Alleged Mathematical Error in the Qur'anic Law of Inheritance

Question:
I appreciate the rationalistic spirit with which you approach the Quran. On the basis of this appreciation, I am asking for your help concerning the allegation that there is a mathematical error in Quran's allocation of inheritance. The allegation is that when a man dies leaving three daughters, one wife, one mother and one father the shares Quran gives exceeds 1 and hence there is a mathematical error.

The shares according to Quran are:
2/3 daughters, 1/6 mother, 1/6 father, 1/8 wife
If you add these you get 1.25 instead of 1 which is really a big problem. Not enough inheritance would exist to distribute to all these people!!!

Some have suggested that the denominators of these shares should be equalized and new shares should be created accordingly (the so-called AVL method). When we equalize the denominator (for example when we make 24 denominator for each) we get 16/24, 4/24, 4/24, 3/24.
These people suggest that we then neglect the denominator and solve for X in 16X + 4X + 4X + 3X= Total Inheritance. If inheritance is 27 golds, for example, then three daughters would get 16, mother would get 4, father would get 4, and wife would get 3. While this may be a pragmatic solution, we are kind of changing the Quranic formula a bit arbitrarily (although not totally arbitrarily but still arbitrarily). For example, we are giving three daughters 16 whereas they should get 18 because the verse clearly and literally states that three daughters should get 2/3 of the total inheritance. 2/3 of 27 should have been 18. Above all, the Quran is giving shares with respect to the whole inheritance and to analyze the shares with respect to each other has no linguistic Quranic background

Some other solutions have been suggested but I think problem still remains awaiting that rational Muslims give serious consideration for it. This issue has impacted me severely and I am on the edge of losing my belief in Quran. In my view, God cannot have made a mathematical error to leave it to humans to correct it with a method that they invented. I would appreciate your help.

Response:
My mentor, Javed Ahmad Ghamidi, had a similar problem more than three decades ago as you are going through now. However, since he had the gift of proper understanding of the classical Arabic, he solved the problem in the following manner: The parents and the widow are going to get their respective shares from the total inheritance. It’s only then the left over inheritance shall be available for the sons and daughters. Going by this understanding, there will be some amount still left, which, according to Quran, can either be willed to be distributed in some charitable avenue or another relative (kalala) can be appointed to receive that amount.

Suppose an individual leaves twenty-four units, his widow shall receive 3 units (1/8th) and the parents 4 units (1/6th) each. From the thirteen units left, daughters shall be eligible to get 2/3rd and the 1/3rd can either be willed or a close relative (kalala) can also be appointed for the purpose.

I hope it helps.

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