# Solutions to exercises

##### Exercise 1
 Heirs 2 Daughters Mother Father Shares 2/3 1/6 1/6 + residue Base number 6 Portions Each daughter = 2 1 1

Note that brother and sister are excluded by father.
2 daughters: 6 × 2/3 = 4 portions. Each daughter inherits 2.
Mother: 6 × 1/6 = 1 portion
Father: 6 × 1/6 = 1 portion
Check for residue: 6 – 4 – 1 – 1 = 0   or   6 – (4 + 1 + 1) = 0
Since there is no residue, the father receives just 1 portion like the mother.

##### Exercise 2
 Heirs 2 Wives 5 Daughters 3 Full brothers Shares 1/8 2/3 Residue Base number 8 x 3 = 24 Portions 3 16 5 New base number 2 x 5 x 3 x 24 = 720 New portions Each = 45 Each = 96 Each = 50

None of the three categories of heirs can share their portions. So let’s consider the relationship between their number of heads and number of portions.
“Wives” category: 2 and 3 are tabayin (parallel)
“Daughters” category: 5 and 16 are tabayin (parallel)
“Full brothers” category: 3 and 5 are tabayin (parallel)
Since all of them are parallel, their number of heads is considered. Taking wives and daughters first, 2 and 5 are tabayin, so multiply them. 2 × 5 = 10. Now what is the relationship between 10 and 3 (heads of full brothers)? Tabayin. Again, multiply them. 10 × 3 = 30.
Hence, new base number = 30 × 24 = 720
New portion of 2 wives: 720 × 1/8 = 90; each has 45
New portion of 5 daughters: 720 × 2/3 = 480; each is given 96
New portion of 3 full brothers: 720 – (90 + 480) = 150; each inherits 50.

##### Exercise 3

a) 1/6 of the estate

 Heirs Husband 2 Daughters Mother Grandfather Full brother Shares ¼ 2/3 1/6 1/6 Residue Base number 12 Portions 3 8 2 2 0 Increased base number 15 Values 0.2 0.53 0.13 0.13 0

b) 1/3 of residue

 Heirs Husband 2 Daughters Mother Grandfather Full brother Shares ¼ 2/3 1/6 Residue Base number 12 Portions 3 8 2 0 Increased base number 13 Values 0.23 0.62 0.15 0 0

There is no residue, so 1/3 of residue does not exist. Hence, grandfather and full brother inherits nothing.

c) Muqasama

Here, grandfather is expected to share the residue with full brother. But from the table above, there will be no residue to share. Hence grandfather and full brother gets nothing. Therefore, 1/6 of the estate is the most favourable to grandfather. The two other options do not entitle him to any share of the estate.