How is the denominator determined when a fixed share cannot be cleanly divided among a group of heirs?
Chapter on the Roots of Inheritance Shares that Increase (Awl)
Al-Mughni
Book of Inheritance Shares (Farā'id)
Primary text
If the shares allotted to a group of heirs cannot be justly divided among them, the number of heirs in that group must be multiplied by the current primary denominator (including Awl, if applicable) to establish a new corrected denominator (Tas'hih). The 'Juz' al-Sahm' (Share Fraction) is then determined by multiplying the group's number by the original denominator. The final share for each individual in that group is found by multiplying their original allottment by this Share Fraction.
Supporting text
If the number of heirs in the group is compatible with their shares by a common factor (like one-half or one-third), one only multiplies the Wafq of their number by the primary denominator. If the heirs are single individuals, they receive the amount calculated by multiplying their share by the Share Fraction. If they are a group, the total amount is divided among them.