receives one-third, and the remainder goes to the closest male agnate, as stated in the hadith.

Or [a half] with a sixth, or a sixth and the remainder, is based on six; it may be proportionally increased to ten, whether even or odd. A quarter together with two-thirds, a third, or a sixth, is based on twelve. …

His statement, “Or a sixth”: a half together with a sixth is based on six. We do not say twelve, because whenever it is possible to reduce the denominator, it must be adopted. An example is a deceased person who leaves a full sister, a uterine sister, and a paternal uncle. The case is based on six: the full sister receives one-half, or three; the uterine sister receives one-sixth, or one; and the remainder goes to the closest male agnate, namely the paternal uncle.

His statement, “Or a sixth and the remainder, based on six,” means a sixth and what remains. An example is a uterine brother and a paternal uncle. The case is based on six: the uterine brother receives one-sixth, or one, and the remainder goes to the paternal uncle.

It may be proportionally increased to seventeen, an odd number. An eighth together with a sixth or two-thirds is based on twenty-four, and it may be proportionally increased to twenty-seven. If anything remains after the prescribed shares have been allotted and there is no male agnate, it is returned to each prescribed-share heir in proportion to his or her share, excluding the two spouses.

His statement, “It may be proportionally increased to ten, whether even or odd”: it admits deficiency, increase, and equality, and is termed the generous denominator. Thus, it may increase to seven, which is odd; to eight, which is even; to nine, which is odd; and to ten, which is even.

An example of a deficient case is a daughter, a mother, and a paternal uncle. The case is based on six: the daughter receives one-half, or three; the mother receives one-sixth, or one; and the remainder goes to the paternal uncle.

Or, a full sister, a mother, and a paternal uncle. The case is based on six: the full sister receives one-half, or three; the mother receives one-third, or two; and the remainder goes to the paternal uncle.

An example of an equitable case is a deceased person who leaves a husband, a mother, and two uterine brothers. The case is based on six: the husband receives one-half, or three; the mother receives one-sixth, or one; and the two uterine brothers receive one-third, or two. The total is six.

An example of a case subject to proportional reduction: