Determining the correct distribution when an initial deduction (five/fifth) is made from the remaining estate after a primary share, followed by a bequest (one-third) from the remainder after the first deduction.
General Chapter
Al-Mughni
Book of Bequests
Primary text
When the exception states five units remain after the primary share, and another party is entitled to one-third of what remains after the first party's share, the total shares are calculated by taking the initial five, adding one-fifth of that total (making six), then subtracting one-third due to the bequest, leaving four units as the primary share. A secondary calculation involves taking one share, adding five units, subtracting one-third of that sum, resulting in four-fifths, which is then added to the sons' shares and multiplied by five to find the total estate, yielding nineteen. Distribution mandates paying the first claimant four units, reserving one-fifth of the remaining three units (three-fifths), leaving one unit. The second claimant receives one-third of the remainder, which is six units, leaving twelve units for the heirs, meaning each son receives four units.
Supporting text
The distribution can also be managed through direct algebra (*al-jabr*): take the estate, subtract the primary share, recover one-fifth of the remainder, which results in the estate plus five units minus one share and one-fifth. Subtract one-third of that quantity, leaving four-fifths of the estate minus four-fifths of the share, equating to three shares. Solving this yields the estate as nineteen and the primary share as four.