Inheritance numbers do not add up!

Question

In the case of a deceased man, with both parents alive, 3 daughters and a wife. The Quranic law states that the 3 sisters get 2/3 of his estate. The parents get 1/6 each, and his wife gets 1/8. How can these ratios by maintained when they add to more than 1?

The total of the ratios do not have to add to a perfect 1 in order to be distributed correctly. The reply below applies to the
distribution of the estate of the deceased according to the case you proposed, and also to all other cases where the total exceeds one.

In the case you proposed we have the following ratios:
3 daughters = 2/3
Father = 1/6
Mother = 1/6
Wife = 1/8

To add the above ratios, we reduce them to a common denominator:
2/3 = 16/24
1/6 = 4/24
1/6 = 4/24
1/8 = 3/24
Total = 16 + 4 + 4 + 3 = 27/24

Indeed,
27/24 is greater than 1, but that should not be a problem because what matters is that the Quranic ratios between the inheritors is maintained.
To maintain the Quranic ratios the money of the dead man is divided into 27 equal shares, then distributed according to the above ratios.

For example if a dead man leaves \$1000, this is divided into
27 shares.
Each share = \$37.037

The 3 daughters get 16 out of the 27 shares = 16 x 37.037 = \$592.592
The father gets 4 shares = 4 x 37.037 = \$148.148
The mother gets 4 shares = 4 x 37.037 = \$148.148
The wife gets 3 shares = 3 x 37.037 = \$111.111

592.592 + 148.148 + 148.148 + 111.111 =
\$999.999 (\$1000)

In such a way, the ratios between the receivers is maintained in accordance with the Quranic rules.
The 3 daughters get 2/3 which is double what the 1/3 which the 2 parents (together) get. That is why \$592.59 is double \$296.29 (combined share of the 2 parents). The same applies to the ratios between all inheritors.