Inheritance Shares of Half and Full Siblings

Question: A woman dies leaving behind no parents, nor husband, nor any children. She has one real brother from the same mother and father and three sisters from her father but from another mother. How would the inheritance shares be calculated and what is the reference to such calculation?

Since the woman dies with no heirs or parents, her siblings are considered like her children. Although their mothers are different, the father of all of these children is the same. They are not step-siblings but half-siblings from the father’s side (A step-sibling has no biological relation to others, a half-sibling has one parent in common, and a full-sibling has both parents in common).
What matters in the calculation of inheritance is the father of the heir.  So, sisters are just like full-siblings in this calculation, and there is no distinction between the children except their genders. (If the common parent was the mother, the calculation  would be different.)
So, the boy receives twice the share of a girl as commanded in verse 11 of Surah al-Nisa.
Consequently, 2/5 of the inheritance belongs to the brother, and each sister receives 1/5 of the inheritance.

For further details about inheritance issues please see:

http://www.islamandquran.org/fatwas/why-men-inherit-twice-the-women.html

http://www.islamandquran.org/fatwas/inheritance-discrimination.html