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Being able to give the whole inheritance algorithm with only 2 verses is such a simple thing for Almighty Allah, who has created the whole universe with measurements and with infinite knowledge.

In fact, while only the verses 11 and 12 of surah Nisa are sufficient, people had difficulties in calculating in some special situations and demanded further explanations, Almighty Allah sent the third verse (176) for extra clarifications.

Among my explanations, I will include the reasons for people’s misunderstandings of those verses.

One very important fact: The spouse (wife or husband) is not an heir of the deceased, but he or she is a contractual obligation/liability. Thus, the share of the spouse as per verse 12 must be given first before distributing the tereke to the heirs.

The charts are made in case a married man passes away. We ca use these charts also for the case when a married woman passes away. The only difference is; if the deceased had chil(ren), his husband would receive 1/4 and or if she had no child then the husbad will receive 1/2. The rest is the same.

First of all, I want to emphasize a very important point. The Quran is written in clear Arabic. But the Qur'an is also written in another language: The Universal Language. The only universal language available to us is the "mathematics", and this is why the entire universe has been created to an unfailing measure, and the Qur'an is invariably filled with mathematics, which is the ancestor of all sciences.
My explanations are a detailed review of mathematics language and show us how fair and equitable is Almighty Allah; such that daughters and sons have equal shares when girls/boys ratio is equal or less than 1. With this provision being made, in principle, daughters and sons or sisters and brothers have equal share rights, and only when the ratio of boys to girls increases in favour of girls, only with this condition a situation in favour of a son or brother is created. The explanation of the reason for these changing rates in favour of men is given in the 34th verse of Nisa.
One of the problems with inheritance is that, nobody realized to who is the addressee of those verses, especially verse nr 176. This will be explained under the relevant verse. The same addressing problem exists in verse 11: The addressee is the closest remaining male heir (either son or brother). You will understand as you read the extensive explanations given earlier. 
Another problem people face is the following: they fail to realize the integrity of the verse and perceive it piece by piece and think that one such piece is unmistakably true. Because if it is read that way, for example, according to the 4th verse of the chapter Muhammad, you will have to stab all the deniers because the verse begins with these sentences. However, we see throughout the verse that this command is valid only in war and up to a certain situation. Hence, it is obvious that it is not correct by taking a part of the verse and to say "it is always like this" after cropping it out of the verse. Similar problem emerged in the 11th verse of the chapter of Nisa.
By reading "boy gets as much as the share of 2 girls…” and then saying "This is always like this" by breaking its integrity with the rest of the verse is an example of the error in the 4th verse of the chapter of Muhammad. If we read carefully and rationally with the same “subject”, the judgment that will come is this:
 "The boy gets two girls’ shares, can be true and correct if and only if there are two girls against 1 boy.
                 if there are more than 2 girls then a boy gets 1/3, the girls share the 2/3 equally.
                               if there is only one girl and one boy then boy gets half and the second half is for the girl.
 In any case, distribution among heirs will be made after fulfilling of the contractual obligations/debts of the deceased. So, the "remainders" after such fulfilment is called the "taraka" to be distributed among the heirs. 
From this stand point, the word tereke is different from the wealth of the deceased "heritage. Taking the word tereke as "full heritage" breaks the integrity and perfection of the detailed examples. It is seen that one of the main problems originates from this word.
Another problem is the “kalala” drama. Almost everyone uses this word as “no mother, no father and no child” situation. A small number of others read it as "without father and son". However, this word would have to mean "if both parents are dead”. Otherwise, it would have been impossible to construct a sentence in verse 176 like this: “In the case of Kelale… If the deceased has no children…”, because if "kelale" had the meanings I said wrong above, it would not be possible for someone who does not have children to say again "if they don't have children" separately and repeatedly -twice. As an additional confirmation, I will also put a numerical proof under the 12th verse for "kelale".
Let's examine the verses one by one and see how, when understood correctly, an algorithm as easy as a computer program can be created, and also that no possibilities are left out.

Nisa 7 reads: There is a share for men in what their parents and relatives leave (as an inheritance).. There is also a share for women in what their parents and relatives leave (as an inheritance). It is a share determined (by Allah) small or big (from what is inherited).

According to this verse, the direct heirs of the inheritor of a woman and/or man can only be their relatives. Those who are in the first degree are 1. Children 2. Mother 3. Father 4. Siblings. In this way, apart from the distribution verses, some other verses explain who the “direct heirs” are.

When we look at the 11th verse below, if the deceased has children and both father and mother (the parents) are alive, there is no direct share for the siblings of the deceased. In such a case, the share of the siblings will be transferred to them only when the mother or father dies.

If a child who would normally be a heir has already died earlier and he had children, these children (or grandchildren) also inherit the share of their deceased parents at the rates specified in these verses. This situation is applied in the same way if the mother and/or father have died; The shares that should be left to the mother and/or father are also re-distributed according to these verses.

The issue that people have difficulty in solving and calculating the distribution that I have written above is, how the remaining inheritance will be distributed to the siblings in the case where "both parents (both mother and father) of the deceased were already dead and he have never had any child" has been decreed in verse 176.

Nisa 8 reads: If relatives, orphans and the needy are present at/during the (inheritance) distribution, let them benefit (from the inheritance) and speak kindly to them.

It goes without saying what a beautiful and humane piece of advice it is. The Quran system is already based on sharing, helping and justice.

Nisa 11 reads: Regarding your children Allah advises you to give sons the shares of two daughters. If she (girls) is more than two, two-thirds are their right. If the (girl) is only one, half is hers. If the (inheritor) has children, each parent receives a sixth share. If (the deceased) has no children and the parents are is his heirs, the mother receives one-third. If (the deceased) has siblings, the mother gets one sixth. All this happens after the deceased's will is fulfilled and his debts are paid. Your fathers and sons! You don't know which one is closer to you in benefit. (These shares) have been determined by Allah as fard. Undoubtedly, Allah is the Alim and Hakim.

This verse 11 is addressed to the first-degree heirs as indicated by verse 7. The phrase "after wills and debts" added means "the remainder will be distributed among heirs", and thus the word "taraka" does not correspond to the "full inheritance" as all the wealth of the deceased.

The verse is in two parts: first, the ratio of the children is given by gender, then the parents' shares are given, and if there are no children, a share is allocated from the mother to the siblings.

The important point that should not be missed is that the decree in each part of a verse is the continuation of the previous one, because when they are taken as a separate decree, there is nothing logical to be shared.

The equivalent of the verse in the language of mathematics and also in computer programming is:

If all the children are all girls (or all boys), the remainder will be divided equally among them. Even making a statement on this matter would be meaningless. However, if the children consist of both boys and girls, then the ratio between boys and girls is given, so that the remaining amount is shared one hundred percent in all cases. Namely;

a)      a boy will get as much as two girls’ shares, that is, a boy's share will be twice the share of a girl.
b)     If there is one boy and more than two girls, the girls take 2/3 of it and share it equally, the boy gets 1/3 and this ratio continues until one boy gets two girls share. In other words, a man can get a maximum of two girls' shares if there are several girls.
c)      If there is one girl and one boy, the girl gets half and the boy gets the other half.

As I said, these are the proportions for the children, as in the following examples;

1) If there are "one girl and one boy" or "two girls and two boys", this means that there is one boy against one girl, so girls and boys get equal shares in accordance with item "c".

2) In cases where this ratio of girls to boys exceeds one and reaches two, option “a” above comes into play and the number of boys is multiplied by two and added to the number of girls to find the total number of shares. Then each boy gets 2 shares and each girl gets 1 share. For example, if there are 3 girls and 2 boys; The number of boys is multiplied by 2 to get 4, and this is added to the number of girls, 3 to get a total of 7 shares. Each boy gets 2/7 shares and each girl gets 1/7 share. If the inheritance left to the children is 100, each girl is 14.28 and each boy is 28.56.

and the provision of 1 boy's share = 2 girl's share, as stated in the verse, will be fulfilled.

3) When the ratio of the number of girls to the number of boys exceeds two, option "b" is applied. The girls get 2/3 of the remainder and the boys take 1/3 and divide it equally among themselves. As a first example of this, if there are 3 girls and 1 boy, then the girls get 2/3 and divide it equally between them, while the boy gets 1/3. Thus, the ratio of each of the girls is 2/9. For example, if there are 100 left, the boys get 33.3 and the girls get 22.2 each. As can be seen, the share of a man is now less than the share of two girls. If there are 5 girls and 2 boys, the ratio of girls to boys is more than two, and as per the verse, girls get 2/3 in total and divide equally, while boys take 1/3 and divide it equally. Again, with the example of remaining 100 liras; Girls get 13.3 lira each by dividing 2/3 of it, which is 66.6, while boys share the 1/3 of it equally, which is 33.3, and get 16.6 each. You should notice that the difference between each girl and each boy is getting lesser and lesser than 2.

What is clearly seen here is: 1. If the number of daughters and sons are equal, full justice is provided. 2. As the ratio of the number of girls to the number of boys increases, there is a slow development in favor of boys. The explanation of these rates changing in favor of men is given in the 34th verse of Nisa. “Men are protectors over women because Allah has made some people superior to others and men spend their wealth and all kinds of money.” (this may not be a fully correct translation but is enough to give us a reason)

The numbers reported for the parents are the exact shares, not the proportions; namely,

If there are children, the mother gets 1/6 and the father gets 1/6 from the remainder.

If there is no child, the mother gets 1/3, the father gets 2/3.

If there are no children and there are siblings, the mother's share is reduced to 1/6 and her deducted share of 1/6 will be given to the siblings. This 1/6 share should now be considered as transferred/inherited to those siblings from their mother and thus the ratio that Almighty Allah applies to sons and daughters are also applied to sisters and brothers.

Nisa 12 reads. If they have no children, half of the inheritance left by your women belongs to you. If they have children, a quarter of what remains after their will is fulfilled and their debts are paid is yours. If you do not have children, a quarter of the inheritance you leave belongs to your women. If you have children, after your will is fulfilled and your debts are paid, one-eighth of the remainder belongs to your women. If a man or woman is inherited in case of kelale, and if they have a brother or a sister, each of them receives one sixth. If they are more than that, they are partners in one-third after the will is fulfilled and the debts are paid. (All this must happen in order not to harm the heir and inheritor). (These decrees are for you) a testament from Allah. Allah is Alim, Halim

The part of the verse up to the "kalala" is very clear and almost everyone has understood it correctly. But then it seems that everybody was in trouble. First of all, it should be noted that immediately after the share of the spouse - woman or man - is declared, "after will and debt" is added for both cases. Then, at the end of the verse, this expression is written again for the third time. However, in the previous verse 11, it was written only once at the very end. These repetitions are not in vain that Almighty Allah did not waste a single word. Every repetition in the Qur'an has a purpose. The repetitions here indicate that the share to be given to the spouse of the deceased means the remainder after the debt and will. Only then, whatever remains after the payment to the spouse, is distributed to the other heirs (children and parents). The proof of this is also given and confirmed in the following verse 13.

Now, let's show with very simple mathematics that the word "kalala" in this verse can only mean the case where "the death of both parents; both the mother and the father had had already passed away":

The decree given by writing that “if there is a sister or a brother, each of them will be given 1/6”, and then” if there are more siblings, they will receive a total of 1/3” means the following: In verse 11, if there are children, the parents would receive 1/6 each, that is, a total of 1/3: now as both parents are dead, this 1/3 is being distributed to siblings. It is surprising to me that people could not notice until now how these ratios are compatible with each other. In this case, it means that the in the case of kalala, the deceased has children, because if he did not have children, then the share of the parents would be 1/3 plus 2/3, a total of one hundred percent, and the siblings would have already shared all of it.

After understanding these, it is clear that the 176th verse was sent to clarify the situation of "both mother and father died (kelale) plus there are no children left”, which was excluded from the possibilities in verses 11 and 12, and thus it becomes certain that the word "kelale" means "without mother and father". Yet, as I wrote at the beginning, if people could have understood the verses 11 and 12 correctly and fully, there would be no need for the verse 176. This is why verse 176 says, “They are asking you for a fatwa. Say:” and after making the explanation, it continues to say “Allah explains it to you so that you do not go astray”.

Nisa 33 reads: We made heirs for each of the parents and close relatives left behind. Give their share to those whom your oath (or agreements) has bound. Surely, Allah is Witness to everything.

The meaning of this verse is clear. It stipulates that "give the rights of the spouses to whom you are bound by marriage vows to be given first of all" by saying "give their rights to the people you have bound by your oath". The final conclusion to be drawn from this is that the ratios and shares in verse 11 cover the remainder after the share of the spouses is given, if any, in addition to debts and bequests. Otherwise, the algorithm created perfectly by Almighty Allah would be completely useless and destroyed.

Nisa 176 reads: They are asking you for a fatwa. Say: “Allah gives you a fatwa about kalala: If someone dies, does not have children, if he has a sister (heir), she (his sister) has half the inheritance. But if his sister is dead and he has no children, he (his brother) will inherit it. If the girls are two, they get two-thirds (of the brother's inheritance). If there are more brothers and sisters (heirs) than this, men get twice the share of women. God explains to you so that you do not go astray. Allah is all-knowing.”

I think I have explained well enough that the word kalala is "the case when both parents are dead". In the case both the parents have already died plus the deceased has no children, the inheritance will be divided among the siblings similar to the girl/boy ratios for the children as in the 11th verse.

It seems no one so far has ever asked to whom this verse 176 was addressed, thus have completely misread it. Just as in the case of kids, if the deceased's siblings were "brothers noly" or "sisters only", the taraka would have been equally distributed among them anyway, and people would not need further explanation. Thus, we understand that the deceased had both brothers and sisters. However, the person asking the question here must be the brother, and the explanation was made for this brother. The expressions in the verse fully confirm this and the biggest proof of this is to say that "if your sister dies and there is no other brother, you will get all of her inheritance". YOU= The brother of the deceased.

Accordingly, when we read it correctly, the provisions of the verse 176 must be as follows:

If there is a sister, half is hers and half is yours (the deceased’s brother's)

If there is only one brother is left behind, the entire taraka goes to that brother. So, if you as a male heir, don't have brothers and sisters, all is yours. This has to be valid whether the deceased is a man or a woman, and if the surviving sibling is only one brother, or onle one sister. 

If there are 2 sisters, they get a total of 2/3, the brother gets 1/3. Thus, each of the girls also gets 1/3. 

 If you have both brothers and more than 2 daughters, then each brother gets as much as two sisters' share.

Since the explanations and examples of these cases are given in the "children" section, I do not write them again. This sharing between sisters and brothers also constitutes proof for the accuracy of my explanations for yhe children. 

The relevant algorithm is presented below:


1) Check if there is any wish list or debts
If yes => pay them and deduct it from the total inheritance to find “remaining 1”

2) Check if there is a husband or wife
If yes => Check if any kids and distribute the “remaining 1” as follows
        If yes => husband receives 1/4 and wife receives 1/8
        If no => husband receives 1/2 and wife receives 1/4

         Deduct it from “remaining-1” to find “remaining-2”

 If no => "remaining-2" = "remaining-1", proceed to next step

3) Check if mother and father are both alive and then distribute the “remaining-2”

 If yes => check if any kids 
             If yes => mother receives 1/6 and father receives 1/6
             If no => mother receives 1/3 and father receives 2/3 then BUT if any sisters/brothers
                      then ==> mothers 1/3 share decreases to 1/6 and other 1/6 goes to sisters and brothers

If no => so, both parents already died, check if any kids
                                    If no => Go to 5, (Verse 176)

4) If only one of the parents is alive and the other is not
            ==> share of the deceased father or deceased mother gets distributed same as this full algorithm

5) in case there are no kids and both parents had already died,

 Check the deceased's siblings’ gender
If all the same gender, “remaining-2” gets shared equally


   - If only one girl and only one boy, share equally
    - If two girls and 1 boy, girls receive 2/3 and boy receives 1/3, so again equally shared
    - If minimum 2 boys and minimum 2 girls, then each boy receives twice the share of each girl.


6) Deduct what is paid under point 3 from “remaining-2” to find “remaining-3”
  Check kids’ gender. 

                If different genders, check girls/boys ratio, R

                       If R ≤ 1, then each girl and each boy gets the same share
                       If 1 < R = 2, then each boy receives twice of  each girl's share
                       If R > 2, and until the share of a boy becomes maximum twice of a girl then girls get 2/3 whereas boys get 1/3 to share equally,
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