Dr. Monzer Kahf, a prominent Muslim economist and counselor, answers: “Allah, Exalted and Glorified be He, mentions in the Qur’an the general cases only, and the details are drawn by us. This is the rule always in the Qur’an and can’t be attributed to a mistake. It is rather the right thing because our religion is founded on trusting human intelligence. It always leaves a great deal of the rulings of Shari’ah to be drawn by human intelligence.
In inheritance, there are two groups of heirs. A share group (called As-hab Al-Fara’id) and a residual group (called As-hab Al-‘Asabah). The shares are given in their general forms as 1/8, 1/6, 1/4, 1/3, 1/2, and 2/3 and the distribution of residual is given as a formula of “a male having twice as much as a female.”
The application of these principles is left to the human intelligence as it always depends on the number of heirs and their relationship to the deceased. In most actual cases there are heirs of the two groups. There are also several cases where the total of shares adds to more (or less) than one. These cases cannot be considered as mistakes because the distribution remains in the same proportion of the shares as given in the Qur’an. The cases that add to more than one are known in Fiqh as cases of “`Awl” which means “reverting to”. In other words, these cases revert to a distribution that maintains the same internal proportions of the given shares although they add up to more than one. It works as in the following examples:
Husband + 2 daughters + one parent: 1/4+2/3+1/6=13/12, shares are distributed out of 13;
Husband + 2 daughters + two parents: 1/4+2/3+1/6+1/6=15/12, shares are distributed out of 15;
Husband + 2 sisters + mother: 1/2+2/3+1/6=8/6, shares are distributed out of 8;
Husband + 2 sisters: 1/2+2/3=7/6, shares are distributed out of 7;
Wife + 2 daughters + two parents: 1/8+2/3+1/6+1/6=9/8, shares are distributed out of 9.
By the same token, human intelligence also works in cases that add up to less than one. This is known in our Fiqh as cases of “Radd” which literally means “rendering” as in the following examples:
One daughter (or one sister) only, alone with no other heirs: 1/2. Remaining 1/2 is rendered back to her;
Two daughters (or sisters) only: 2/3. Remaining 1/3 is rendered back to them;
Wife + 2 sisters + mother: 1/8+2/3+1/6=23/24, (by the way, you quoted this example wrong because when there are sisters mother takes only 1/6 as indicated in 4:11) the remainder is distributed to sisters and mother in the same proportion, no rendering to either husband or wife;
Mother alone, and mother with daughter(s) (or sisters) only, there is always a remainder of two third, one third or one sixth, it is rendered to them proportionally.
These examples indicate that the issue is not a matter of mistakes, but of giving the principles and leaving the numerous details to human intelligence. Only those who are not satisfied by getting principles only and do not want to use human intelligence may think of errors or mistakes!