Dividing Property Among Family Members: A Mathematical Exploration

When a property owner passes away, the distribution of the property among their family members can be handled in various ways, depending on the local laws and the wishes of the deceased. This article explores a specific scenario where a father divides his property among his wife, daughter, and son. We'll use mathematical fractions to solve the problem of how much each family member receives, and explain how to calculate the remaining fraction.

Mathematical Division of Property

In this scenario, a man has devised his property in a specific manner amongst his close relatives: 5/12 to his wife, 6/12 to his daughter, and the rest to his son. Let's break down the problem step by step to find out how much of the property the son receives.

Step 1: Calculating the Property Divided

First, we need to determine the total fraction of the property that has been given to the wife and daughter combined.

Based on the given fractions:

The wife received: ( frac{5}{12} ) The daughter received: ( frac{6}{12} )

Now, let's add these fractions together to find the total fraction given to the wife and daughter:

[ frac{5}{12} frac{6}{12} frac{5 6}{12} frac{11}{12} ]

This means that the wife and daughter together received ( frac{11}{12} ) of the property.

Step 2: Calculating the Remaining Fraction for the Son

Since the whole property is represented as 1 (or ( frac{12}{12} )), we can find the fraction that the son received by subtracting the fraction given to the wife and daughter from the whole property:

[ text{Son’s share} 1 - frac{11}{12} frac{12}{12} - frac{11}{12} frac{1}{12} ]

Thus, the son received ( frac{1}{12} ) of the property.

Alternative Examples

Example 1: Property Division on Hectares

In another scenario, a person named X owns 5/7 hectare of land. He gives 1/2 of this property to his son and 3/4 to his daughters combined.

The amount given to the son is calculated as follows:

[ frac{1}{2} times frac{5}{7} frac{5}{14} ]

The amount given to the daughters combined is calculated as follows:

[ frac{3}{4} times frac{5}{7} frac{15}{28} ]

Adding the fractions to find the total amount given to the son and daughters:

[ frac{5}{14} frac{15}{28} frac{10}{28} frac{15}{28} frac{25}{28} ]

Thus, the amount left is:

[ 1 - frac{25}{28} frac{3}{28} ], which is approximately 0.1071 hectare, or 10.71% of the total property.

Example 2: Combined Mathematical Allocation

A father has 5/7 hectare of land. He gives 1/2 of it to his son and 1/4 to his daughter. Let's calculate the remaining land:

[ frac{1}{2} times frac{5}{7} frac{5}{14} ]

[ frac{1}{4} times frac{5}{7} frac{5}{28} ]

Adding these fractions together:

[ frac{5}{14} frac{5}{28} frac{10}{28} frac{5}{28} frac{15}{28} ]

Subtracting from the whole property:

[ frac{5}{7} - frac{15}{28} frac{20}{28} - frac{15}{28} frac{5}{28} ]

Thus, the remaining land is ( frac{5}{28} ) of a hectare, or approximately 0.1785 hectare.

Complex Example: Inheritance Involving Multiple Heirallocations

A father with 5/7 hectare of land gives 1/8 of it to a charity. He then gives 77/160 to his son and 49/160 to his daughter. Additionally, he gives 7/80 to his wife.

First, calculate the portion given to the charity:

[ 1/8 0.125 ]

Then, add up the portions given to the son, daughter, and wife:

[ 0.55 0.114 0.0875 0.7515 ]

Check if the total exceeds 100%:

[ 1 - 0.7515 0.2485 ]

This indicates that the son and daughter, along with the wife, are dividing the remaining portion of the land. Make sure to consult a legal expert for clarity on the exact distribution and any legal requirements.

Conclusion

Understanding the distribution of property among family members is crucial for ensuring that all parties receive what they are entitled to. By using fractions and simple mathematical operations, we can accurately determine the portions and ensure fair allocation. Always consult legal advice for specific situations and adhere to local laws and customs.