Cake Division in a Family: The Mathematical and Practical Approach

In a familiar household scenario, a mother brings home a cake, and the rest of the cake is shared among the family. This simple act of sharing can be a complex problem involving fractions and logical reasoning. Let's explore the mathematics behind distributing the cake among the family members.

The Problem

A mother brings home a cake. She eats 1/6 of it, and the father eats 1/4 of it. The rest of the cake is shared equally among her three children. What fraction of the cake does each child receive?

Step-by-Step Solution

To solve this problem, we need to follow a series of steps involving fractions. Here is the detailed process:

Step 1: Calculate the Total Amount of Cake Eaten by the Mother and Father

The mother ate 1/6 of the cake, and the father ate 1/4 of the cake. We can add these fractions to find out how much of the cake they both ate together. However, before adding, we need to find a common denominator.

Step 1.1: Find the least common multiple (LCM) of 6 and 4, which is 12.

Step 1.2: Convert the fractions to have a common denominator.

Step 2: Add the Fractions Together

Now we add the two fractions:

2/12 3/12 5/12

This means that the mother and father together ate 5/12 of the cake.

Step 3: Calculate the Remaining Cake

The total amount of cake left after the mother and father have eaten is:

1 - 5/12 7/12

Step 4: Share the Remaining Cake Among the Children

The remaining 7/12 of the cake is shared equally among the three children. We divide this fraction by 3:

7/12 ÷ 3 7/36

Therefore, each child receives 7/36 of the cake.

Conclusion

The answer to the question, based on the given fractions, is 7/36. The correct option is (d) 7/36.

Practical Consideration

While the mathematical solution is clear, let's consider the practical aspect of sharing a cake. Dividing the cake into 36 slices is a practical and equal distribution. If we divide the cake into 36 slices, each child will get 7 slices. This is a fair and manageable way to distribute the cake, ensuring each child gets a fair share.

Final Thoughts

The question highlights the importance of clear communication and context in problem-solving. Understanding the exact meaning of the problem can significantly alter the solution. In this case, the initial problem statement was clear, but any ambiguity can lead to different interpretations.

As a mother, the act of bringing home the cake and sharing it with her family can be a challenging yet rewarding experience. Teaching children about sharing and dividing resources fairly is an important life lesson. The cake problem serves as a fun and engaging way to practice fractions and problem-solving skills in a real-world context.

Key Takeaways

Fractions: Understanding and working with fractions is essential for various practical and theoretical applications.

Problem-Solving: Clear communication and logical reasoning are crucial for solving complex problems.

Family Dynamics: Sharing resources and finding fair solutions in a family setting can teach valuable life lessons.