Computation Problems — Sunni Inheritance

Worked Examples | Step-by-Step Method | 15+ Scenarios | Exam Preparation

AT A GLANCE

This topic PROVIDES WORKED EXAMPLES of Sunni Muslim inheritance calculations — from simple configurations to complex Aul and Radd scenarios. Mastering the computation method is essential for judicial services examinations, where inheritance problems are frequent and require systematic application of the Sharer-Residuary-Distant Kindred framework along with Aul and Radd doctrines.

THE FIVE-STEP METHOD: (1) IDENTIFY all heirs and classify them (Sharer / Residuary / Distant Kindred / Excluded); (2) ASSIGN Quranic shares to Sharers based on configuration (child presence, siblings, etc.); (3) CHECK total — compare sum of Sharers to unity; (4) APPLY Aul if sum > 1, Radd if sum < 1 and no Residuary, straightforward residue if sum < 1 with Residuary; (5) CALCULATE actual amounts using the estate value.

The fifteen worked examples in this topic cover: simple single-generation cases (wife + son), spouse + multiple classes configurations, Umariyatan adjustments, Aul cases with various denominators (6, 12, 24), Radd cases (with and without spouse), Residuary-by-Another transformations, Residuary-With-Another scenarios, Distant Kindred situations, and mixed complex configurations. Each example shows the step-by-step method applied systematically.

1. The Five-Step Computation Method

Step 1 — Identify and Classify Heirs

List all surviving relatives of the deceased. For each, determine:

Is he / she a SHARER from the 12 classical list? (Husband, wife, father, mother, true grandfather, true grandmother, daughter, son's daughter, full sister, consanguine sister, uterine brother, uterine sister.)
Is he / she a RESIDUARY (male agnatic relative or a female whose status transforms)?
Is he / she DISTANT KINDRED (inherits only in default of Sharers + Residuaries)?
Is he / she EXCLUDED (predeceased, homicide, different religion, displacement by nearer heir)?

Step 2 — Assign Quranic Shares

For each Sharer, determine the fractional share based on configuration:

Husband: 1/2 (no child) or 1/4 (with child).
Wife: 1/4 (no child) or 1/8 (with child).
Father: 1/6 (with child) or Residuary.
Mother: 1/6 (child or 2+ siblings) or 1/3 (otherwise).
Umariyatan: Husband/Wife + Mother + Father — mother 1/3 of RESIDUE.
Daughter: 1/2 (one) or 2/3 (two+); Residuary-by-Another with son.
Son's daughter: 1/2 / 2/3 / 1/6 with daughter; excluded by son; by 2+ daughters.
Full sister: 1/2 (one) / 2/3 (two+); Residuary-by-Another with full brother; Residuary-With-Another with daughter.
Uterine siblings: 1/6 (one) or 1/3 shared; equal, no 2:1.

Step 3 — Sum Sharer Shares

Express all Sharer shares with a COMMON DENOMINATOR. Sum the numerators. Compare to the denominator:

Sum = denominator: exactly 1. No Aul, no residue.
Sum > denominator: Aul required.
Sum < denominator: Residue exists; goes to Residuary if any; else Radd.

Step 4 — Apply Aul or Find Residue

If Sum > denominator: AUL. New denominator = sum of numerators. Each Sharer's share: original numerator / new denominator.
If Sum = denominator: No adjustment. Sharers take exactly their fractional share.
If Sum < denominator: Residue = (denominator - sum) / denominator. Residuary takes residue. If no Residuary, apply Radd (Sunni: spouse excluded).

Step 5 — Calculate Actual Amounts

Convert each heir's fractional share to actual rupee amount:

Heir's amount = Heir's fraction × Estate value.
Check: sum of all heirs' amounts = Estate value.

2. Example 1 — Simple: Wife + Son

Facts

Deceased Muslim man leaves: Wife + 1 Son. Estate: Rs. 8,00,000 (after funeral, debts, no bequest).

Step 1 — Classify

Wife: Sharer.
Son: Residuary-in-Own-Right.

Step 2 — Assign Shares

Wife: 1/8 (child exists).
Son: Residuary (residue).

Step 3 — Sum

Sharer sum: 1/8. Much less than 1. Son (Residuary) takes residue 7/8.

Step 4 — Residue

No Aul needed. Son takes 7/8.

Step 5 — Amounts

Wife: 1/8 × Rs. 8,00,000 = Rs. 1,00,000.
Son: 7/8 × Rs. 8,00,000 = Rs. 7,00,000.

Total: Rs. 1,00,000 + Rs. 7,00,000 = Rs. 8,00,000. ✓

3. Example 2 — Wife + 1 Son + 1 Daughter

Facts

Estate: Rs. 12,00,000.

Step 1 — Classify

Wife: Sharer.
Son: Residuary-in-Own-Right.
Daughter: Residuary-by-Another (transformed by son's presence).

Step 2 — Assign Shares

Wife: 1/8 (child exists).
Son + Daughter: Residuaries; take residue together in 2:1 ratio.

Step 3 — Sum

Sharer: Wife 1/8. Residue: 1 - 1/8 = 7/8.

Step 5 — Amounts

Wife: 1/8 × Rs. 12,00,000 = Rs. 1,50,000.
Residue: Rs. 10,50,000. Divided 2:1 (son:daughter).
Son: 2/3 × Rs. 10,50,000 = Rs. 7,00,000.
Daughter: 1/3 × Rs. 10,50,000 = Rs. 3,50,000.

Total: Rs. 1,50,000 + Rs. 7,00,000 + Rs. 3,50,000 = Rs. 12,00,000. ✓

4. Example 3 — Husband + Mother + Father (Umariyatan)

Facts

Deceased Muslim woman leaves: Husband + Mother + Father. No children, no siblings. Estate: Rs. 12,00,000.

Step 1 — Classify

Husband: Sharer.
Mother: Sharer (Umariyatan configuration).
Father: Residuary (no child exists).

Step 2 — Umariyatan Adjustment

Husband + Mother + Father — Umariyatan triggered.

Husband: 1/2 = Rs. 6,00,000.
Residue: 1/2 = Rs. 6,00,000.
Mother: 1/3 of RESIDUE (not of total) = 1/3 × 1/2 = 1/6 of total = Rs. 2,00,000.
Father: Rest of residue = 2/3 of residue = 1/3 of total = Rs. 4,00,000.

Verification: Rs. 6,00,000 + Rs. 2,00,000 + Rs. 4,00,000 = Rs. 12,00,000. ✓

5. Example 4 — Wife + Mother + Father (Umariyatan)

Facts

Deceased man leaves: Wife + Mother + Father. No children. Estate: Rs. 12,00,000.

Umariyatan Calculation

Wife: 1/4 = Rs. 3,00,000.
Residue: 3/4 = Rs. 9,00,000.
Mother: 1/3 of residue = 1/3 × 3/4 = 1/4 of total = Rs. 3,00,000.
Father: 2/3 of residue = 1/2 of total = Rs. 6,00,000.

Verification: Rs. 3,00,000 + Rs. 3,00,000 + Rs. 6,00,000 = Rs. 12,00,000. ✓

6. Example 5 — Aul (Husband + 2 Full Sisters)

Facts

Deceased woman leaves: Husband + 2 Full Sisters. No parents, no children. Estate: Rs. 7,00,000.

Step 1-2 — Classify and Shares

Husband: 1/2 (no child).
2 Full Sisters: 2/3 shared (as Sharers).

Step 3 — Sum

Common denominator 6. Husband 3/6; Sisters 4/6. Sum: 7/6. Sum > 1. AUL required.

Step 4 — Apply Aul

New denominator = 7 (sum of numerators). Each share / 7.

Husband: 3/7.
Each Sister: 2/7.

Step 5 — Amounts

Husband: 3/7 × Rs. 7,00,000 = Rs. 3,00,000.
Each Sister: 2/7 × Rs. 7,00,000 = Rs. 2,00,000.

Total: Rs. 3,00,000 + Rs. 2,00,000 + Rs. 2,00,000 = Rs. 7,00,000. ✓

7. Example 6 — Aul from 12 (Husband + Mother + 2 Daughters)

Facts

Deceased woman leaves: Husband + Mother + 2 Daughters. No father. Estate: Rs. 13,00,000.

Step 1-2 — Classify and Shares

Husband: 1/4 (children exist).
Mother: 1/6 (children exist).
2 Daughters: 2/3 shared.

Step 3 — Sum

Common denominator 12. Husband 3/12; Mother 2/12; Daughters 8/12. Sum: 13/12 > 1. AUL.

Step 4 — Apply Aul

New denominator = 13. Each share / 13.

Husband: 3/13.
Mother: 2/13.
Each Daughter: 4/13.

Step 5 — Amounts

Husband: 3/13 × Rs. 13,00,000 = Rs. 3,00,000.
Mother: 2/13 × Rs. 13,00,000 = Rs. 2,00,000.
Each Daughter: 4/13 × Rs. 13,00,000 = Rs. 4,00,000.

Total: Rs. 3,00,000 + Rs. 2,00,000 + Rs. 4,00,000 + Rs. 4,00,000 = Rs. 13,00,000. ✓

8. Example 7 — Aul from 24 (Wife + Father + Mother + 2 Daughters)

Facts

Deceased man leaves: Wife + Father + Mother + 2 Daughters. Estate: Rs. 27,00,000.

Wife: 1/8 (children exist).
Father: 1/6 (children exist).
Mother: 1/6 (children exist).
2 Daughters: 2/3 shared.

Sum

Common denominator 24. Wife 3/24; Father 4/24; Mother 4/24; Daughters 16/24. Sum: 27/24 > 1. AUL.

Apply Aul to /27

Wife: 3/27.
Father: 4/27.
Mother: 4/27.
Each Daughter: 8/27.

Amounts

Wife: Rs. 3,00,000.
Father: Rs. 4,00,000.
Mother: Rs. 4,00,000.
Each Daughter: Rs. 8,00,000.

Total: Rs. 3 + 4 + 4 + 8 + 8 = Rs. 27 lakh. ✓

9. Example 8 — Radd (Daughter Only)

Facts

Deceased leaves: Only Daughter. No spouse, no parents, no siblings. Estate: Rs. 6,00,000.

Daughter: 1/2 (alone) as Sharer.
No Residuary.
Surplus: 1/2.

Apply Radd

Sunni Radd — surplus returns to Sharers. Only Sharer is daughter. Daughter takes 1/2 Quranic share + 1/2 Radd = entire estate.

Amount

Daughter: Rs. 6,00,000 (entire estate).

10. Example 9 — Radd (Mother + Daughter)

Facts

Estate: Rs. 12,00,000. No spouse, no father, no son.

Mother: 1/6 (child exists).
Daughter: 1/2.
No Residuary.
Sum: 1/6 + 1/2 = 2/3.
Surplus: 1/3 = Rs. 4,00,000.

Apply Radd

Both Mother and Daughter are Sharers; no spouse to exclude. Surplus distributed in proportion to Quranic shares.

Mother's share ratio: 1/6 ÷ 2/3 = 1/4.
Daughter's share ratio: 1/2 ÷ 2/3 = 3/4.
Mother's Radd portion: 1/4 × Rs. 4,00,000 = Rs. 1,00,000.
Daughter's Radd portion: 3/4 × Rs. 4,00,000 = Rs. 3,00,000.

Final Amounts

Mother: Rs. 2,00,000 (Quranic) + Rs. 1,00,000 (Radd) = Rs. 3,00,000.
Daughter: Rs. 6,00,000 (Quranic) + Rs. 3,00,000 (Radd) = Rs. 9,00,000.

Total: Rs. 12,00,000. ✓

11. Example 10 — Radd with Spouse Exclusion (Wife + Mother)

Facts

Deceased husband leaves: Wife + Mother. No children, no father, no siblings. Estate: Rs. 12,00,000.

Wife: 1/4 (no child).
Mother: 1/3 (no child, no 2+ siblings).
Sum: 1/4 + 1/3 = 3/12 + 4/12 = 7/12.
Surplus: 5/12.

Sunni Radd — Spouse Excluded

Surplus returns only to blood Sharers. Wife is excluded from Radd. Mother is the only eligible Sharer; she takes entire surplus.

Mother's Radd: 5/12 = Rs. 5,00,000.

Final Amounts

Wife: Rs. 3,00,000 (Quranic 1/4 only).
Mother: Rs. 4,00,000 (Quranic 1/3) + Rs. 5,00,000 (Radd) = Rs. 9,00,000.

Total: Rs. 12,00,000. ✓

12. Example 11 — Husband + Daughter + Full Sister (Residuary-With-Another)

Facts

Deceased woman leaves: Husband + 1 Daughter + Full Sister. No other heirs. Estate: Rs. 12,00,000.

Classification

Husband: Sharer.
Daughter: Sharer (no son of deceased to transform her).
Full Sister: Residuary-With-Another (inheriting with daughter).

Husband: 1/4 (child exists).
Daughter: 1/2 (alone Sharer, no son).
Full Sister: Residue.
Sum of Sharers: 1/4 + 1/2 = 3/4. Residue: 1/4.

Amounts

Husband: 1/4 × Rs. 12,00,000 = Rs. 3,00,000.
Daughter: 1/2 × Rs. 12,00,000 = Rs. 6,00,000.
Full Sister: 1/4 × Rs. 12,00,000 = Rs. 3,00,000 (as Residuary-With-Another).

Total: Rs. 3,00,000 + Rs. 6,00,000 + Rs. 3,00,000 = Rs. 12,00,000. ✓

13. Example 12 — Husband + Mother + Full Brother

Facts

Deceased woman leaves: Husband + Mother + Full Brother. No father, no children. Estate: Rs. 12,00,000.

Husband: 1/2 (no child).
Mother: 1/3 (no child, only one sibling — full brother counts as one).
Wait — mother's share depends on sibling count. 1 sibling → mother still gets 1/3. (Reduction to 1/6 requires 2+ siblings.)
Full Brother: Residuary.
Sum of Sharers: 1/2 + 1/3 = 5/6. Residue: 1/6.

Amounts

Husband: 1/2 × Rs. 12,00,000 = Rs. 6,00,000.
Mother: 1/3 × Rs. 12,00,000 = Rs. 4,00,000.
Full Brother: 1/6 × Rs. 12,00,000 = Rs. 2,00,000 (as Residuary-in-Own-Right Class III).

Total: Rs. 12,00,000. ✓

14. Example 13 — Wife + Mother + 2 Full Brothers + 2 Full Sisters

Facts

Deceased man leaves: Wife + Mother + 2 Full Brothers + 2 Full Sisters. No father, no children. Estate: Rs. 18,00,000.

Wife: 1/4 (no child).
Mother: 1/6 (2+ siblings present).
Full Brothers + Full Sisters: Residuaries (siblings as Residuary-by-Another or joint Residuary).

Calculation

Wife 3/12 + Mother 2/12 = 5/12. Residue: 7/12.
Residue divided among siblings — 2 brothers + 2 sisters (2:1 ratio, so 6 shares — each brother 2 shares, each sister 1 share).
Each brother: 2/6 × 7/12 = 7/36.
Each sister: 1/6 × 7/12 = 7/72.

Amounts

Wife: 3/12 × Rs. 18,00,000 = Rs. 4,50,000.
Mother: 2/12 × Rs. 18,00,000 = Rs. 3,00,000.
Each Brother: 7/36 × Rs. 18,00,000 = Rs. 3,50,000.
Each Sister: 7/72 × Rs. 18,00,000 = Rs. 1,75,000.

Total: Rs. 4,50,000 + Rs. 3,00,000 + Rs. 7,00,000 + Rs. 3,50,000 = Rs. 18,00,000. ✓

15. Example 14 — Distant Kindred (Wife + Daughter's Son)

Facts

Deceased husband leaves: Wife + Daughter's Son. No other heirs. Estate: Rs. 8,00,000.

Classification

Wife: Sharer.
Daughter's Son: Distant Kindred (Sub-Class 1).
No Residuary.

Wife: 1/4 (no Sharer-child; daughter's son doesn't reduce wife's share).
Daughter's Son: takes residue as Distant Kindred (wife as spouse doesn't exclude DK).

Amounts

Wife: 1/4 × Rs. 8,00,000 = Rs. 2,00,000.
Daughter's Son: 3/4 × Rs. 8,00,000 = Rs. 6,00,000.

16. Example 15 — Complex: Husband + Mother + 1 Daughter + Son's Daughter

Facts

Deceased woman leaves: Husband + Mother + 1 Daughter + Son's Daughter. Estate: Rs. 12,00,000.

Husband: 1/4 (children exist).
Mother: 1/6 (children exist).
Daughter: 1/2 (alone as daughter-Sharer).
Son's Daughter: 1/6 (to complete the 2/3 daughter quota — daughter 1/2 + son's daughter 1/6 = 2/3).
No Residuary.

Sum

Common denominator 12. Husband 3/12 + Mother 2/12 + Daughter 6/12 + Son's daughter 2/12 = 13/12 > 1. AUL.

Apply Aul to /13

Husband: 3/13.
Mother: 2/13.
Daughter: 6/13.
Son's Daughter: 2/13.

Amounts

Husband: 3/13 × Rs. 12,00,000 ≈ Rs. 2,76,923.
Mother: 2/13 × Rs. 12,00,000 ≈ Rs. 1,84,615.
Daughter: 6/13 × Rs. 12,00,000 ≈ Rs. 5,53,846.
Son's Daughter: 2/13 × Rs. 12,00,000 ≈ Rs. 1,84,615.

17. Computation Quick Reference Table

Scenario	Method	Key Notes
Spouse + child + Residuary	Spouse Sharer + Residue	Spouse reduced share (1/8 or 1/4) with child
No spouse, Residuary present	Sharers' Quranic + Residue to Residuary	Father Residuary if no male descendant
Husband/Wife + Mother + Father	Umariyatan — mother 1/3 of residue	Preserves father's superior share
Shares exceed 1	AUL — new denominator = sum of numerators	Common: 6→7,8,9,10; 12→13,15,17; 24→27
Shares < 1, no Residuary, no DK	RADD — surplus to Sharers proportionally	Sunni: spouse EXCLUDED from Radd
Shares < 1, no Residuary, DK present	Radd to Sharers; DK after (often excluded)	Spouse + DK scenario — spouse + DK both take
Daughter + son	Daughter Residuary-by-Another with son (2:1)	Daughter loses Sharer status
Daughter + full sister	Daughter Sharer 1/2 + Sister Residuary-With-Another	Sister honorary Residuary
Only daughter, no spouse	Daughter 1/2 + Radd 1/2 = entire estate	Classical Radd application

XVIII. Common Exam Scenarios

Scenario 1 — Simple Family

Spouse + children + parents. Apply Quranic shares; residue to Residuary descendants (sons) or Residuary-by-Another (with daughters + sons).

Scenario 2 — No Children

Spouse + parents + siblings. Apply Umariyatan if spouse + both parents. Siblings as Residuaries.

Scenario 3 — Aul Triggered

Husband + mother + daughters / sisters. Often produces sum > 1. Apply Aul systematically.

Scenario 4 — Radd Required

Daughters without sons, no spouse. Daughters' shares total 1/2 or 2/3; surplus returns.

Scenario 5 — Distant Kindred

Only spouse (optional) + distant relative (daughter's son, maternal aunt, etc.). Classical narrow-gateway rule applies.

XIX. Exam Corner

RAPID-FIRE COMPUTATION FACTS

5-Step Method: Classify → Assign Shares → Sum → Aul/Radd/Residue → Amounts.

Common denominators: 6, 12, 24.

Aul denominators: 6→7/8/9/10; 12→13/15/17; 24→27.

Umariyatan: mother 1/3 of residue when spouse + mother + father present.

Husband 1/2 no child; 1/4 with child.

Wife 1/4 no child; 1/8 with child.

Mother 1/3 normal; 1/6 with child or 2+ siblings.

Father 1/6 with child; Residuary without male descendant.

Daughter 1/2 alone; 2/3 two+; Residuary-by-Another with son.

Son's daughter 1/6 with daughter (completes 2/3); excluded by son.

Full sister Residuary-With-Another with daughter.

Sunni Radd — spouse excluded.

Daughter alone + Radd = entire estate.

Daughter's son = Distant Kindred Sub-Class 1.

Always verify: total must equal estate.

When in doubt: common denominator + sum check + Aul/Radd application.

Practice Questions

A Muslim dies leaving wife, mother, father, and 2 daughters. Estate Rs. 24 lakh. Calculate shares. (10 marks)
Deceased leaves husband and 2 full sisters. Estate Rs. 7 lakh. Show Aul application. (10 marks)
A Muslim widow has only one daughter surviving. Estate Rs. 6 lakh. Calculate shares under Radd. (10 marks)
Deceased leaves wife, mother, and 2 daughters. Estate Rs. 13 lakh. Apply 5-step method. (15 marks)
Compare the computation under Sunni Aul vs Shia No-Aul for: Husband + Mother + 2 Daughters. Estate Rs. 12 lakh. (15 marks)
A Muslim woman dies leaving husband, mother, father, 1 daughter, 1 son's daughter. Estate Rs. 13 lakh. Calculate. (15 marks)
MCQ: A Muslim dies leaving wife + 1 son + 1 daughter; estate Rs. 8 lakh. Wife's share is — (a) Rs. 1,00,000 (b) Rs. 2,00,000 (c) Rs. 50,000 (d) Rs. 4,00,000. Answer: (a).
MCQ: Husband + 2 full sisters; estate Rs. 7 lakh. Aul denominator is — (a) 6 (b) 7 (c) 12 (d) 24. Answer: (b).
MCQ: Deceased leaves only daughter; estate Rs. 6 lakh. Daughter's share under Sunni law is — (a) Rs. 3,00,000 (b) Rs. 4,00,000 (c) Rs. 6,00,000 (d) Rs. 2,00,000. Answer: (c) (after Radd).

XX. Conclusion

Muslim inheritance computation, though appearing complex at first glance, yields to a SYSTEMATIC 5-STEP METHOD: classify heirs, assign Quranic shares, sum shares, apply Aul / Radd / Residue rules, and calculate actual amounts. The fifteen worked examples in this topic cover the full range of scenarios examiners typically set — simple configurations, Umariyatan adjustments, Aul cases with various denominators, Radd with and without spouse, Residuary-by-Another transformations, Residuary-With-Another mechanics, and Distant Kindred situations.

For the judicial aspirant, three anchors secure computation mastery. First, memorise the 12 Sharers' basic shares and configuration triggers. Second, recognise Umariyatan cases immediately (spouse + mother + father without children). Third, check sum of Sharers at each problem — if > 1, Aul; if < 1 and no Residuary, Radd (spouse excluded in Sunni). With practice, even complex configurations become tractable — and examination problems are DESIGNED to yield to the systematic application of classical rules. Topic 77 focuses specifically on women's inheritance rights (daughter, wife, mother); Topic 78 details exclusion and partial exclusion rules; Topic 79 addresses posthumous and illegitimate children; Topic 80 completes the succession framework with escheat.

XXI. Frequently Asked Questions

Q1. What is the 5-step method for Muslim inheritance computation?

(1) Classify each heir — Sharer / Residuary / Distant Kindred / Excluded; (2) Assign Quranic shares to Sharers based on configuration; (3) Sum Sharer shares (find common denominator); (4) Apply Aul if sum > 1, Radd if sum < 1 with no Residuary, simple residue if Residuary exists; (5) Calculate actual rupee amounts from the estate value. Always verify total = estate.

Q2. When does Umariyatan apply?

In two specific configurations: (1) Husband + Mother + Father (deceased woman); (2) Wife + Mother + Father (deceased man). In both cases, the mother takes 1/3 of the RESIDUE (not of the total). Without this adjustment, the mother would get more than the father — contrary to the classical male-preference rule. Attributed to Caliph Umar.

Q3. What are the common Aul denominators?

Classical Hanafi recognises three Aul families: (1) Aul from 6 → 7, 8, 9, 10 (denominator 6 when shares are multiples of 1/2, 1/3, 1/6); (2) Aul from 12 → 13, 15, 17 (with 1/4 and 1/12 components); (3) Aul from 24 → 27 (with 1/8). Learn the families; specific denominators follow from the configuration.

Q4. What are the most common exam configurations?

Typical: (i) Spouse + children + parents (requires child-presence adjustment); (ii) Spouse + mother + father (Umariyatan); (iii) Husband + sisters (often Aul); (iv) Wife + mother (Radd); (v) Only daughter (Radd returns entire estate); (vi) Son + daughter (Residuary-by-Another 2:1); (vii) Daughter + full sister (Residuary-With-Another).

Q5. How do I verify my calculation is correct?

After calculating all individual amounts, SUM them. The sum must equal the estate value. If it doesn't, review: (a) Correct configuration-based share assignment? (b) Correct Aul denominator or Radd application? (c) Correct Residuary identification? (d) Correct treatment of spouse in Radd (Sunni: excluded)?

Q6. What's the difference between Sharer and Residuary?

SHARER has a FIXED QURANIC SHARE (1/2, 1/3, 1/4, 1/6, 1/8, 2/3). RESIDUARY has NO fixed share — takes whatever remains after Sharers. In a configuration, a person may be BOTH: father is Sharer (1/6) with a child AND Residuary in some other configurations. Daughter is Sharer alone but becomes Residuary-by-Another with a son (her Sharer share is displaced; she takes residue 2:1 with son).

Q7. When should I apply Radd vs Aul?

AUL when shares EXCEED unity (sum > 1). RADD when shares are LESS THAN unity (sum < 1) AND no Residuary exists to take the residue. Aul reduces shares proportionally; Radd returns surplus to Sharers (Sunni: spouse excluded). If sum = 1 exactly, no adjustment — sharers take exactly their Quranic share; no residue.