Regarding the distribution in the Akdariyya case, how is the fractional division between the grandfather and the sister resolved?
Chapter on Inheritance of the Grandfather
Al-Mughni
Book of Inheritance Shares (Farā'id)
Primary text
In the Akdariyya case, the original shares total six, which leads to an excess distribution to nine. The shares of the sister and the grandfather (four shares combined) cannot be divided over three portions correctly. Thus, the root of the issue (nine) is multiplied by three, resulting in 27 shares. Each original shareholder's portion from the issue of nine is multiplied by three. The husband receives nine shares (3x3), the mother receives six shares (2x3), and the remaining twelve shares are divided between the grandfather and sister (8 for the grandfather, 4 for the sister).
Supporting text
If there is another sister or one or more brothers with the sister, the mother's share is reduced to one-sixth, and the remainder is divided between the sister and grandfather, without the issue escalating further.