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When total shares yield improper fraction.

Published: 27/08/2011 06:04:00 PM GMT
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Some non-Muslims are claiming that there is a mathematical error in the Qur'an regarding inheritance. Here is the arithmetic. Acording to the Qur'an, the wife receives 1/4 of the estate, the mother receives 1/3, 2 full sisters receive 2/3 and 3 half-sisters from the mother collectively receive 1/3 (together). Now, we take the lowest common denominator, which is 12... We adjust the numerator to make the fractions equal to their original value. So now the equation is: (3+4+8+4)/12 = 19/12.

Could you please explain this?

Answered by

Sheikh `Abd al-Wahhâb al-Turayrî, former professor at al-Imâm University in Riyadh

There is nothing wrong in the method of calculation. What is happening here is a failure in application and a misunderstanding of the verses in question.

Scholars have divided inheritance matters into three categories: “al-`âdilah” in which both the estate and the inheritors’ shares are equal, “al-`â’ilah” in which the inheritors’ shares are more than the estate, and “al-radd” when the inheritance is more than the inheritors’ shares. All three situations are commonplace and are clearly discernable consequences of the division of the estate outlined in the Qur’ân that anyone will realize form an even cursory reading of the verses. It presented no problem to the Companions at the time of the prophet (peace be upon him) or for anyone who came after them.

What we are dealing with here is the principle in inheritance law known as al-`â’ilah which causes a reduction in the shares across the board for all inheritors.

For example, in case we have the following shares: a half and a two-thirds, this obviously yields seven sixths. Therefore, the shares will be reduced from a sixth of the estate to a seventh of the estate (a smaller share). The party entitled to a half will receive three-sevenths of the estate. The party entitled to two-thirds will receive four-sevenths of the estate. This has been the practice in matters of inheritance since the time of the Prophet (peace be upon him) up until today.

People trying to use this to show a contradiction in the Qur’ân are grasping at straws. They fail to recognize the fact that these rulings were put into practice immediately from the time the verses were revealed without the least problem. They can only advance such a deceptive argument to an audience in the West that is totally unfamiliar with Islamic practices and Muslim history.

Allah says: “If the deceased left brothers, the mother has a sixth”. The term “brothers” here includes any combination of brethren, whether male or female. The mother in the said example deserves a sixth of the inheritance, not a third, due to the existence of sisters.

Let us take the example cited in your question where a man dies leaving behind a wife, a mother, two full sisters, and two half sisters – since this will produce an improper fraction – and discuss what will happen. The calculation will be as follows:

The wife will get quarter, the mother a sixth, the two full sisters two thirds, and the two half sisters a third. The lowest common denominator is 12 as you have mentioned.

Since the inheritors shares cross together, all inheritors will be effected by an even reduction in their shares and, therefore, the denominator 12 will be changed to 17. This is the application of the principle know as al-`â’ilah.

The wife will receive 3/17 instead of 3/12

The mother will receive 2/17 instead of 2/12.

The two full sisters will share in 8/17 instead of 8/12.

The three half sisters 1will share in 4/17 instead of 4/12.

May Allah guide us all, and may His peace and blessings be upon our Prophet, his family, and companions.

Source: Islam Today

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