of the remainder or than one-sixth of the estate. Yet that remainder cannot, as it stands, be divided between the grandfather and the brother. Accordingly, the number of those two heirs is multiplied by the original denominator of the estate (2), producing a new denominator of 4. The husband’s fixed share is one-half of the estate—one part out of two—so when the denominator is doubled he receives 2 shares. The grandfather and the brother together are likewise entitled to one part out of two; doubling gives them 2 shares, leaving each of them with 1.

This may be set out as follows:

Denominator: 4
Husband: 2 shares (½)
Grandfather: 1 share
Brother: 1 share

Second sub-case: one-third of the remainder is more beneficial than either muqāsama or one-sixth. An example is: mother, grandfather, and five brothers—a situation in which the fixed shares amount to less than one-half of the estate, and the number of siblings exceeds twice that of the grandfather.

The reason the grandfather is here given one-third of the remainder is that, after the mother’s one-sixth has been taken, 5 shares remain to be divided between the grandfather and the five brothers. One-third of that remainder is 1⅔ shares, which is undeniably more than he would receive through muqāsama or one-sixth. Because this remainder does not admit of an exact third, the divisor for the third (3) is multiplied by the estate’s original denominator (6), yielding 18. The mother’s one-sixth thus becomes 3 shares out of 18; the grandfather’s one-third of the remainder is 5 shares; and the 10 shares left over are divided among the five brothers, giving each of them 2 shares.