and are relatively prime. We multiply their number, five, by the base of the case, four, yielding twenty; thus the case is adjusted to twenty. The wife’s quarter—one share—multiplied by five becomes five, while the paternal uncles’ three shares multiplied by five become fifteen. Since they are five, each receives three. The author says: “Each individual receives what had belonged to the entire group.” In the first example, the five paternal uncles collectively had three shares; now each one has three. Thus, each individual receives what had belonged to the entire group. This applies where the numbers are relatively prime.

In the case of a common factor: if a deceased person leaves behind a wife and six paternal uncles, the base of the case is four. The wife receives one quarter, one share, and the paternal uncles receive the remaining three shares, which cannot be divided evenly among them but have a common factor. Reduce the six—their number—to its corresponding factor, two, and multiply this by the base of the case: two times four equals eight. The wife’s one share multiplied by two becomes two, and the paternal uncles’ three shares multiplied by two become six. Since they are six, each receives one share.

If someone were to say: “The base of the case is four: the wife receives one quarter, one share, and the paternal uncles receive the remaining three shares. They are six, so the shares cannot be divided evenly. We multiply their number by the base of the case: six times four equals twenty-four. The wife’s one share multiplied by six becomes six, and their three shares multiplied by six become eighteen, so each receives three”—we would say: this is correct in result, but invalid in technical terminology and method. In the science of inheritance, whenever the smaller number is possible, one should not use the larger one. It has already become clear that the case can be adjusted to twelve, so why go to twenty-four? Whenever simplification is possible, unnecessary enlargement is not allowed. This is undoubtedly easier, especially when there are successive inheritances, for the calculations otherwise become lengthy.

The author’s discussion—may Allah have mercy on him—concerns a fractional division affecting one group. When a group’s share cannot be divided evenly among its members, first consider whether, between it and their shares