Chapter on Adjustment, Successive Inheritances, and the Division of Estates

When a group’s share cannot be divided evenly among its members, multiply the base of the case by their number if it is relatively prime to their shares; or, if it shares a common factor with their shares—such as a third or the like—multiply it by the corresponding reduced factor. If the case has undergone ʿawl (proportional reduction), use its augmented base. The resulting number is the corrected base of the case, and each individual then receives what had belonged to the entire group, or the corresponding fraction thereof. …

Adjustment means determining the smallest number that can be divided among the heirs without fractions, since inheritance calculations may never contain fractions.

Establishing the base means determining the smallest number from which the shares of the case can be allocated without fractions.

His statement: “When a group’s share cannot be divided evenly among its members, multiply the base of the case by their number if it is relatively prime to their shares; or, if it shares a common factor with their shares—such as a third or the like—multiply it by the corresponding reduced factor. If the case has undergone ʿawl, use its augmented base. The resulting number is the corrected base of the case, and each individual then receives what had belonged to the entire group, or the corresponding fraction thereof.”

If a deceased person leaves behind a husband and five paternal uncles, the base of the case is two. The husband receives one half, one share, and the five paternal uncles receive the remaining one share. Dividing their one share among five is a case of relative primeness without doubt, since one is relatively prime to every number. We therefore multiply their number, five, by the base of the case, two, producing ten. The husband’s one share multiplied by five becomes five, and these men’s one share multiplied by five becomes five, leaving one share for each of them.

If a deceased person leaves behind a wife and five paternal uncles, the base of the case is four. The wife receives one quarter, one share, and the remaining three shares go to the five paternal uncles; they cannot be divided evenly among them