This chapter completes the calculation engine: what to do when the furudh exceed the estate (‘awl), when the estate has a remainder with no ‘ashabah (radd — including Ibn Uthaymin’s preferred ruling), and when shares don’t divide evenly by head count (tashih).
’Awl: furudh exceed the base number
Sometimes the total of the furudh shares is greater than the base number. The solution is not to strike out one of the heirs, but to raise the base number to the total of the shares — everyone still gets a share, everyone shrinks proportionally. This is the practical ijma’ of the Companions, dating back to a case in the time of Umar ibn al-Khattab.
Example: a husband + 2 full sisters. Husband 1/2 (no descendants) = 3/6; the two sisters 2/3 = 4/6. Total 7 > 6 → the base is ‘awl-raised from 6 to 7: husband 3/7, sisters 4/7 (2/7 each).
Not every base number can undergo ‘awl. Only three can:
| Base | Can rise to | Famous example |
|---|---|---|
| 6 | 7, 8, 9, 10 | Husband + 2 full sisters (→7); the “Mubahalah” case: husband + mother + sister (→8) |
| 12 | 13, 15, 17 | Wife + mother + 2 full sisters (→13) |
| 24 | 27 only | Al-Minbariyyah: wife + father + mother + 2 daughters (→27) — answered by Ali ibn Abi Talib from the pulpit: “her eighth becomes a ninth” (wife 3/27 = 1/9) |
Bases 2, 3, 4, and 8 never undergo ‘awl.
Radd: estate left over, no ‘ashabah
The opposite of ‘awl: the furudh have been paid, the estate still has a remainder, and there is not a single ‘ashabah. The text of Tashil al-Faraidh settles it:
“If, after the furudh, a remainder still exists and there is no ‘ashabah, the remainder is returned (radd) to each owner of a furudh share in proportion to their share — except the husband/wife.”
Two points from that statement:
- Radd is proportional — the remainder is not split evenly, but follows the ratio of each person’s furudh.
- The husband/wife does not receive radd — because their inheritance rests on the marriage bond, which ends at death, not on blood kinship. (This is the majority scholarly opinion held by Ibn Uthaymin; compare: Uthman ibn Affan is reported to have allowed radd to a husband, and the classical Maliki/Shafi’i madhhabs hand the remainder over to the baitul-mal — discussed in chapter 13.)
A practical shortcut without messy fractions: if there is no husband/wife, make the total of the furudh shares the new base number. Example: mother (1/6 = 1 share) + 1 daughter (1/2 = 3 shares) → total 4 → new base 4: daughter 3/4, mother 1/4. Done — the whole estate is distributed.
If there is a husband/wife: pay the spouse’s share from the original base first, then divide the remainder among the radd group in the ratio of their furudh. A fully worked example is in case study 11.
Tashih: shares don’t divide evenly by head count
When a group’s shares don’t divide evenly by its head count (17 shares for 2 sons, 5 shares for 3 sisters, etc.), multiply the whole problem by the smallest number that fixes it — called the juz’us-sahm (the multiplier).
The procedure:
- Count the heads of the group that’s stuck (a male ‘ashabah bil-ghair counts as 2 heads, a female as 1).
- Compare shares vs. heads:
- No common factor (tabayun) → multiplier = the full head count.
- A common factor exists (tawafuq) → multiplier = heads ÷ GCD (called the wafq, “the matching part”).
- Multiply the base number and all shares by that multiplier.
- If more than one group is stuck, combine their multipliers (multiply them together, or take their LCM if they coincide on the same number).
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["Group's shares ÷ heads<br/>whole number?"]:::proses -- yes --> Z["No tashih needed"]:::hasil
A -- no --> B{"GCD(shares, heads)?"}:::proses
B -- "= 1 (tabayun)" --> C["Multiplier = head count"]:::furud
B -- "> 1 (tawafuq)" --> D["Multiplier = heads ÷ GCD"]:::furud
C --> E["Base & all shares × multiplier"]:::hasil
D --> E
Tawafuq example: 2 wives… no — take the classic one: 6 full sisters receive 2/3 of a base of 3 = 2 shares for 6 heads. GCD(2,6) = 2 → multiplier = 6 ÷ 2 = 3 → base 3 × 3 = 9; sisters 2 × 3 = 6 shares → each sister gets 1. (Without tawafuq you’d multiply by 6 and get a larger number than necessary — valid, but not the “most reduced” tashih that faraidh scholars require.)
Order of the three corrections
Always: furudh → (‘awl OR radd — the two can never happen together) → tashih last. ‘Awl and radd change the base number; tashih only multiplies the final result to make it whole.
Sources: Tashil al-Faraidh, bab al-‘awl, ar-radd, wa tashihul-masa’il (Shamela 11095); ash-Sharh al-Mumti’, bab Faraidh; the Al-Minbariyyah case is cited in faraidh texts from the report (athar) of Ali. Full list in 15-references.