with the sixth. One may instead take six—the denominator that yields a sixth—as the original root: the mother is then given one share, leaving five, from which no exact third can be drawn. Hence the denominator of one-third, namely three, is multiplied by the six, producing a new root of eighteen. From this new base the mother’s statutory sixth is 1 × 3 = 3 shares. Fifteen shares remain; the grandfather takes 5 of them, a third of the residue, and the full sister receives one-half of the estate, 9 shares. This leaves a single share for the paternal siblings, which cannot be divided among their five heads. Their number (five) is therefore multiplied by the corrected root, eighteen, giving a final base of ninety.

Thus, on the base of ninety the distribution is:
– Mother: 3 × 5 = 15
– Grandfather: 5 × 5 = 25
– Full sister: 9 × 5 = 45
– Paternal siblings: 1 × 5 = 5, of which each of the two paternal brothers receives 2 and the paternal sister 1.

The schematic layout according to the two methods is:
18/5 90 6/3 18/5 90
Mother 3 15 Mother 1 3 15
Grandfather 5 25 Grandfather 5 25
Full sister 9 45 Full sister 9 45
Paternal brothers – – Paternal brothers 4 1 5
Paternal sister – – Paternal sister 1

This concludes the present discussion. What remains is the discipline known as the “arithmetic of inheritances,” which comprises the chapter on computation, the chapter on successive inheritances, and the chapter on the actual division of estates—matters dealt with in the specialized works on farāʾiḍ (the laws of succession).