How should an estate (a total amount to be divided) be apportioned when the number of shares exceeds twenty-four qirats (units)?
Chapter on the Roots of Inheritance Shares that Increase (Awl)
Al-Mughni
Book of Inheritance Shares (Farā'id)
Primary text
When the total quantity to be divided exceeds twenty-four, two methods exist for determining the share per qirat. The first method requires observing the factors composing the total quantity. If one factor is less than twenty-four, its ratio to twenty-four is taken. This ratio is then applied to the other factor to determine the share per qirat. Alternatively, if the second factor is taken, divide the total quantity by twenty-four; the resulting quotient is multiplied by the other factor to yield the share value per qirat. For example, dividing 600, known to be 20 multiplied by 30, by 24 yields the share per qirat. Using the first factor, 20 is two-thirds of 24, so take two-thirds of 30, resulting in 20. Using the second factor, divide 30 by 24, yielding one and a quarter; multiplying this by 20 gives 25, which contradicts the example's stated result of 25 derived from the first method (where 20/24 = 2/3, and 2/3 * 30 = 20, not 25 as stated in the example's conclusion for the first method, indicating the description of the first method's application is flawed or interpreted based on the resulting number 25). The text implies 25 is the result using the fraction approach on 30 (30 / 24 = 1.25; 1.25 * 20 = 25), thus confirming the share per qirat is 25 for the total 600.
Supporting text
The second method involves finding a number that, when multiplied by twenty-four, approximates or equals the divisible quantity. Any remainder is then multiplied by another number until the remainder is less than the divisor. The sum of these multipliers is then related to the remainder, defining the share per qirat.