Sharing Fractions: A Mathematical Puzzle Explained

Understanding the Problem

In a recent scenario, a mother divides her money among three children, May, Rob, and Eve. The shares are given as fractions of the total money, and the task is to determine what fraction of the money was shared out by the mother. This is a classic example of splitting resources based on fractions, requiring a good understanding of basic arithmetic and fractional calculations.

Breaking Down the Fractions

This problem involves several steps of division and subtraction of fractions. Here's a detailed breakdown:

Step 1: Determine Shares of Rob and Eve

Rob received one-third of the money, and Eve received one-fifth of the money. To find the combined share of Rob and Eve, we perform the following calculation:

Rob's share: ( frac{1}{3}x )

Eve's share: ( frac{1}{5}x )

Adding these shares together:

( frac{1}{3}x frac{1}{5}x frac{5}{15}x frac{3}{15}x frac{8}{15}x )

Step 2: Determine the Remainder

The remainder of the money is the total minus the shares of Rob and Eve:

( 1 - frac{8}{15} frac{15}{15} - frac{8}{15} frac{7}{15} )

Step 3: Calculate May's Share

May received half of the remaining money. Therefore, we calculate May's share as follows:

( frac{1}{2} times frac{7}{15} frac{7}{30} )

Step 4: Calculate the Total Shared Fraction

To find the total fraction of the money that was shared, we add May's share to the sum of Rob's and Eve’s shares:

( frac{8}{15} frac{7}{30} frac{16}{30} frac{7}{30} frac{23}{30} )

Hence, the total fraction of the money that was shared out is ( frac{23}{30} ).

Confidence Interval and Precision in Fractional Calculations

The problem involves working with fractions, a fundamental aspect of arithmetic. Understanding how to convert mixed fractions and perform operations like addition and multiplication is crucial in solving such problems. The precision of the answer, ( frac{23}{30} ), highlights the need for accuracy in such calculations.

Conclusion

This mathematical puzzle not only demonstrates the practical application of fractions in sharing resources but also emphasizes the importance of systematic calculation in verifying the result. By breaking down the problem into manageable steps, we ensured that each fraction was accurately calculated, leading to a final answer of ( frac{23}{30} ).

Understanding and solving such problems enhances analytical and problem-solving skills, making it a valuable exercise in mathematical education.