Fixed shares (الفروض)

Fixed shares (al-furud, the singular is fardh) are the prescribed Quranic fractions assigned to specific heirs. Every other rule (residuary, blocking, Awl, Radd) works on top of them.

The six fractions

Every fixed-share heir receives one of exactly six fractions, all stated directly in the Quran:

1/2, 1/4, 1/8
2/3, 1/3, 1/6

Most of them come from three verses of Surah An-Nisa: 4:11, 4:12, and 4:176.

Who receives what

Spouse

Husband: 1/2 if no descendants, 1/4 if descendants exist (4:12).
Wife (or wives, sharing): 1/4 if no descendants, 1/8 if descendants exist (4:12).

Parents

Mother: 1/3 normally, reduced to 1/6 if descendants exist or there are 2+ siblings (4:11).
Father: 1/6 when descendants exist; otherwise purely residuary (no fixed share, takes the remainder).

Daughters

One daughter (no sons): 1/2.
Two or more daughters (no sons): together 2/3.
With a son present: residuary, sharing 2:1 with brothers.

Sisters

Same pattern as daughters: one sister gets 1/2, two or more share 2/3, with a brother they're residuary at 2:1.

Maternal half-siblings

One of either gender: 1/6. Two or more (regardless of gender mix): together 1/3, shared equally. Uniquely, male and female maternal half-siblings inherit equal shares.

Fixed doesn't mean guaranteed

"Fixed" doesn't mean "always paid in full." If the sum of fixed shares exceeds the estate, Awl reduces them proportionally. If it falls short and no residuary claims the remainder, Radd redistributes the surplus. And blocking (Hajb) can prevent a heir from receiving anything at all.