In regards to these verses from the Holy Quran and the traditions of the Infallibles (a), the jurisprudents have derived rules and portions for the division of inheritance; these rules have been mentioned in their books of jurisprudential rulings. In order to make clear the various issues pertaining to the division of inheritance, it is necessary to gain in depth knowledge of the rules, basic and individual principles, as well as the inheritors themselves. In addition, knowledge of mathematics is also necessary.
Inheritors are divided into three levels and ranks. The first level involves the father, mother, and children (immediate or distant). The second level involves the grandfather and the grandmother (immediate or distant), and the brothers, sisters, and nieces and nephews (immediate or distant). The third level includes the aunts and uncles from both sides and their children (what is meant here by aunts and uncles includes one’s immediate aunts and uncles and his/her parents’ aunts and uncles and his grandparents’ aunts and uncles and so on.)
Each level of inheritors is an impediment to inheritance reaching the next level and in some cases will completely block out the next one from receiving any of the inheritance.
The portion of relatives (both blood relatives and relatives through marriage) is sometimes specified by a specific subtraction; such a subtraction is called fardh (فرض) and inheritors who inherit in this way are called “صاحب الفرض” (fardh holders), while there are also some relatives whose portion isn't determined by a certain subtraction; this type of inheritance is referred to as qaraabah (قرابه).
The six fardhs that have been mentioned in the Quran are as follows: one half, one fourth, one eighth, one third, one sixth, two thirds, each of which belong to a certain group of relatives.
Keeping these rules and the portions specified for each relative, in the case of the remaining relatives of the deceased (man) being a father, mother, wife and four daughters, the wife’s portion will be one eighth (ثُمن), each of the mother and father will receive one sixth (سُدُس) and the rest of the wealth will be divided equally among the four daughters. In the second case you asked about, when the inheritors of the deceased (man) are a mother, two sisters and a wife, the portions will be as follows: one fourth of the wealth (of the belongings that wives can inherit from, because wives don’t inherit from all the belongings) for the wife, and the rest is given to the mother and the sisters don’t get anything (because they are located in the next level of inheritors, and as was said, each level is an impediment to the next).
Nothing regarding inheritance portions or the way of dividing inheritance has been mentioned in verses 13 and 14 of surah Nisa’, but verses 11 and 12 say:
Allah enjoins you concerning your children: for the male shall be the like of the share of two females, and if there be [two or] more than two females, then for them shall be two-thirds of what he leaves; but if she be alone, then for her shall be a half; and for each of his parents a sixth of what he leaves, if he has children; but if he has no children, and his parents are his [sole] heirs, then it shall be a third for his mother; but if he has brothers, then a sixth for his mother, after [paying off] any bequest he may have made or any debt [he may have incurred]. Your parents and your children you do not know which of them is likelier to be beneficial for you. This is an ordinance from Allah. Indeed Allah is all-knowing, all-wise (11) For you shall be a half of what your wives leave, if they have no children; but if they have children, then for you shall be a fourth of what they leave, after [paying off] any bequest they may have made or any debt [they may have incurred]. And for them [it shall be] a fourth of what you leave, if you have no children; but if you have children, then for them shall be an eighth of what you leave, after [paying off] any bequest you may have made or any debt [you may have incurred]. If a man or woman is inherited by siblings and has a brother or a sister, then each of them shall receive a sixth; but if they are more than that, then they shall share in one third, after [paying off] any bequest he may have made or any debt [he may have incurred] without prejudice. [This is] an enjoinment from Allah, and Allah is all-knowing, all-forbearing (12).
It is based on these and other verses and hadiths that jurists have derived the rules and principles for dividing inheritance.
Regarding inheritance, inheritors are divided into three ‘levels’. Each of the first two levels is divided into two categories, while the third level is only one category.
The two categories of the first level are as follows:
1- Father and mother
2- Children (immediate or distant)
The two categories of the second level are as follows:
1- Grandfather and grandmother (immediate or distant)
2- Brother and sister and niece and nephew (immediate and distant)
The third level in which all are of one category:
Uncle, aunt (from both the mother’s and father’s side) and their children.
Uncle in this context covers one’s immediate uncle, and also his mother and father’s uncle, and his grandfather and grandmother’s uncle and so on, as is the case with the aunt. The same goes for their children; it covers both their immediate children and their children’s children and so on.
There are three main rules regarding the different levels of inheritance that need to be listed here:
Rule one: Each of these levels has precedence and preference over and is an impediment to the next. In the case of the existence of a previous level, the next level will not receive anything of the inheritance wealth, even if there is only one person in that level alive and the next level has many individuals. Therefore, if there is a first level, nothing goes to the second, and if there is a second, nothing is given to the third.
Rule two: In each category, the relative that is nearer to the deceased has precedence over one who is more distant but the same doesn’t apply to levels. Therefore, one’s child has precedence over his grandchild, and in the case of there being a child, nothing is given to the grandchild, because they are from the same category of the same level, but there is no precedence between one’s father and grandchild, because although they are in the same level, they are from two different categories. Also, one’s grandfather has precedence over his great grandfather, and one’s brother has precedence over his nephew or niece, but there is no precedence between one’s grandfather and niece or nephew nor between one’s brother and distant grandfather, once again because they each belong to a different category.
Rule three: A relative from both sides (i.e., full-blood relative) has precedence over a relative from one side (i.e., half-blood relative), given that the two are of one distance from the deceased. Thus in the case of there being a difference in distance, the relative from both sides will no longer have precedence and the nearer relative will have precedence, even if the nearer relative is only related through one’s father or mother and the more distant relative is related through both.
Wives and husbands don’t fit into any of the three abovementioned inheritance ‘levels’ and inherit with all the levels, and they also aren't impediments to any of the levels either.
The portions of inheritance for relatives are sometimes specified with a certain deduction and fraction, this deduction is referred to as fardh (فرض) and the person inheriting like this is referred to as ‘the holder of fardh’ (صاحب الفرض), and sometimes inheritors’ portions aren't specified with a deduction which is referred to as qarabah (قرابة).
The fardhs that have been mentioned in the Quran are as follows: one half, one fourth, one eighth, one third, one sixth and two thirds. Those who inherit according to these fractions and deductions are:
1- One half belongs to:
a) One daughter (in the case that the deceased only has one daughter without any other children).
b) Husband (in the case of the deceased not having any children, immediate or distant).
c) One sister from both sides or only paternal (without any brother).
2- One fourth goes to:
a) Husband (in the case of the deceased having immediate or distant children).
b) Wife (in the case of the deceased not having any immediate or distant children).
3- One eighth belongs to one’s wife when he has immediate or distant children.
4- One third:
a) Mother (in the case of the deceased not having any immediate or distant children and the deceased’s father not being alive either)
b) Two or more maternal brothers, and two or more maternal sisters, and a maternal brother and sister (in the case of the inheritors of the deceased only being a paternal brother and sister along with a number of maternal brothers and sisters, which in such a case, one third of the wealth is equally divided among the maternal brothers and sisters of the deceased).
5- One sixth:
a) Mother (in the case of the deceased having children).
b) Father (in the case of the deceased having children). In this portion of the mother and father, it doesn’t make a difference whether they are both alive or only one is, they get the portion anyway.
c) Mother (in the case that the deceased doesn’t have any children and the father of the deceased is still alive).
d) One maternal brother or sister
6- Two thirds:
a) Two or more daughters (without any sons)
b) Two or more full-blood or paternal sisters (without any brother)
The husband and wife always inherit from each other, no matter which level is also in inheriting from them, meaning that the wife’s share of inheritance, in the case of him having children is one eighth, and one fourth in the case of him not having any children. The share of the husband in the case of his wife having child(ren) is one fourth, and one half if she doesn’t.
Now, keeping all of the above in mind, the answer to your question becomes clear; if the inheritors of a deceased man are a father, mother, wife and four daughters, the wife’s share will be one eighth (of the things that wives inherit), the father and mother will each get one sixth and the daughters will equally divide the rest of the wealth amongst themselves. In the second case you asked about, where the relatives of the deceased are a mother, two sisters and a wife, the wife’s share is one fourth of those things that wives are entitled to inherit, and the rest of the wealth goes to the mother and nothing is given to the sisters, because the mother is situated in the first level of inheritors and is an impediment to the next levels, preventing them from receiving anything.
 Nisa:11 and 12, translation of Qara’i.
 Tawdih al-Masa’el (annotated by Imam Khomeini), vol. 2, pg. 718, issue 2747.
 Tawdih al-Masa’el (annotated by Imam Khomeini), (verdict of Ayatullah Zanjani), vol. 2, pg. 704.
 Tawdih al-Masa’el (annotated by Imam Khomeini), (verdict of Ayatullah Zanjani), vol. 2, pg. 741, issue 2882.
 Tawdih al-Masa’el (annotated by Imam Khomeini), vol. 2, pg. 741, issue 2770.
 Tawdih al-Masa’el (annotated by Imam Khomeini), vol. 2, pg. 741, issue 2771.