are relatively prime? If they are, multiply their number by the base of the case. If they have a common factor, reduce their number to its corresponding factor, then multiply it by the base of the case. If the shares divide evenly, no adjustment is needed.

Know that the adjusted total to which a case increases through ʿawl is treated exactly like the base of the case; there is no difference. For example, if a deceased person leaves five full sisters and a husband, the base of the case is six. The full sisters receive two-thirds, four shares, and the husband receives one-half, three shares, so the case increases through ʿawl to seven. The sisters have four shares, and their number is five; the shares do not divide evenly among them, and the two numbers are relatively prime. The rule is that any two consecutive numbers are relatively prime. We therefore multiply the number of persons—five—by the adjusted total of the case—seven—giving thirty-five, to which the case is adjusted. The sisters receive four multiplied by five, making twenty; each sister receives four. The husband receives three multiplied by five, making fifteen. This totals thirty-five. This is easy—praise be to Allah.

However, the author—may Allah have mercy on him—mentioned only a fractional division affecting one group. There may also be a fractional division affecting two, three, or four groups; we have explained this in al-Burhāniyyah.