# An Arab died.  He had three daughters, two parents, and a wife.  His estate is 100 sheep. How do the heirs divide the sheep? The Quran, as near as I can tell, says in Sura 4:11-12 that the...

An Arab died.  He had three daughters, two parents, and a wife.  His estate is 100 sheep. How do the heirs divide the sheep?

The Quran, as near as I can tell, says in Sura 4:11-12 that the daughters share two thirds of the sheep, the parents share one third of the sheep, and the wife gets one eighth of the sheep.

Using what I learned about fractions in middle school, this problem has no solution because the parts sum to more that the whole.

Muhammad, the Prophet (pbuh) was a wealthy Qureshi merchant.  The must have understood fractions. How would he have solved this problem?

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The order is very important here and apparently, in terms of the Quran, the parents and wife would receive first together with any creditors or special nequests of the deceased.Thus

wife:       `1/8 times 100= 12` (rounded off obviously)

parents:  `1/3 times 100 = 33` They actually get 1/6 each which would be approximately 16 and a half.

Only AFTER this division do the daughters get consideration. There are 55 sheep left:

daughters: `2/3 times 55= 37`

Sources:

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The previous answer only distributes 82 sheep.  What happened to the other 18 sheep?

There is no indication of how any excess is distributed. It does not indicate that they should get what is left so I can only assume that the process repeats itself; for example, the wife will now get 1/8 of the 18 ( 2 sheep)and the parents 1/3 (6 sheep)between them then the daughters get 2/3 of 10 ( 3 or 4 sheep) and again back to the wife until there are no sheep left. As we are rounding off it will eventually reduce to zero but usually with a question involving ratios like this , the process would never end, just get smaller and smaller.

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I have found two examples in which people deal with the sum being greater than the parts.

First example:

In American public schools teachers give grades based on a percentage of the grade for tests, quizes, homework, and class participation. The sum of these is 100%.  Then they assign points or extra credit which might be used to increase the percentage of any of the categories.  So in reality the sum is greater than the parts.

Second example:

When settling debts after bankruptcy, the debt is greater than the assets.  The debt is greater than the sum of the assets.  Normally in the United States, creditors have an order of priority. The first creditor gets its money. The second creditor gets its money, and so one until there are no more assets.

Using this last criteria, the parents and the daughters get their inheritance, and the wife gets nothing.

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Okay, maybe they would round up.

In the first round, the wife would get 1/8 of 100 or 13 sheep. The parents would get 1/3 of 87 or 30 sheep. The daughters would get 2/3 57 or 39 sheep.

With 18 sheep left at the beginning of the second round, the wife would get 3 more sheep; the parents would get 6 more sheep; the daughters would get 7 more sheep.

With 2 sheep left for the third round, the wife and the parents would each get 1 more sheep.

Now we need an imam to read this and tell us if we got it right.

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The previous answer only distributes 82 sheep.  What happened to the other 18 sheep?

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