Three corrections for the calculation engine. The content is the same across the books (including at-Tahqiqat and al-Mulakhkhash); what matters here is al-Fawzan’s own formulation of radd and practice in its mode of thinking.
‘Awl: furudh exceed the base
Raise the base number to match the total share units — everyone shrinks proportionally, no one is struck out. Only base 6 (→7, 8, 9, 10), 12 (→13, 15, 17), and 24 (→27, the single al-Minbariyyah case) can undergo ‘awl; bases 2, 3, 4, 8 never do.
Quick example: husband (1/2 = 3/6) + 2 full sisters (2/3 = 4/6) → 7/6 → the base becomes 7: husband 3/7, sisters 4/7.
Radd: a remainder with no ‘ashabah
Al-Mulakhkhash al-Fiqhi’s formulation (following the position of Ahmad and Abu Hanifah): when the furudh do not exhaust the estate and no ‘ashabah is present, the remainder is returned to the furudh holders in proportion to each one’s share — except the husband/wife, because their basis for inheriting is marriage, not blood kinship.
Practical method:
- Without a spouse present: the sum of the furudh share units becomes the new base. Mother (1/6=1) + daughter (1/2=3) → base 4: daughter 3/4, mother 1/4.
- With a spouse present: the spouse is paid from their own base (1/4 or 1/8, etc.), then the remainder is divided among the radd group in the ratio of their furudh. Worked in full in chapter 12 case studies.
Tashih: share units stuck at the head count
When a group’s share units do not divide evenly by its head count:
flowchart TB
classDef proses fill:#713f12,stroke:#ca8a04,color:#fef9c3
classDef furud fill:#1e3a8a,stroke:#3b82f6,color:#dbeafe
classDef hasil fill:#3b0764,stroke:#a855f7,color:#f3e8ff
A["shares ÷ heads whole number?"]:::proses -- yes --> Z["done"]:::hasil
A -- no --> B{"GCD(shares, heads)"}:::proses
B -- "= 1 (tabayun)" --> C["multiplier = heads"]:::furud
B -- "> 1 (tawafuq)" --> D["multiplier = heads ÷ GCD (wafq)"]:::furud
C --> E["base & all shares × multiplier<br/>(combine multipliers across groups:<br/>multiply / take the LCM)"]:::hasil
D --> E
Heads are counted male = 2, female = 1 within an ‘ashabah bil-ghair group. Tawafuq example: 6 sisters receive 2 share units → GCD(2,6)=2 → multiplier 3 (not 6) — correct tashih always uses the smallest possible multiplier.
Order
Furudh → (‘awl OR radd) → tashih last. ‘Awl and radd change the base; tashih only rounds off the final result. None of the three ever changes who inherits — only the numbers.
Sources: al-Mulakhkhash al-Fiqhi, Book of al-Faraidh — chapters on al-‘awl and ar-radd (Shamela 11811); at-Tahqiqat al-Mardhiyyah, chapters on al-‘awl, ar-radd, tashihul-masa’il. Full list in 15-references.