A woman died and left behind three daughters, grandchildren (daughter’s children), a full brother, a full sister, and sons of the full brother

If the woman died and left behind three daughters, a full brother and sister, children of the full brother, and sons and daughters of a deceased daughter, then the estate is to be divided as follows: 

The daughters get two thirds, because Allah, may He be exalted, says (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 full brother and the full sister get the remainder, on the grounds that they are relatives on the father’s side, with the male getting the share of two females, because Allah, may He be exalted, says (interpretation of the meaning):

“if there are brothers and sisters, the male will have twice the share of the female”

[an-Nisa’ 4:176]. 

The children of the full brother do not get anything, because they are prevented from inheriting by the presence of their paternal uncle. 

Similarly, the children of the deceased daughter do not get anything, because the children of daughters do not get a share of inheritance, whether it is an allocated share or by virtue of being relatives on the father’s side. 

So the estate is divided into thirds: the daughters get two thirds, and the brother and sister get one third. 

As the share of the daughters cannot be divided properly – because their share is two parts, and their number is three – and this is also the case with regard to the brother and sister – their number is three and their share is one part – the estate should be divided into nine parts, then the correct way to divide it is as follows: 

The daughters get two thirds of nine parts, which is six parts, each daughter getting two parts. 

The full brother and the full sister get the remainder, which is three parts, with the male getting the share of two females. So the brother gets two parts and the sister gets one part. 

And Allah knows best.