabisa b. Dhu’aib said that when a grandmother came to Abu Bakr asking him for her share of an estate he told her that nothing was prescribed for her in God’s Book or in the sunna of God's Messenger, but asked her to go home till he had questioned the people. When he did so, al-Mughira b. Shu'ba said he had been present with God's Messenger when he gave her a sixth. Abu Bakr asked if anyone had been with him and Muhammad b. Maslama said the same as al- Mughira had said, so Abu Bakr made it apply to her. Another grand-mother came to ‘Umar asking him for her share of an estate and he said, “It is that sixth. If there are two of you it is shared between you, but whichever is the only one left gets it all.”
Malik, Ahmad, Tirmidhi, Abu Dawud, Darimi and Ibn Majah transmitted it.
A man came to God’s Messenger and said, “My son’s son has died, so what do I receive from his estate?” He replied, “You receive a sixth;” then when he turned away he called him and said, “You receive another sixth;” and when he turned away he called him and said, “The other sixth is an allowance ,” (It would seem, although it is not explicit, that the grandson had left two daughters who were therefore entitled to two-thirds of the estate. The grandfather was entitled only to a sixth, but was given another sixth, as a favour, presumably because there were no other heirs).
Ahmad, Tirmidhi and Abu Dawud transmitted it, Tirmidhi saying this is a hasan sahih tradition.
Ibn Mas'ud said about a case where there was a grandmother and her son that she was the first grandmother to whom God’s Messenger gave a sixth which was not due to her when she had a son who was still alive.
Tirmidhi and Darimi transmitted it, but Tirmidhi declared it to be a weak tradition.
Abu Musa was asked about a case where there were a daughter, a son’s daughter and a sister and replied, “The daughter gets half and the sister gets half. Go to Ibn Mas'ud and you will find that he agrees with me.” When Ibn Mas'ud was asked and told what Abu Musa had said he replied, “I would then be in error and not be one of those who are rightly guided. I decide concerning the matter as the Prophet did: The daughter gets half and the son’s daughter a sixth, making two-thirds, and what remains goes to the sister.” We then went to Abu Musa and when we told him what Ibn Mas'ud had said he replied, “Do not question me as long as this learned man is among you.”
Bukhari transmitted it. (Here again we find a tradition by Bukhari in Section 2.)
