Objection from an atheist to the ‘awl process in cases of inheritance
Question

                This question was put to me by an atheist, who said that there are mathematical errors in the Qur’an – exalted and glorified be Allah above that. If a person dies and the heirs are three daughters, his parents and his wife, the share of the three daughters is two thirds of the estate, based on the verse (interpretation of the meaning): “if (there are) only daughters, two or more, their share is two thirds of the inheritance” [an-Nisa’ 4:11]; the share of the parents is one sixth + one sixth = one third of the estate, “For parents, a sixth share of inheritance to each if the deceased left children” [an-Nisa’ 4:11]; and the wife’s share = one eighth of the estate, “…they get an eighth of that which you leave” [an-Nisa’ 412]. The total number of shares is two thirds for the daughters + one third for the parents + one eighth for the wife = 1.125. … In other words, if the deceased left behind 1000 dinars, the qaadi (judge) would need 1125 dinars to distribute to them according to the Qur’an. This is what this atheist said; I have quoted it to you verbatim. I hope that you can respond to that.
Praise be to Allah.
	This problem that this atheist presented to you is not a 
	problem in reality. The scholars have responded to it. 

	This problem is not limited to the scenario that he 
	mentioned. Rather there are many other similar scenarios. The scholars call 
	this type of issue ‘awl. What it means according to the scholars of 
	inheritance is a case where the sum of the prescribed shares is greater than 
	the inheritance. 

	The way to resolve this kind of issue is to reduce the share 
	of each of the heirs proportionately in each case of ‘awl. This is what is 
	fair, so that no one heir will bear the entire shortfall whilst others lose 
	nothing [that is, they will all be affected equally]. 

	No case of ‘awl occurred at the time of the Prophet 
	(blessings and peace of Allah be upon him) or of Abu Bakr (may Allah be 
	pleased with him). Rather the issue first arose at the time of ‘Umar ibn al-Khattaab 
	(may Allah be pleased with him), and he was the first one to issue a ruling 
	concerning it, when the case was referred to him of a husband and two 
	sisters (either full sisters or sisters through the father). ‘Umar said: 
	Allah has allocated half to the husband and two thirds to the sisters. If I 
	start with the husband, the two sisters will not be able to have their full 
	share, and if I start with the two sisters, the husband will not be able to 
	have his full share. He consulted the Sahaabah concerning that and they 
	suggested the process of ‘awl, comparing it to the case of debts if they are 
	greater than the estate, in which case the estate is to be divided 
	proportionately so that the shortfall is borne by all the creditors. 

	The Muslims adopted that from the time of ‘Umar (may Allah be 
	pleased with him) onwards, then ‘Abdullah ibn ‘Abbaas came up with a 
	different view concerning the issue, as he did not favour the view of ‘awl. 
	… Then this difference of opinion ceased to exist, and all the scholars 
	adopted the view of ‘Umar and the majority of the Sahaabah.

	Ibn Qudaamah (may Allah have mercy on him) said in al-Mughni: 

	Today we do not know of anyone who favours the view of Ibn 
	‘Abbaas (may Allah be pleased with him), and we do not know of any 
	difference of opinion among the contemporary fuqaha’ concerning the issue of 
	‘awl, praise be to Allah. End quote. 

	See: at-Tahqeeqaat al-Mardiyyah fi’l-Mabaahith al-Fardiyyah
	by Shaykh Saalih ibn Fawzaan al-Fawzaan (may Allah preserve him), p. 
	161-166 

	Based on that, the solution to the problem mentioned by that 
	atheist is as follows: 

	The wife gets one eighth, the daughters get two thirds, the 
	father gets one sixth, and the mother gets one sixth. 

	In order to distribute the estate to the heirs, the estate is 
	to be divided into twenty-four equal parts, which is what the scholars call 
	the “basic figure”, which is the lowest number that will allow the shares of 
	inheritance to be represented by whole numbers. This is similar to the issue 
	of finding the lowest common denominator when adding fractions that have 
	different denominators such as one half and one third. 

	If we work out the share of each heir in this case, then the 
	share of the wife, which is one eighth, becomes 3/24; the father and mother 
	each get one sixth, which becomes 4/24; and the daughters get two thirds, 
	which becomes 16/24. The total of these shares is 27/24, which is greater 
	than the basic figure, namely 24. This is the issue of ‘awl, which is what 
	that atheist is objecting to. 

	It is not possible to give each of the heirs his or her share 
	in full, because the estate is not sufficient. In that case, justice 
	dictates that the share of each heir should be reduced commensurate with the 
	shortfall in this scenario. So instead of dividing the estate into 
	twenty-four equal shares, it is divided into twenty-seven equal shares, 
	which is the sum of the shares of all heirs. 

	So the final division will be as follows: 

	The wife gets three out of twenty-seven shares, instead of 
	twenty-four, so the one eighth to which she is entitled becomes one ninth, 
	because of the ‘awl process. 

	Each of the parents gets four shares out of twenty-seven, 
	instead of twenty-four. 

	The daughters get sixteen shares out of twenty-seven, instead 
	of twenty-four. 

	So we find that the shortfall affects the shares of all of 
	the heirs, and thus justice is served and the problem mentioned by this 
	atheist is solved. 

	We would like to take this opportunity to call this person to 
	check himself and reflect upon the path that he is following, and compare it 
	to Islam. He will never find anything more just and better than Islam, for 
	it is the religion of Allah that is preserved from distortion and 
	alteration. Let him look again at the laws of Islam, including this type of 
	inheritance issue, namely ‘awl. He will never find in any other religion 
	that claims to have been divinely revealed, or in any man-made laws, 
	anything more just or better than that. 

	Let him hasten to enter this religion, so that he will be 
	among those who are saved from the punishment and wrath of Allah, and so 
	that he may attain victory after which there will be no loss. 

	We ask Allah to guide him. 

	And Allah knows best.