The fundamental sources of Islam are the Qur'an and the Hadith. However, legal prescriptions and ritual observances have not been explained in the Qur'an. Even the explanations for zakaat, fasting, Hajj and other such most important acts of worship are absent in the Qur'an. These details are to be found within the Hadith. So is the case with the laws of inheritance. In short, therefore, any law in Islam can be determined completely only on the basis of the Qur'an and Hadith.
It is only the fundamental idea concerning the order of allocation which has been expressed in the verses 11 and 12 of Surat Nisa. On the basis of these fundamental ideas it has been explained in the Hadith as to how the wealth of inheritance is to be shared in a precise, and systematic, fashion. It is also in the explanatory books on Hadith and jurisprudence that the expositions as to how the wealth is to be shared in a way in which the fundamental ideas in the Qur'an are not violated, are to be found.
There are many instances wherein the share of the heirs to inheritance fall short of the amount actually stipulated. The books of jurisprudence have mentioned that in all such instances the number of shares are to be increased in such a way that the shortage is shared amongst each one of the heirs by increasing the number of divisions. The method of increasing the divisions made to fulfill the shares when the allocated shares fall short of the rightful due is termed Awl. Awl means 'to increase'. It is the injunction of Islamic law that in all such cases wherein the shares allocated becomes insufficient, the wealth is to be divided on the basis of this method of Awl.
The scholars of jurisprudence have stipulated the divisions that will be required in the allocation of the wealth of inheritance as being seven in number. These basic divisions comprise 2,3,4,6,8,12 and 24. Out of these it is only the three divisions 6, 12 and 24 which can be subjected to the process of Awl. In the cases where the four numbers 2,3,4 and 8 come in for division, since their parts can never be greater than their whole, there will not be the necessity for Awl at all. If the basic division is by six then, in the instances where Awl becomes necessary, the wealth can be approportioned by increasing the division to seven, eight, nine or ten. If the basic division is by twelve, the wealth can then be divided through Awl by increasing it to thirteen, fifteen, or seventeen and if the division is by twenty four, then to twenty seven. It is in such a strict and exacting manner that the ways of approportioning wealth, by resorting to a corresponding increase, in part, of the order of allocation, has been mentioned in the books of jurisprudence.
In the problem raised by the question, the daughters would receive 16/27 portion, the parents 8/27 portion and the wife would receive 3/27 portion of the total wealth. In other words, the division that was to have been by 24 here is now to be raised to 27 in the process of making the allocations in the wealth. Indeed, if the Qur'an and the Hadith are examined together the solution is not difficult to find. Indeed, it is in the very interest of the Holy Qur'an which teaches that, 'Verily in the messenger of God ye have the best example.' (33:2) and that 'O ye who believe! Obey God, and obey the Messenger, and those charged with authority among you.' (4:59) that the laws dealt within it should be understood on the basis of the practices of the Prophet and on the explanations made by his companions. When understood in such fashion, it will hardly be a difficult proposition to find answers to other similar problem.