Ratio of Numbers in Inheritance (Warāthah)Excerpt from the book “Islami Qanun-e-Warāthah” by Maulana Abu Nu’man Basheer Ahmad
❖ Understanding Ratios in Inheritance Calculations
When there are multiple fixed-share heirs (Aṣḥāb al-Furūḍ) in a case of inheritance, the number for rectifying the problem (ʿadad al-taṣḥīḥ) is determined using the four types of numerical ratios, known as:
➊ Tamāthul (تماثل)
➋ Tadākhul (تداخل)
➌ Tawāfuq (توافق)
➍ Tabāyun (تباین)
➊ Tamāthul (Equality)
When two numbers are equal, the relationship is called Tamāthul.
Example: 3 : 3
In such cases, any one of the numbers can be taken as the base of the problem.
Example: If the heirs are a husband and a sister, both receive ½, so the base number becomes 2.
➋ Tadākhul (Inclusiveness / Direct Divisibility)
When one number is smaller and divides the larger exactly, this is called Tadākhul.
Example: 6 : 3
Here, the larger number becomes the base.
Example: If the heirs are a mother and a maternal brother, with shares of ⅓ and ⅙ respectively, then since 6 : 3 is a case of Tadākhul, the base number is 6.
➌ Tawāfuq (Agreement)
When one number is smaller, and does not divide the larger, but there exists a third number that divides both, the ratio is called Tawāfuq.
Example: 8 : 6 (common divisor is 2)
In such cases, use the Wifq (accordance):
- Multiply the wifq of one number by the total of the other.
Example:
Heirs: Husband, Mother, Three Sons, and One Daughter
- Husband: ¼
- Mother: ⅙
- Children: remainder (boys and girl as aṣabah)
→ Between 6 (mother’s base) and 4 (husband’s base), the ratio is Tawāfuq.
- Wifq of 6 is 3, wifq of 4 is 2.
- Multiply: 3 × 4 = 12 or 2 × 6 = 12
→ Base number becomes 12
➍ Tabāyun (Complete Difference)
When neither number divides the other, nor is there a common divisor, the ratio is Tabāyun.
Example: 9 : 7
Here, multiply both numbers together to find the base.
Example:
Heirs: Husband, Mother, and Brother
- Husband: ½
- Mother: ⅓
- Brother: ʿAṣabah
→ 3 : 2 is Tabāyun - Multiply: 3 × 2 = 6
→ Base number becomes 6
❖ Summary Table of Ratios:
Ratio Type Definition Example Method for Finding Base Number Tamāthul Equal Numbers 3:3 Take either number Tadākhul Smaller divides larger 6:3 Use the larger number Tawāfuq Common divisor exists 8:6 Multiply wifq × total of other Tabāyun No common divisor 9:7 Multiply both numbers
| Ratio Type | Definition | Example | Method for Finding Base Number |
|---|---|---|---|
| Tamāthul | Equal Numbers | 3:3 | Take either number |
| Tadākhul | Smaller divides larger | 6:3 | Use the larger number |
| Tawāfuq | Common divisor exists | 8:6 | Multiply wifq × total of other |
| Tabāyun | No common divisor | 9:7 | Multiply both numbers |
