Mathematical Problem: Land Distribution and Fraction Calculation

The problem of land distribution can be a practical application of mathematical concepts, specifically fractions and proportions. This problem revolves around a scenario where a man sells and divides his land among his children. Let us explore this problem in detail.

Problem Breakdown

A man sold one-third of his land. After selling this portion, he gave one-third of the remaining land to his son and one-third of the remaining land to his daughter. We need to determine what fraction of the land is left with him.

Step-by-Step Solution

Initial Land: Let's denote the entire land as 1. This represents the total land he initially owned.

Land Sold: The man sold one-third of his land. Therefore, the remaining land is:

[1 - frac{1}{3} frac{2}{3}]

Land Given to Children: He then gave one-third of the remaining land to his son and one-third of the remaining land to his daughter. The remaining land is 2/3. Thus, one-third of the remaining land is:

[frac{1}{3} times frac{2}{3} frac{2}{9}]

So, he gave away 2/9 of his total land to each child. Therefore, the total land given to the children is:

[frac{2}{9} frac{2}{9} frac{4}{9}]

Land Left with Him: To find out how much land he has left, we subtract the sold land and the given land from the initial land:

[1 - frac{1}{3} - frac{4}{9}]

To perform this calculation, we need a common denominator, which is 9:

[1 frac{9}{9}, quad frac{1}{3} frac{3}{9}]

Therefore:

[frac{9}{9} - frac{3}{9} - frac{4}{9} frac{9 - 3 - 4}{9} frac{2}{9}]

Hence, the fraction of land left with him is 2/9.

Conclusion

Through this problem, we have demonstrated how to effectively use fractions to solve real-life scenarios, such as land distribution. By following the step-by-step solution, we can see that he has 2/9 of his original land remaining.

Additional Examples and Exercises

To further enhance your understanding, you can try similar problems involving land distribution. Here are a few examples:

Problem: A farmer sells 1/4 of his land, gives 1/5 of the remaining land to his son, and then gives 1/6 of what’s left to his daughter. What fraction of the land does he have left? Exercise: A person divides their land among 3 children, each receiving 1/6 of the land. How much land does the person have left?

By practicing these problems, you can improve your skills in fraction calculation and problem-solving.