Among the situations in which something does remain for the paternal siblings are the four cases called “the Zaydīyāt,” so named after Zayd, for he was the one who issued the ruling concerning them. They are:

1. The “Ten-Case” (al-ʿashariyyah). The heirs here are a grandfather, a full sister, and a paternal brother. The original root (the number of “heads”) is five, but the case is ascribed to ten because that is the figure on which the division becomes sound. The reason is that the full sister is entitled to one-half, and ½ cannot be expressed with a denominator of five. Hence the denominator of the half—two—is multiplied by the original root of five, producing ten. Out of these ten shares the grandfather receives two-fifths, i.e., four shares; the full sister receives her half, i.e., five shares; and the remaining one share goes to the paternal brother.

   Schematic layout:
   5/2 10
   Grandfather 2 → 4
   Full Sister 2 → 5
   Paternal Brother 1

2. The “Twenty-Case” (al-ʿishrīniyyah), so called because its correct solution requires a base of twenty. The heirs are a grandfather, a full sister, and two paternal sisters. As in the previous case the root is five, representing the number of heirs. The grandfather takes two shares by co-division, and the full sister one-half of the estate. Because ½ is incompatible with a denominator of five, the divisor two is multiplied by the root, giving ten. From the original five, the grandfather’s two shares become 2 × 2 = 4, and the full sister’s half is five shares.