Level two – part 3

Level 2(c): Two categories of heirs cannot share their portions of the estate. However, the number of heads and number of portions of one category HAVE a common divisor, while the number of heads and the number of portions of the other category ARE PARALLEL.

Recall that whenever two or more numbers converge, it means that they have a common divisor. Now, if any on the numbers is divided by the common divisor, the result is called WAFQ of that number which I translate as ADJUST. For instance, 6, 15 and 21 converge because their common divisor is 3.

6 ÷ 3 = 2          15 ÷ 3 = 5        21 ÷ 3 = 7

Thus, the wafq or adjust of 6 is 2, adjust of 15 is 5 and adjust of 21 is 7. Notice that it is the technical name used to identify the result of the division that is being introduced here; otherwise nothing is new.

Rule O: If the ADJUST of the category that has a common divisor is the same with the NUMBER OF HEADS of the category that has no common divisor, select any of them and multiply by the base number. The result is the new base number.

Example 24

HeirsMother6 Daughters3 Grandsons
Shares1/62/3Residue
Base number6
Portions141
Number of heads163
New base number18
New portions3Each = 2Each = 1

Mother gets her 1 portion. She has no problem. 6 daughters cannot share 4 portions. Likewise, 3 grandsons cannot share 1 portion. But in the “daughters” category, the number of heads, 6, and the number of portions, 4, have a common divisor, 2. Consequently,

6 ÷ 2 = 3          4 ÷ 2 = 2

So, adjusts of the “daughters” category are 3 and 2. But a general rule is that only the adjust resulting from division of number of heads is considered. Therefore, 3 will be used in this case.

As for the “grandson” category, the number of heads, 3, and the number of portions, 1, have no common divisor. Applying the rule, the adjust of the “daughters” category which has a common divisor, 3, is the same with the number of heads of the “grandson” category that has no common divisor. So, one of them is selected. Thus,

New base number = 3 × 6 = 18
New portion of Mother: 18 × 1/6 = 3
New portion of 6 Daughters: 18 × 2/3 = 12
New portion of 3 Grandsons: 18 – (3 + 12) = 3
Each daughter and grandson inherits 2 and 1 portions respectively.

Rule P: Examine the ADJUST of the category whose number of heads and number of portions have a common divisor along with the NUMBER OF HEADS of the category with no common divisor. If one is a multiple of the other, multiply the higher one with the base number to arrive at the new base number

Example 25

Heirs4 Wives2 Full brothers; 2 Full sisters
Shares¼Residue
Base number4
Portions13
Number of heads46
New base number16
New portionsEach wife = 1Each brother = 4; each sister = 2

“Wives” category: 4 wives cannot share 1 portion; and there is no common divisor between 4 (number of heads) and 1 (number of portions).
“Full brothers and sisters” category: 2 full brothers and 2 full sisters cannot share 3 portions; but there is a common divisor between 6 (number of heads) and 3 (number of portions). It’s 3. Note that since the category has both male and female heirs, each male is taken to have “2 heads.” Therefore,

Adjust = 6 ÷ 3 = 2

But the number of heads of “wives” category, 4, is a multiple of 2, the adjust of the “full brothers and full sisters” category. So,

New base number = 4 × 4 = 16
New portion of 4 Wives: 16 ÷ ¼ = 4
New portion of 2 Full brothers and 2 full sisters: 16 – 4 = 12
Each wife, full brother and full sister is given 1, 4 and 2 portions respectively.

Rule Q: In a situation whereby there is a parallel relationship between the ADJUST of the category whose number of heads and number of portions have a common divisor and the NUMBER OF HEADS of the category that has no common divisor, multiply the adjust with the number of heads, then further multiply the answer with the base number to get the new base number.

Example 26

Heirs4 DaughtersGrandson; granddaughter
Shares2/3Residue
Base number3
Portions21
Number of heads43
New base number18
New portionsEach daughter = 3Grandson = 4; granddaughter = 2

“Daughters” category: 4 daughters cannot share 2 portions; but their number of heads, 4, and number of portions, 2, have a common divisor, 2. Thus,

Adjust = 4 ÷ 2 = 2

“Grandchildren” category: 1 grandson and 1 granddaughter cannot share 1 portion; and there is no common divisor of 3 (number of heads) and 1 (number of portions).

But, the adjust and number of heads, 2 and 3 respectively are parallel.
New base number = 2 × 3 = 6 × 3 = 18
New portion of 4 daughters: 18 × 2/3 = 12
New portion of grandson and granddaughter: 18 – 12 = 6
Each daughter is given 3 portions. Grandson and granddaughter each receive 4 and 2 portions respectively.

Rule R: Whenever the ADJUST of the category whose number of heads and number of portions have a common divisor and the NUMBER OF HEADS of the category that has no common divisor converge, divide any of them by the common divisor and multiply by the other. Again, multiply the answer by the base number to generate a new base number

Example 27

Heirs8 Daughters6 Consanguine brothers
Shares2/3Residue
Base number3
Portions21
Number of heads86
New base number36
New portionsEach daughter = 3Each brother = 2

“Daughters” category: 8 daughters cannot share 2 portions; but there is a common divisor of 8 (number of heads) and 2 (number of portions). It’s 2. Thus,

Adjust = 8 ÷ 2 = 4

“Consanguine brothers” category: 6 brothers cannot share 1 portion; and there is no common divisor of 6 (number of heads) and 1 (number of portions).

Now, the adjust and the number of heads of brothers, 4 and 6 respectively incidentally converge. Therefore, what is the common divisor of 4 and 6? 2.

New base number = 4 ÷ 2 = 2 × 6 = 12 × 3 = 36
Alternatively, 6 ÷ 2 = 3 × 4 = 12 × 3 = 36
New portion of 8 daughters: 36 × 2/3 = 24
New portion of 6 consanguine brothers: 36 – 24 = 12
Each daughter and brother receives 3 and 2 portions respectively.


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