Determining the estate value when the sons' shares constitute the remainder after a third of the total estate has been bequeathed.

Primary text

If the sons' shares represent the residue after a one-third bequest, one must add half of the sons' portion to establish the full share plus the bequest. The bequest itself is defined as one share minus one-fifth of the remainder, which equals one-half share plus one-fifth share, and one-fifth of the bequest. This resulting fraction is subtracted from the primary share, leaving a calculated remainder which is set equal to the bequest. Through algebraic simplification (*al-jabr wa al-muqabalah*), three units of the share are found to equal twelve units of the bequest. Adjusting for common divisors, one unit equals four. Therefore, the bequest is one unit, the primary share is four units, and the total estate is nineteen.