cases. No inheritance case has a denominator other than one of these. So when does a case have a denominator of two? The author, may Allah have mercy on him, says:

“Two halves, or a half and the remainder, have a denominator of two;
Two-thirds, or a third and the remainder—or both together—have a denominator of three;
A quarter or an eighth, with the remainder or with a half, have a denominator of four or eight.
These four are not subject to proportional reduction;
And a half with two-thirds or a third …”

An example of two halves is where a woman dies leaving a husband and a full sister: two halves, one-half for the husband and one-half for the full sister. Likewise, if she dies leaving a husband and a paternal half-sister, it is two halves.

Examples of a half and the remainder are: a deceased woman leaving a husband and a paternal uncle; a daughter and a paternal uncle; a son’s daughter and a paternal uncle; a full sister and a paternal uncle; or a paternal half-sister and a paternal uncle. These are five cases; there are no others.

His statement, “Two-thirds, or a third and the remainder—or both together—have a denominator of three,” refers to three categories: two-thirds and the remainder, one-third and the remainder, and two-thirds together with one-third. These have a denominator of three.

There are four cases of two-thirds and the remainder: two daughters and a paternal uncle; two son’s daughters and a paternal uncle; two full sisters and a paternal uncle; and two paternal half-sisters and a paternal uncle.

There are two cases of one-third and the remainder: a mother and a paternal uncle, and uterine siblings and a paternal uncle. There are no others.

“Or both together” means two-thirds and one-third: two full sisters and two uterine sisters, or two paternal half-sisters and two uterine sisters. There are no others.

His statement, “A quarter or an eighth, with the remainder or with a half, have a denominator of four or eight”: a quarter and the remainder applies to a wife and a paternal uncle. A quarter together with a half applies to a husband, a daughter, and a paternal uncle; a husband, a son’s daughter, and a paternal uncle; a wife, a full sister, and a paternal uncle,