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Basic Skills Mathematics Program 
Description:
This lesson describes how a woman’s estate is divided among her beneficiaries according to Islamic inheritance law. The method involves adding and subtracting fractions which represent the parts of the woman’s estate, keeping in mind that sons receive twice as much as daughters, and a stranger’s share must be paid first.
Curriculum Objectives:
To reinforce the skills of fraction addition, subtraction and multiplication.
To introduce students to complex problem solving.
To expose students to a mathematical process from a nonEuropean culture.
Key Words:
algebra
inheritance
fractions
problem solving
representations
Suggested Use:
Islamic Inheritance Mathematics could be used in a basic skills mathematics, prealgebra or algebra course to use complex problem solving to reinforce the concepts and skills of fraction addition, subtraction and multiplication.
ISLAMIC INHERITANCE MATHEMATICS
A major Arab mathematician named Muhammad ibn Musa alKhwarizmi wrote an influential textbook in about 820 called Hisab aljabr w’almuqabala (Calculation by Restoration and Reduction) that is known today as the Algebra. This book was the starting point for Arab work in algebra, and it is credited for giving the subject its name. AlKhwarizmi was probably born in Soviet Central Asia but he did most of his work in algebra in Baghdad, where he was an astronomer and head of the library at the House of Wisdom.
AlKwarizmi was a Muslim and the second half of his book Algebra contains problems about the Islamic law of inheritance. According to the law, when a woman dies her husband receives onequarter of her estate, and the rest is divided among her children so that a son receives twice as much as a daughter. If the woman chooses to leave money to a stranger, the stranger cannot receive more than onethird of the estate without the approval of the heirs. If only some of the heirs approve, the approving heirs must pay the stranger out of their own shares the amount that exceeds onethird of the estate. Whether approved by all heirs or not, the stranger’s share must be paid before the rest is shared out among the heirs.
Here is an example problem from AlKwarizmi’s Algebra:
A woman dies leaving a husband, a son, and three daughters. She also leaves a bequest consisting of 1/8 + 1/7 of her estate to a stranger. She leaves $224,000. Calculate the shares of her estate that go to each of her beneficiaries.
Solution: The stranger receives 1/8 + 1/7 = 15/56 of the estate, leaving 41/56 to be shared out among the family.
The husband receives onequarter of what remains, or 1/4 of 41/56 = 41/224.
The son and the three daughters receive their shares in the ratio 2:1:1:1 so the son’s share is two fifths of the estate after the stranger and husband have been given their bequests and each daughter’s share is one fifth. (2+1+1+1=5).
If the total estate is $224,000, the shares received by each beneficiary will be:
Stranger: 15/56 of $224,000 = $60,000.
Husband: 41/224 of $224,000 = $41,000.
Son: 2/5 of ($224,000  101,000) = $49,200.
Each daughter: 1/5 of ($224,000  101,000) = $24,600.
TOTAL = $224,000.
YOUR PROJECT:
1. Solve the following Islamic law inheritance problem.
A woman’s estate totals $72,000. She dies leaving a husband, two sons and two daughters. In her will, she leaves a bequest of 1/9 + 1/6 of her estate to a stranger. Calculate how much of her estate each of her beneficiaries will receive.
2. Write out all of your calculations.
3. Check to make sure your beneficiary sums equal the total estate.
References: Islamic Inheritance Mathematics
Gullberg, Jan. (1997). Mathematics: From the Birth of Numbers. New York: W.W. Norton & Company.
Joseph, George Gheverghese. (1991). The Crest of the Peacock: NonEuropean Roots of Mathematics. London: Penguin Books.
Nelson, D., Joseph, G. and Williams, J. (1993). Multicultural Mathematics: Teaching Mathematics from a Global Perspective. New York: Oxford University Press.
San Joaquin Delta College
Basic Mathematics Program
Communications Skills Division
5151 Pacific Avenue
Stockton, CA 95207
Tel. (209) 9545252
Division Chairperson: Mary Ann Cox
Division Secretary: Joann Hymes
Designed by Patricia Donovan
San Joaquin Delta College
