of two females. If the estate is subjected to ʿawl (the proportional reduction that occurs when the fixed shares together exceed the estate), the grandfather’s sixth is reduced along with the shares of the other heirs; whatever affects them also affects him. No case of ʿawl occurs with the grandfather and the brothers or sisters except in one single problem, the so-called Akdariyyah. It consists of a grandfather, a husband, a mother, and one sister—whether she is a full sister or a paternal sister. In that case the husband is given one-half, the mother one-third, the grandfather one-sixth, and the sister one-half; her share is the very cause of the ʿawl. There is no other problem involving the grandfather and siblings in which ʿawl arises.

After the initial distribution, the grandfather adds his sixth to the sister’s half, and the two of them divide the combined amount as though they were brother and sister, the male taking the portion of two females. The original denominator is six; the ʿawl adds three, so it becomes nine. Hence the mother receives two parts, the grandfather one, the sister three, and the husband three. To correct the fractions the total is raised to twenty-seven: the husband receives nine parts, the sister nine, the mother six, and the grandfather three. The grandfather then joins the sister’s nine parts to his three, and they divide those twelve parts between them as brother and sister, the male again taking twice the share of the female, so the grandfather receives eight parts and the sister four.

If you prefer, say instead: the grandfather and the sister together hold four shares out of nine; that joint share is divided between them, the male receiving twice the female. Because the division would otherwise produce fractions, the ʿawl-adjusted base is multiplied by three, giving twenty-seven: the husband takes nine, the mother six, the grandfather eight, and the sister four. This division treats the grandfather as though he were a brother, awarding him the equivalent of two sisters’ shares.

Full brothers and sisters (those related through both father and mother) are brought back against the grandfather in the redistribution (muʿādah) through the paternal brothers. Nothing eventually remains in the hands of the paternal brothers, except where there is only a single paternal sister whose portion, after the muʿādah, exceeds one-half of the whole estate; in that situation she receives one-half and the balance reverts to the paternal brothers, for she may never inherit more than one-half. The expression “they are brought back against the grandfather” means that they augment the number of brothers taken into account against him.