بِسْمِ اللَّهِ الرَّحْمَٰنِ الرَّحِيمِ
It is incumbent upon the believers that when facing death, one should leave a ‘will or testament’ for the parents and the close relatives. The will should not be unjust ( غَيْرَ مُضَارٍّ)to any one, for example if one or more of the close relatives have circumstances because of a particular situation that he/she deserves extra provisions, then that should be granted in the will.
2:180 كُتِبَ عَلَيْكُمْ إِذَا حَضَرَ أَحَدَكُمُ الْمَوْتُ إِن تَرَكَ خَيْرًا الْوَصِيَّةُ لِلْوَالِدَيْنِ وَالْأَقْرَبِينَ بِالْمَعْرُوفِ ۖ حَقًّا عَلَى الْمُتَّقِينَ
It is written on you (people) that, when death approaches any of you, if he leaves any good that he makes a bequest for parents and next of kin in a known/reasonable manner; it is binding on those who take guard.
The above Ayat is not abrogated after the 4:1112. It simply means that if you don’t leave instructions to distribute your inheritance as per injunctions of Allah, it will not be automatically distributed as per Allah’s orders. Also, you are the best judge of particular circumstances of your family, therefore any adjustments which needs be made can be made in the will as some family members may need more or less than others due to their particular situation.
4:33 وَلِكُلٍّ جَعَلْنَا مَوَالِيَ مِمَّا تَرَكَ الْوَالِدَانِ وَالْأَقْرَبُونَ ۚ وَالَّذِينَ عَقَدَتْ أَيْمَانُكُمْ فَآتُوهُمْ نَصِيبَهُمْ ۚ إِنَّ اللَّهَ كَانَ عَلَىٰ كُلِّ شَيْءٍ شَهِيدًا
For everyone, We have made heirs out of inheritance of parents and relatives. And to those people who have taken pledge from your right hand, give them their due portion. Verily Allah is witness to all things.
Those people who have pledges/(I owe you) notes, they should be paid their due share.
2:240 وَالَّذِينَ يُتَوَفَّوْنَ مِنكُمْ وَيَذَرُونَ أَزْوَاجًا وَصِيَّةً لِّأَزْوَاجِهِم مَّتَاعًا إِلَى الْحَوْلِ غَيْرَ إِخْرَاجٍ ۚ فَإِنْ خَرَجْنَ فَلَا جُنَاحَ عَلَيْكُمْ فِي مَا فَعَلْنَ فِي أَنفُسِهِنَّ مِن مَّعْرُوفٍ ۗ وَاللَّهُ عَزِيزٌ حَكِيمٌ
Those of you who die and leave pairs/spouses, should enjoin for their spouses allowance and provision towards an environment of non exit ; but if they leave, there is no blame on you for what they do with themselves, reasonably and Allah is Exalted in Power, Wise.
First step logically for a person facing death, is to ensure that the spouse has enough provision to keep on living in the same environment with family/kids after him, without having to exit that environment . If the wives later decide for themselves to exit to improve their conditions for example get a job etc. or to marry again, then no blame on the person as obviously he may not be able to provide for indefinite period of time. Normally, in many developed countries this is achieved by having some kind of insurance policy.
5:106 يَا أَيُّهَا الَّذِينَ آمَنُوا شَهَادَةُ بَيْنِكُمْ إِذَا حَضَرَ أَحَدَكُمُ الْمَوْتُ حِينَ الْوَصِيَّةِ اثْنَانِ ذَوَا عَدْلٍ مِّنكُمْ أَوْ آخَرَانِ مِنْ غَيْرِكُمْ…..
Ye who believe! When death approaches any of you, (take) witnesses among yourselves when making bequests, two just men of your own (brotherhood) or others from outside….
The will or testament should be documented and signed off by at least two witnesses.
After adjustment of payment of debts/liabilities and adjustments made for particular situations for close relatives in the will (Quran does not put any limitation on this amount), the remaining amount of inheritance to be distributed among close relatives according to instruction in Ayas 4:1112 and 4:176.
4:11 يُوصِيكُمُ اللَّهُ فِي أَوْلَادِكُمْ ۖ لِلذَّكَرِ مِثْلُ حَظِّ الْأُنثَيَيْنِ ۚ فَإِن كُنَّ نِسَاءً فَوْقَ اثْنَتَيْنِ فَلَهُنَّ ثُلُثَا مَا تَرَكَ ۖ وَإِن كَانَتْ وَاحِدَةً فَلَهَا النِّصْفُ ۚ وَلِأَبَوَيْهِ لِكُلِّ وَاحِدٍ مِّنْهُمَا السُّدُسُ مِمَّا تَرَكَ إِن كَانَ لَهُ وَلَدٌ ۚ فَإِن لَّمْ يَكُن لَّهُ وَلَدٌ وَوَرِثَهُ أَبَوَاهُ فَلِأُمِّهِ الثُّلُثُ ۚ فَإِن كَانَ لَهُ إِخْوَةٌ فَلِأُمِّهِ السُّدُسُ ۚ مِن بَعْدِ وَصِيَّةٍ يُوصِي بِهَا أَوْ دَيْنٍ ۗ آبَاؤُكُمْ وَأَبْنَاؤُكُمْ لَا تَدْرُونَ أَيُّهُمْ أَقْرَبُ لَكُمْ نَفْعًا ۚ فَرِيضَةً مِّنَ اللَّهِ ۗ إِنَّ اللَّهَ كَانَ عَلِيمًا حَكِيمًا
4:12 وَلَكُمْ نِصْفُ مَا تَرَكَ أَزْوَاجُكُمْ إِن لَّمْ يَكُن لَّهُنَّ وَلَدٌ ۚ فَإِن كَانَ لَهُنَّ وَلَدٌ فَلَكُمُ الرُّبُعُ مِمَّا تَرَكْنَ ۚ مِن بَعْدِ وَصِيَّةٍ يُوصِينَ بِهَا أَوْ دَيْنٍ ۚ وَلَهُنَّ الرُّبُعُ مِمَّا تَرَكْتُمْ إِن لَّمْ يَكُن لَّكُمْ وَلَدٌ ۚ فَإِن كَانَ لَكُمْ وَلَدٌ فَلَهُنَّ الثُّمُنُ مِمَّا تَرَكْتُم ۚ مِّن بَعْدِ وَصِيَّةٍ تُوصُونَ بِهَا أَوْ دَيْنٍ ۗ وَإِن كَانَ رَجُلٌ يُورَثُ كَلَالَةً أَوِ امْرَأَةٌ وَلَهُ أَخٌ أَوْ أُخْتٌ فَلِكُلِّ وَاحِدٍ مِّنْهُمَا السُّدُسُ ۚ فَإِن كَانُوا أَكْثَرَ مِن ذَٰلِكَ فَهُمْ شُرَكَاءُ فِي الثُّلُثِ ۚ مِن بَعْدِ وَصِيَّةٍ يُوصَىٰ بِهَا أَوْ دَيْنٍ غَيْرَ مُضَارٍّ ۚ وَصِيَّةً مِّنَ اللَّهِ ۗ وَاللَّهُ عَلِيمٌ حَلِيمٌ
4:176 يَسْتَفْتُونَكَ قُلِ اللَّهُ يُفْتِيكُمْ فِي الْكَلَالَةِ ۚ إِنِ امْرُؤٌ هَلَكَ لَيْسَ لَهُ وَلَدٌ وَلَهُ أُخْتٌ فَلَهَا نِصْفُ مَا تَرَكَ ۚ وَهُوَ يَرِثُهَا إِن لَّمْ يَكُن لَّهَا وَلَدٌ ۚ فَإِن كَانَتَا اثْنَتَيْنِ فَلَهُمَا الثُّلُثَانِ مِمَّا تَرَكَ ۚ وَإِن كَانُوا إِخْوَةً رِّجَالًا وَنِسَاءً فَلِلذَّكَرِ مِثْلُ حَظِّ الْأُنثَيَيْنِ ۗ يُبَيِّنُ اللَّهُ لَكُمْ أَن تَضِلُّوا ۗ وَاللَّهُ بِكُلِّ شَيْءٍ عَلِيمٌ
4:11 Allah enjoins you in your offsprings. For the male, the example is of the portion of two females. If the women are more than two, their share is twothirds of what he left; if only one, her share is a half. For each of the parents, a sixth , if he (deceased) has a son/child; if he has no son/child and both parents inherit him, then for the mother is the third; if the deceased left brothers (siblings) then for the mother is the sixth, after carrying out the will or debts. You do not know whether your parents or your children are nearer to you in your benefit. This is an obligation from Allah; and Allah is Allknowing, Allwise.
4:12 For you is half in what your wives leave, if they leave no son/child; but if they leave a son/child, then for you is the fourth in what they leave; after carrying out the will and debts. In what you leave, their(wives) share is a fourth, if you leave no son/child; but if you leave a son/child, then for them the share is an eighth; after carrying out the Will and debts. In case the man or woman is inherited by Kalalah, and has a brother or a sister, each one of the two gets a sixth; but if they are more than two, then all share in the third; after payment of legacies and debts; so that no loss is caused (to any one). Thus is it ordained by Allah; and Allah is Allknowing, Most Forbearing.
4:176 They ask you (messenger) for a fatwa/advice. Say. Allah gives you fatwa/advice in Kalalah. If a man dies for him there is no son/child, and he has a sister then for her is half of what he left and he will inherit her if she does not have a son/child, and If they are two (females) they shall have twothirds out of what he left and if there are brothers and sisters, then for a male is a share like share of two females. Thus Allah makes clear to you, lest you go astray, and Allah has knowledge of all things
The claimants on inheritance as per above three Ayahs are the following relatives of the deceased:
 Children
 Parents
 Spouses
 Siblings
Basic assumptions of inheritance calculations in this post are given below:
 Total amount of inheritance available for distribution is assumed to be 100 units i.e after will and payment of debts/liabilities.
 Sum of the distributable shares should equal the total inherited amount. E.g if the inheritors of deceased are his Children, parents, Spouse and Siblings, then the sum of all shares of share holders should equal to the total i.e 100.
Share of children + share of parents + share of spouses + share of siblings = Total (100)
Above equation is the basic equation for inheritance calculation. We will substitute the values of each in the above equation.
Ratio of distribution of inheritance between male and female children:
4:11 يُوصِيكُمُ اللَّهُ فِي أَوْلَادِكُمْ ۖ لِلذَّكَرِ مِثْلُ حَظِّ الْأُنثَيَيْنِ ۚ فَإِن كُنَّ نِسَاءً فَوْقَ اثْنَتَيْنِ فَلَهُنَّ ثُلُثَا مَا تَرَكَ ۖ وَإِن كَانَتْ وَاحِدَةً فَلَهَا النِّصْفُ ۚ
Allah enjoins you with regards to your Children’s (Inheritance). For the male, the example is portion of two females. If the women are more than two, their share is twothirds of what he left; if only one, her share is a half.
The above statement defines the ratio between males and females shares in offspring’s as this Ayat states male share as an example of females shares when females are 1 or more.
In case of upto two daughters: ratio of son to daughter share is 2:1 (1 / 0.5 = 2)
In case of more than two daughters: ratio of son to daughter is 1.5 : 1 ( 1 / (2/3) = 1.5)
Point to note here is that above statement is describing the ratio of inheritance between the male and female children e.g the expression in Ayat 4:11, ‘if only one, her share is a half’ is referring to the ratio of son’s to daughter’s share, and not to half of total inheritance value.
There is a school of thought who considers above injunction of 1/2 (incase of 1 female) and 2/3 ( in case of more than 2 females), applicable to whole of inheritance, instead of considering it as a ratio between male and female children.
However, with this line of thinking, several problem arise, as given below:
1 – What is the injunction in case of exactly two females?
2. Just after Allah enjoined the ratio between male and females then why He would fix 2/3rd portion of total inheritance for more than 2 females, instead of keeping it on basis of ratios just mentioned.
3. If 2/3 is a fixed portion of inheritance for more than 2 females instead of a ratio, then there will be certain cases where we will not able to distribute shares for example, when there are 3 daughters, 1 husband and mother and father. In this case three daughters will get 2/3, husband gets 1/4 and parents each get 1/6. There will be not enough to distribute if we consider it as fixed amount instead of a ratio.
An objection by some people is, why Allah discriminates in distribution of inheritance giving preference to males over females. The reason could be because in general males have more responsibilities in providing for household, than females. However, if a particular family situation is different, e.g females carry more responsibility of the household expenditure, then extra provision for them can be provided in the will, which is to be carried out before distribution of shares.
Example 1: (1 son and 1 daughter only)
Lets assume total inheritance =100. The total of shares of all inheritors should equal 100. Now, assume daughter’s share to be ‘x;, then son’s share becomes 2x, and the formula becomes as below :لِلذَّكَرِ مِثْلُ حَظِّ الْأُنثَيَيْنِ
Total inheritance= Son’s share + Daughter’s share=  100 
2x + x =  100 
3x=  100 
x=  100/3 
Daugher’s share x=  33.33 
Son’s share 2x =  2 x 33.33= 66.67 
Example 2: (One daughter only)
Lets assume total inheritance =100. First equation is, total share of inheritors should equal 100. Now, as one daughter is the only share holder other shareholder’s share will be 0, so daughters share will be 100.
Total inheritance= All other inheritors + Daughter’s share=  100 
0 + Daughter’s share  100 
x + 0  100 
x=  100 
Daugher’s share is =  100 
Example 3: (2 son and 3 daughter only)
The equation is total shares of all inheritors should equal 100. Now, assume daughter’s share is x, then son’s share becomes 1.5x, and the formula becomes as below: لِلذَّكَرِ مِثْلُ حَظِّ) (الْأُنثَيَيْنِ ۚ فَإِن كُنَّ نِسَاءً فَوْقَ اثْنَتَيْنِ فَلَهُنَّ ثُلُثَا مَا تَرَكَ
Share of sons + share of daughters = 100
1.5x + 1.5x + x + x +x = 100
3x + 3x = 100
6x = 100
x = 100/6 = 16.67
Each daughter share = x = 16.67
Each son’s share = 1.5x = 25
Share of Parents:
…. وَلِأَبَوَيْهِ لِكُلِّ وَاحِدٍ مِّنْهُمَا السُّدُسُ مِمَّا تَرَكَ إِن كَانَ لَهُ وَلَدٌ…..
For each of the parents, a sixth , if he (deceased) has son/child;
Example 4: Father, 1 daughter, 1 son
Total inheritance 100. Lets assume daugher’s share to be ‘x’ , then son’s share will be 2x and Fathers share is 1/6th
Total share of inheritors = 100
Sons’ share + daughter’s share + Father’s share = 100
2x + x + 100/6 = 100
3x + 100/6 = 100
3x = 100 – 100/6
3x = 83.33
x= 27.78
Daughter’s share = x = 27.78
Son’s share = 2x = 55.56
Fathers share= 100/6 = 16.67
Example 5: Father, mother, 3 daughters, 3 sons
Lets assume total inheritance= 100, assume each daughter’s share to be ‘x’, then each son’s share will be 1.5x, Father’s share is 1/6th and Mother’s share is also 1/6th of inheritance
Total shares of inheritors = 100
Sons’ share + daughters’ share + Father’s share+ Mother’s share = 100
1.5x + 1.5x +1.5x +x + x + x + 100/6 + 100/6 = 100
7.5x + 200/6 = 100
7.5 x = 100 – 200/6
7.5x = 66.67
x = 8.89
Each daughter’s share = 8.89
Each son’s share = 1.5x = 1.5 x 8.89 = 13.33
Father’s share = Mothers share = 16.67
4:11 ….. فَإِن لَّمْ يَكُن لَّهُ وَلَدٌ وَوَرِثَهُ أَبَوَاهُ فَلِأُمِّهِ الثُّلُثُ ….
if no son or daughter, and both parents are heirs, mother has a third;
Example 6: Only Mother and father and no children
Mother’s share + Father’s share = 100
assume fathers share as x,
100/3 + x = 100
x = 100 – 100/3 = 66.67 = Father’s share
Mother’s share = 100/3 = 33.67
وَلَكُمْ نِصْفُ مَا تَرَكَ أَزْوَاجُكُمْ إِن لَّمْ يَكُن لَّهُنَّ وَلَدٌ4:12
Your share is a half in what your wives leave, if for them is no child….
Example 7: husband and Father only, no kids
Assume total inheritance 100. Husband share is 1/2. There are two heirs only so the equation is:
Husband’s share + Father’s share = 100
100/2 + Father’s share = 100
Father’s share = 100 – 50 = 50
Husband’s share = 50
Ex 8: husband, father and mother only, no kids
Assume total inheritance 100. Husband’s share is 1/2. Mother’s share is 1/3 and assume father’s share to be x:
(فَإِن لَّمْ يَكُن لَّهُ وَلَدٌ وَوَرِثَهُ أَبَوَاهُ فَلِأُمِّهِ الثُّلُثُ )
Husband + Mother + Father’s share = 100
100/2 + 100/3 + x= 100
x= 100 – 100/2 – 100/3
Father’s share = 16.67
Mother;s share = 33.33
Husband’s share = 50
4:12 … فَإِن كَانَ لَهُنَّ وَلَدٌ فَلَكُمُ الرُّبُعُ
Ex 9: One daugher 1 son, and husband
Assume x for the daughter, then son gets 2x and husband gets 1/4 of inheritance
x + 2x + 100/4 = 100
3x = 100 – 25
x = 25
Daughter’s share = 25, Son’s share = 50, Husband’s share = 25
Ex 10: One daughter and husband
Assume total amount =100. Assume x for daughter’s share, Husband’s share is 100/4.
x + 100/4 = 100
x = 75
Daughter’s share = 75, Husband’s share = 25
4:12 …. وَلَهُنَّ الرُّبُعُ مِمَّا تَرَكْتُمْ إِن لَّمْ يَكُن لَّكُمْ وَلَدٌ ۚ
Ex 11: 1 wife, mother and father only no kids
Wife get 1/4 of inheritance, mother get 1/3 of inheritance as per 4:11, assume x for father
x + 100/3 + 100/4 = 100
x = 100 33.33 – 25= 41.66
Mother gets 33.33, Father gets 41.66, wife gets 25
Ex 12: 1 wife and mother only no kids
Wife get 1/4 of inheritance as per 4:12, mother’s share was to be 1/3 when both parents were present as in Ayat 4:11, in this case as both parents are not there, therefore mother’s share is not fixed at 1/3 but is variable. Assume mother’s share = x
x + 100/4 = 100
x = 100 – 25= 75
Mother gets 75, wife gets 25
4:12 … ۚ فَإِن كَانَ لَكُمْ وَلَدٌ فَلَهُنَّ الثُّمُنُ مِمَّا تَرَكْتُم
Ex 13: Two son’s two daughters and 2 wives
Assume x for the daughter’s share, then son gets 2x, both wives share in 1/8
2x + 4x + 100/8 = 100
6x = 87.50
x = 14.58
Each daughter’s share = 14.58, each son’s share = 29.16
Each wife’s share = 6.25
Example 14: husband, mother, father, 2 sons and 3 daughters
Husband’s share is fixed at 1/4. Mothers and father’s each share is 1/6 (4:11). Assume x for the daughter’s share then sons share is 1.5x:
Husband + Mother + Father + Daughters + Sons = 100
100/4 + 100/6 + 100/6 + x +x +x + 1.5x + 1.5x = 100
6x = 100 – 100/4 – 100/6 – 100/6
6x = 100 – 25 – 16.67 – 16.67
6x = 41.67
x= 6.94 = each daughter’s share,
Each son’s share = 1.5x = 10.41, Husband’s share = 25, Father and mothers share each = 16.67
Kalalah Cases:
Quran uses a word ‘Kalalah’ for inheritance distribution in certain cases. The word ‘Kalalah’ however is not well defined in dictionaries. Religious scholars have tried to guess the meanings of ‘Kalalah’ on the basis of two Ayas i.e 4:12 and 4:176. What they came up with the interpretation as ‘a person leaving behind no offsprings nor parents/grandparents’. The problem however remained with this interpretation is that the distribution of shares described in 4:12 and 4:176 both concern siblings however both Ayahs describe different distribution for siblings. The traditionalists found a way out of this predicament by assuming that one Ayat to be used for distribution of shares of real siblings and the other for calculating shares of uterine siblings. However this interpretation at best seems lame and arbitrary as Ayahs don’t mention this distinction.
As these three Ayahs which describe the distribution of shares of inheritance are based on pure mathematics, therefore I believe the correct interpretation of Kalalah will be that which satisfies both cases mathematically. One thing for sure is that ‘Kalalah’ case is the case of distribution of inheritance to the siblings. My understanding of differentiation of these two cases is as below:
First case i.e Ayat 4:12 describe a case in which a person specifically nominates his siblings to be given share in his inheritance while his children are also present. The basis of this assumption is the statement (in case a man or woman is inherited ‘Kalalah’) so it denotes not a normal case but a certain case in which siblings are nominated to be inherited by the deceased.
Second case is described in Ayat 4:176 when siblings in any case get their share in inheritance. This is the case when there are no children of the deceased to share in inheritance.
4:12 إِن كَانَ رَجُلٌ يُورَثُ كَلَالَةً أَوِ امْرَأَةٌ وَلَهُ أَخٌ أَوْ أُخْتٌ فَلِكُلِّ وَاحِدٍ مِّنْهُمَا السُّدُسُ ۚ فَإِن كَانُوا أَكْثَرَ مِن ذَٰلِكَ فَهُمْ شُرَكَاءُ فِي الثُّلُثِ
In case a man or woman is inherited by Kalalah, and for him is a brother or a sister, each one of the two gets a sixth; but if they are more than this, then all share in the third.
4:176 يَسْتَفْتُونَكَ قُلِ اللَّهُ يُفْتِيكُمْ فِي الْكَلَالَةِ ۚ إِنِ امْرُؤٌ هَلَكَ لَيْسَ لَهُ وَلَدٌ وَلَهُ أُخْتٌ فَلَهَا نِصْفُ مَا تَرَكَ ۚ وَهُوَ يَرِثُهَا إِن لَّمْ يَكُن لَّهَا وَلَدٌ ۚ فَإِن كَانَتَا اثْنَتَيْنِ فَلَهُمَا الثُّلُثَانِ مِمَّا تَرَكَ ۚ وَإِن كَانُوا إِخْوَةً رِّجَالًا وَنِسَاءً فَلِلذَّكَرِ مِثْلُ حَظِّ الْأُنثَيَيْنِ ۗ يُبَيِّنُ اللَّهُ لَكُمْ أَن تَضِلُّوا ۗ وَاللَّهُ بِكُلِّ شَيْءٍ عَلِيمٌ
They ask you (messenger) for a fatwa/advice. Say. Allah gives you fatwa/advice in Kalala. If a man dies for him there is no son, and he has a sister then for her is half of what he left and he will inherit her if she does not have a son/child, and If they are two (females) they shall have twothirds out of what he left and if there are brothers and sisters, then for a male is (a share) like share of two females. Thus Allah makes clear to you, lest you go astray, and Allah has knowledge of all things.
 When there are no children then siblings inherit per ratio of males to females. (The brother becomes an inheritor only when there is no child (وَهُوَ يَرِثُهَا إِن لَّمْ يَكُن لَّهَا وَلَد))
 Sister share is half of male’s share in case of 1 sister only. When only one sister, ratio of brother:sister :: 2:1
 If there are two sisters then their share ratio is 2/3 of male’s share. (brother to sister:: 1.5:1)
 If mix of brothers and sisters then share of a males is like of share of 2 sisters. Shares of 2 sisters in this case is defined as 2/3 of male’s share. (male to female: 1.5:1). Therefore this ratio will be maintained for mix of brothers and sisters.
As the case with sons and daughters Ayat 4:11, the ratio of sister and brother’s shares are described here, not total inheritance values. This is obvious from orders in Quran otherwise, if they were fixed inheritance values other than ratios, then husband, no kids and 2 sisters would not be able to be distributed as husband gets 1/2 and 2 sisters would get 2/3rd.
Ex 15: Mother, Father, 1 sister 1 brother, no child
4:11 فَإِن لَّمْ يَكُن لَّهُ وَلَدٌ وَوَرِثَهُ أَبَوَاهُ فَلِأُمِّهِ الثُّلُثُ ۚ فَإِن كَانَ لَهُ إِخْوَةٌ فَلِأُمِّهِ السُّدُسُ..
If no child, and both parents are the heirs, the mother has a third; if the deceased Left brothers (siblings) the mother has a sixth
And as per 4:176 (إِنِ امْرُؤٌ هَلَكَ لَيْسَ لَهُ وَلَدٌ وَلَهُ أُخْتٌ فَلَهَا نِصْفُ مَا تَرَكَ ۚ وَهُوَ يَرِثُهَا إِن لَّمْ يَكُن لَّهَا وَلَدٌ ۚ فَإِن كَانَتَا اثْنَتَيْنِ فَلَهُمَا الثُّلُثَانِ مِمَّا تَرَكَ) in case there is no child and siblings are present then siblings will have distribution as per ratios of brother to sister of 2:1, except in case of 2 or more sisters, the ratio of brother to sister will be 1.5:1
Mother’s and Father’s share is 1/6th each. Assume sister’s share x, then brother’s share is 2x
Mother + Fathers + Sister + Brother = 100
100/6 + 100/6 + x + 2x = 100
3x = 100 – 200/6
Sister’s share x=  22.22 
Brothers share  44.44 
Mothers share  16.67 
Father’s share  16.67 
Ex 15a: Mother, Father, 2 sisters , no child
Mother’s and Father’s share is 1/6th each.
The 2 sister’s share of 2/3 ( فَإِن كَانَتَا اثْنَتَيْنِ فَلَهُمَا الثُّلُثَانِ مِمَّا تَرَكَ) is the ratio of brothers to sisters i.e if sister share is x, brother’s share will be 1.5x. As in this case there is no brother, we will assume each sister’s share is x. Then the equation can be written as follows:
Mother’s share + Father’s share + sister’s share + sister’s share = 100
100/6 + 100/6 + x + x = 100
2x = 100 – 200/6
x = 33.33, each sister’s share
Mother’s and father’s share = 16.66 each
Ex 16: Mother, 1 sister 1 brother, 2 daughters, 1 son (deceased nominated siblings in inheritance)
Since deceased nominates in this case siblings to be given share in inheritance, therefore they will be given shares in inheritance as per Ayat 4:12. Mothers share is 1/6th, Each brother and sister share is 1/6 (إِن كَانَ رَجُلٌ يُورَثُ كَلَالَةً أَوِ امْرَأَةٌ وَلَهُ أَخٌ أَوْ أُخْتٌ فَلِكُلِّ وَاحِدٍ مِّنْهُمَا السُّدُسُ ), assume x as daughter’s share, then son’s share is 2x:
Mother + Sister + Brother + Daughter + Son’s share = 100
100/6 + 100/6 + 100/6 + x + x + 2x = 100
4x = 100 – 300/6
4x = 50
x= 12.5
Sister’s share= 16.66
Brother’s share = 16.66
Mothers share= 16.66
Son’s share= 25
Each Daughter’s share = 12.5
Ex 17: Father, Mother, 2 brother, 2 sisters, 2 sons, 1 daughter
(deceased nominates siblings in inheritance)
Father and mother each has a share of 1/6. ( وَلِأَبَوَيْهِ لِكُلِّ وَاحِدٍ مِّنْهُمَا السُّدُسُ مِمَّا تَرَكَ إِن كَانَ لَهُ وَلَدٌ)
2 brothers and 2 sisters share equally in 1/3 (وَإِن كَانَ رَجُلٌ يُورَثُ كَلَالَةً أَوِ امْرَأَةٌ وَلَهُ أَخٌ أَوْ أُخْتٌ فَلِكُلِّ وَاحِدٍ مِّنْهُمَا السُّدُسُ ۚ فَإِن كَانُوا أَكْثَرَ مِن ذَٰلِكَ فَهُمْ شُرَكَاءُ فِي الثُّلُثِ)
Assume share of daughter as x, then share of son is 2x
Father + Mother + Brothers + Sisters + Daughter + Sons’ share = 100
100/6 + 100/6 + 100/3 + x + 2x + 2x = 100
5x = 100 – 100/6 – 100/6 – 100/3
5x = 33.33
x = 6.67= Daughter’s share
Each son’s share = 13.33
Father and Mother’s each share= 16.66
Total share of 2 brothers and sisters = 33.33, each of them gets 8.33
Ex 18: 3 daughters, 2 sons, father, mothers, 3 wives, 3 sisters, 2 brothers (deceased does not nominate siblings in inheritance)
Assume each daughter’s share= x, then each son’s share will be 1.5x, father and mother each gets 1/6th, 3 wives share in 1/8th. Sisters and brothers don’t get share because of children’s presence and deceased has not nominated siblings in inheritance. Three daughters will be x +x+x = 3x, two sons will be 1.5x +1.5x = 3x
3x + 3x + 100/6 + 100/6 + 100/8 = 100
6x = 100 – 100/6 – 100/6 – 100/8
6x = 54.17
x = 9.03
Total  
Each daughter’s share  9.03  27.08 
Each son’s share  13.54  27.08 
Fathers share  16.67  16.67 
Mothers share  16.67  16.67 
Each wife’s share  4.17  12.50 
Ex 19: Mother, no children, 2 sisters no brother
Mother’s share is 1/6th, sister’s share assume x, then two sisters’ share is 2x: ( 2/3rd for 2 sisters is the ratio, which will be applicable in case there are brother/brothers)
Mother + Sisters = 100
100/6 + 2x = 100
2x = 100 – 100/6
2x = 83.33
x = 41.66 = share of each sister
Mother gets 16.66
Ex 20: Mother and father and no children, 2 sisters, 1 brother
Mother’s share is 1/6th, Father’s share 1/6 (per 4:11, Mother’s and father’s share were both 1/6 each when no children). For sister’s share assume x, then brothers share is 1.5x: ( 2/3rd for 2 sisters is the ratio, which will be applicable in case there is a mix of brothers and sisters)
Mother + Father + Sisters + brother’s share = 100
100/6 + 100/6 + x +x + 1.5x + 1.5x = 100
5x= 66.66
x= 13.33, each sister gets 13.33, each brother gets 20, mother gets 16.66 and father’s share is 16.66.
The Orphans’ case:
Allah admonishes against eating orphans’ wealth in many places in Quran. There are lot of Ayahs warning not to eat orphan’s wealth. It seems that some practices will always be going on in the society where people don’t give orphans their due share. Consider a case where a man dies, and leaves offspring. One of the his offspring may already have died leaving behind his own children. However, these children will not get any share in their grandfather’s inheritance as per traditional practice. A recommendation is to consider the already deceased son (who has orphans or widow) to be a share holder in grandfather’s inheritance. Then this share of the deceased son can be distributed further among his children and spouse according to Quranic injunctions.
4:2 وَآتُوا الْيَتَامَىٰ أَمْوَالَهُمْ ۖ وَلَا تَتَبَدَّلُوا الْخَبِيثَ بِالطَّيِّبِ ۖ وَلَا تَأْكُلُوا أَمْوَالَهُمْ إِلَىٰ أَمْوَالِكُمْ ۚ إِنَّهُ كَانَ حُوبًا كَبِيرًا
Give the orphans their wealth, do not substitute the bad things with (their) good ones; and do not eat their wealth by (by mixing it up) with your wealth; this is indeed a great sin.
4:10 إِنَّ الَّذِينَ يَأْكُلُونَ أَمْوَالَ الْيَتَامَىٰ ظُلْمًا إِنَّمَا يَأْكُلُونَ فِي بُطُونِهِمْ نَارًا ۖ وَسَيَصْلَوْنَ سَعِيرًا
Those who unjustly eat up the property of orphans, eat up a fire into their bellies. They will enter a blazing fire!
89:19 وَتَأْكُلُونَ التُّرَاثَ أَكْلًا لَّمًّا وَتُحِبُّونَ الْمَالَ حُبًّا جَمًّا
And you devour inheritance – all with greed and ye love wealth an intense love!

The Arabic word ‘Walad/( وَلَد) is translated as ‘Child’ in above post as the the Ayat 2:233 also implies the understanding of this word as child.