In the Islamic law of inheritance, the system is known for its precision and fairness, allocating shares of a deceased person’s estate among eligible heirs as ordained in the Qur’an. Yet, real-life situations often do not fit neatly into fixed mathematical divisions. One such situation arises when the estate has more value than the shares assigned to the fixed heirs — and no residual heirs (ʿaṣabah, or agnatic heirs) exist to claim the remainder. In such cases, the remaining wealth is redistributed among the fixed heirs themselves, a process called Radd or reallocation through expansion.

This concept stands in contrast to awl, where the total of prescribed shares exceeds the estate, leading to a proportional reduction in everyone’s share. In Radd, the opposite occurs: since not all the estate is claimed through fixed shares and no other relatives are eligible to inherit, the leftover wealth is re-allocated proportionally to the fixed-share heirs — excluding the spouse, as per scholarly consensus.

Let us illustrate the concept of Radd through a practical example.

Case Example:

A woman passes away, leaving behind:

• One daughter
• Her mother
• Her husband

Let us now assign their original Qur’anic shares:

• Daughter: ½ (when only one daughter and no son)
• Mother: 1/6 (in presence of children)
• Husband: ¼ (in presence of children)

To simplify, take a common denominator of 12 units.

• Daughter receives 6/12
• Mother receives 2/12
• Husband receives 3/12

Total = 6 + 2 + 3 = 11/12

So, 1 unit remains undistributed.

However, there are no residual heirs (like sons, brothers, etc.) to claim this. In such cases, this remaining 1/12 is reallocated to the fixed-share heirs excluding the spouse. So, the husband will retain only his original share and will not receive anything from the surplus.

Step-by-step Redistribution (Radd):

We now distribute the remaining 1 unit between the daughter and the mother based on their original proportions.

• Daughter’s original share: 6
• Mother’s original share: 2
• Total between them = 6 + 2 = 8 parts

Their proportion:

• Daughter: 6/8 = 3/4
• Mother: 2/8 = 1/4

This 3:1 ratio will be used to divide the remaining 1 unit.

To harmonize all shares, multiply the original denominator (12) by 4 (LCM of 4 from 3:1 ratio) → New denominator = 48

Now recalculate all shares:

• Daughter: (6×4) = 24
• Mother: (2×4) = 8
• Husband: (3×4) = 12
• Remaining share: (1×4) = 4

→ Redistribute these 4 units based on the 3:1 ratio:

• Daughter gets 3 out of 4 → 24 + 3 = 27
• Mother gets 1 out of 4 → 8 + 1 = 9

Final Distribution:

• Daughter: 27/48 = 56.25%
• Mother: 9/48 = 18.75%
• Husband: 12/48 = 25%

 Thus, we see:

• The daughter’s share increases from 50% to 56.25%
• The mother’s share increases from 16.66% to 18.75%

This increase — facilitated by Radd — reflects the wisdom of Islamic law in ensuring that no portion of the estate is wasted when deserving recipients exist. It upholds justice while maintaining the clear boundaries of inheritance principles. Radd thus stands as the direct reverse of ‘awl’, where shares are reduced to accommodate more heirs; here, they are increased due to the absence of others.