How is the شبهة (misconception/specious argument) that there are arithmetic errors in the Qur’an regarding the division of inheritance, where the sum of the shares of the heirs (3 daughters, parents, and wife) exceeds the total estate, refuted?

The problem raised by the atheist is not a real problem; it is called "awl" (pro rata reduction), which is when the shares of the heirs exceed the total estate. The way to solve it is to reduce the share of each heir by the amount of the awl, so that the reduction affects everyone. No awl case occurred during the time of the Prophet, peace be upon him, or Abu Bakr. It occurred during the time of Umar ibn al-Khattab, may Allah be pleased with him, whereupon the Companions advised him to apply awl, likening it to debts that exceed the estate and are thus divided proportionally among them. The disagreement over awl has since ceased, and all scholars have returned to what Umar and the majority of the Companions ruled.

To apply this to the aforementioned case: The wife receives one-eighth (3 shares), the daughters receive two-thirds (16 shares), the father receives one-sixth (4 shares), and the mother receives one-sixth (4 shares). The original base of the problem is 24. The total number of shares is 27, which is more than the original base (24), and this is the awl. Instead of dividing the estate into 24 parts, it is divided into 27 parts (the total sum of the heirs' shares). Thus, the wife's share will be 3 out of 27, the parents will each receive 4 out of 27, and the daughters will receive 16 out of 27. In this way, the reduction affects the shares of all heirs, and justice is achieved.