A Boy's Marbles Distribution and Fractions

The problem yoursquo;ve presented is a classic example of fraction subtraction. Letrsquo;s explore this through a real-life scenario, where a boy distributes his marbles among his friends and family, and wersquo;ll break down the solution step-by-step.

The Problem

The problem states: A boy gave 1/5 of his marbles to his friend, 1/4 to his elder brother, and 1/8 to his younger brother. What fraction did he keep?

Step-by-Step Solution

Letrsquo;s use algebra to solve this problem. First, let lsquo;xrsquo; represent the total number of marbles. Wersquo;ll find out how much he gave away first, then the fraction he kept.

1. Determine the Fractions Given Away

The boy gave away:

1/5 of his marbles to his friend: 1/5x 1/4 of his marbles to his elder brother: 1/4x 1/8 of his marbles to his younger brother: 1/8x

2. Find the Common Denominator

To add these fractions, we need a common denominator. The least common denominator (LCD) of 5, 4, and 8 is 40. Letrsquo;s convert each fraction:

1/5x 8/4 1/4x 10/4 1/8x 5/4

3. Add the Fractions Given Away

Now, add the fractions lsquo;given awayrsquo;:

8/4 10/4 5/4 23/4

4. Determine the Fraction Kept

To find out the fraction of marbles kept, subtract the fractions given away from the whole:

x - 23/4 40/4 - 23/4 17/4

Conclusion

The fraction of marbles the boy kept is 17/40. Thus, he kept:

17/40 of his marbles

Verification and Explanation

To verify, we can also perform the subtraction directly:

1 - (1/5 1/4 1/8) 1 - (8/40 10/40 5/40) 1 - 23/40 17/40

This confirms the solution he kept 17/40 of his marbles.

Additional Practice

For further practice, try solving similar problems using fractions and check your answers by finding a common denominator and performing the necessary arithmetic operations.

Understanding these steps and practicing similar problems will help you with better fraction manipulation and problem-solving skills in mathematics.