Assalaamu ‘Alaykum; Please calculate the inheritance according to the following information -Does the deceased have male relatives who are entitled to inherit: (grandson (from the son)) Number 4 -Does the deceased have female relatives who are entitled to inherit : (A daughter) Number 1 (A half sister (from the father)) Number 6

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.

If the deceased did not leave other heirs entitled to inherit except those mentioned in the question, then the daughter gets half of the estate as a fixed share. Allaah, The Exalted, says (what means): {…And if there is only one (daughter), for her is half...} [Quran 4:11]

The remainder of the estate should be divided among the four grandsons by virtue of Ta‘seeb (i.e. by virtue of having a paternal relation with the deceased and not having an allotted share in the estate). The Prophet, sallallaahu ‘alayhi wa sallam, said: “Give the Faraa'idh (the shares of the inheritance prescribed in the Quran) to those who are entitled to receive them; and whatever is left should be given to the closest male relative of the deceased.” [Al-Bukhari and Muslim]

The deceased’s half-sisters from the father’s side get nothing because they are totally excluded by the existence of the grandsons. Ibn Al-Munthir wrote: “Scholars unanimously held that all full brothers and sisters, and half-brothers and sisters from the father are totally excluded by the son, the son of the son, and by the father.” [Al-Ijmaa’]

Hence, the estate should be divided into 8 shares; the daughter gets half of them (4 shares), and each grandson gets one share.

Allaah Knows best.