Distributing Money Among Family: A Father's Fractional Gift

Family traditions vary widely, but sometimes a parent's distribution of assets can be a testament to their wisdom and the precise care they took in planning for their future. In this case, a father distributed his money among his three children in a manner that highlights the intricacies of fractional distribution. Let's explore the details and learn how these fractions are calculated.

Fractional Distribution of a Father's Wealth

The father decided to distribute his money among his three children in fractions that add up to a total of the entire sum. The distribution was as follows:

Child A received 1/2 of the total amount.Child B received 1/4 of the total amount.Child C received 1/12 of the total amount.

These fractions, when added together, reveal the total distribution as a fraction of the entire amount the father had. Let's break it down step by step.

Calculating the Total Distributed

Adding the Fractions

First, we need to add the fractions to determine the total amount distributed:

1/2 1/4 1/12

Step 1: Common Denominator

To add these fractions, we need a common denominator. The least common multiple of 2, 4, and 12 is 12, so we convert each fraction:

1/2 6/121/4 3/121/12 1/12

Now, we can add the fractions:

6/12 3/12 1/12 10/12

Step 2: Simplify the Fraction

The fraction 10/12 can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 2:

10 ÷ 2 / 12 ÷ 2 5/6

So, the total distribution of the father's money is 5/6 of the total amount.

Differences in Distribution

Amount Disparity Among Children

It's clear that there is a significant disparity in the amounts received by the children. Here's how much more or less each child received compared to the others:

Child A (1/2) received the most and is 1/4 more than Child B and 1/6 more than Child C.Child B (1/4) received 1/4 less than Child A and is 1/6 more than Child C.Child C (1/12) received the least and is 5/12 less than Child A and 1/6 less than Child B.

Amount Left with the Father

Calculating the Father’s Remaining Amount

Given that the total fraction distributed is 5/6, the amount left with the father can be calculated as follows:

Total amount - Distributed amount Father's remaining amount

1 - 5/6 1/6

This means the father is left with 1/6 of his total amount.

Summary of Key Points

1. The total distributed is 5/6 of the father's amount, with each child receiving:

Child A (1/2)Child B (1/4)Child C (1/12)

2. The difference between the maximum and minimum distribution is 1/2 - 1/12 5/12.

3. The father is left with 1/6 of his total amount.

These calculations can help in understanding the distribution dynamics within families and in planning for inheritance.