Proportional reduction ('awl) in inheritance

Kharijah bin Zayd (may Allah have mercy on him) narrates from his father (may Allah be pleased with him) that he was the first person to apply 'awl (proportional reduction) to the shares of inheritance, and the most he raised them by was two thirds.

It is narrated from Sayyiduna Ali (may Allah be pleased with him) that if there are a wife, both parents and two daughters, her eighth becomes a ninth.

Ibrahim al-Nakha'i (may Allah have mercy on him) said that Sayyiduna Ali and Sayyiduna Abdullah (may Allah be pleased with them both) applied 'awl in some questions of inheritance.

Ubaydullah bin Abdullah bin Utbah bin Mas'ud said: Zufar bin Aws and I went in to Ibn Abbas (may Allah be pleased with them both) after his sight had gone, and we discussed the shares of inheritance. Ibn Abbas (may Allah be pleased with them both) said: Do you think that the One who counted the number of the sands of Alij did not count (the shares)? How can there be in an estate a half, a half and a third? When a half and a half have gone, where is the place of the third? Zufar said: O Abu Abbas! Who was the first to apply 'awl to the shares? Ibn Abbas (may Allah be pleased with them both) said: Umar bin al-Khattab (may Allah be pleased with him). Zufar said: Why? Ibn Abbas (may Allah be pleased with them both) said: When the shares crowded upon him and overlapped one another, Umar (may Allah be pleased with him) said: By Allah, I do not know what to do with you; by Allah, I do not know which of you Allah has put first and which of you He has put last. And he said: I find nothing better for this estate than to divide it among you in proportion to the shares. Then Ibn Abbas (may Allah be pleased with them both) said: By Allah, had he put first whom Allah put first and put last whom Allah put last, no share would have needed 'awl. Zufar said: Which of them did He put first and which did He put last? Ibn Abbas (may Allah be pleased with them both) said: Every share that moves only to another (fixed) share is one that Allah has put first. Such are these shares: the husband has a half, and if he moves from it, then to a quarter, and he is not reduced below it; the wife has a quarter, and if she moves from it, she goes to an eighth, and is not reduced below it. The sisters have two thirds, and a single sister has a half; if daughters come in with them, they get whatever remains. These are the ones whom Allah has put last. Had he given those whom Allah put first their full share, then divided the remainder among those whom Allah put last in proportion to the shares, no share would have needed 'awl. Zufar said to him: What prevented you from advising Umar (may Allah be pleased with him) of this view? Ibn Abbas (may Allah be pleased with them both) said: By Allah, I held him in awe. Ibn Ishaq said: Al-Zuhri said to me: By Allah, had a guided leader whose way was scrupulous piety not preceded him in this, no two people of knowledge would have differed with Ibn Abbas (may Allah be pleased with them both).