Kwame Was Given An Amount Of Money. He Gave 2 5 \frac{2}{5} 5 2 ​ Of It To His Friends To Share Equally. What Fraction Of The Money Did Each Friend Get?

Introduction

In this problem, we are presented with a scenario where Kwame has a certain amount of money and decides to share it with his friends. The question asks us to find the fraction of the money each friend receives when Kwame gives $\frac{2}{5}$ of it to them to share equally. This problem involves basic concepts of fractions and division, and we will use these concepts to solve it.

Understanding the Problem

Let's break down the problem step by step. Kwame has a certain amount of money, which we can represent as $x$. He decides to give $\frac{2}{5}$ of this amount to his friends to share equally. This means that the amount of money given to the friends is $\frac{2}{5}x$. Since the friends are sharing this amount equally, we need to find the fraction of the money each friend receives.

Finding the Fraction of Money Each Friend Receives

To find the fraction of money each friend receives, we need to divide the amount of money given to the friends ($\frac{2}{5}x$) by the number of friends. However, the problem does not specify the number of friends. Let's assume there are $n$ friends. Then, the amount of money each friend receives is $\frac{\frac{2}{5}x}{n}$.

Simplifying the Expression

We can simplify the expression $\frac{\frac{2}{5}x}{n}$ by multiplying the numerator and denominator by $5$. This gives us $\frac{2x}{5n}$.

Interpreting the Result

The expression $\frac{2x}{5n}$ represents the fraction of the money each friend receives. This means that each friend receives $\frac{2}{5n}$ of the original amount of money $x$. The more friends there are, the smaller the fraction of money each friend receives.

Example

Let's consider an example to illustrate this concept. Suppose Kwame has $100 and gives $\frac{2}{5}$ of it to his friends to share equally. If there are $5$ friends, each friend will receive $\frac{2}{5} \times \frac{100}{5} = \frac{40}{5} = 8$ dollars.

Conclusion

In conclusion, when Kwame gives $\frac{2}{5}$ of the money to his friends to share equally, each friend receives $\frac{2}{5n}$ of the original amount of money. This means that the more friends there are, the smaller the fraction of money each friend receives.

Key Takeaways

• When Kwame gives $\frac{2}{5}$ of the money to his friends to share equally, each friend receives $\frac{2}{5n}$ of the original amount of money.
• The more friends there are, the smaller the fraction of money each friend receives.
• The expression $\frac{2x}{5n}$ represents the fraction of the money each friend receives.

Further Exploration

This problem can be extended to explore other scenarios, such as:

• What if Kwame gives a different fraction of the money to his friends?
• What if there are more or fewer friends?
• How does the amount of money given to the friends affect the fraction of money each friend receives?

Introduction

In our previous article, we explored the problem of Kwame giving $\frac{2}{5}$ of his money to his friends to share equally. We found that each friend receives $\frac{2}{5n}$ of the original amount of money. In this article, we will answer some frequently asked questions related to this problem.

Q&A

Q: What if Kwame gives a different fraction of the money to his friends?

A: If Kwame gives a different fraction of the money to his friends, the fraction of money each friend receives will also change. For example, if Kwame gives $\frac{3}{5}$ of the money to his friends, each friend will receive $\frac{3}{5n}$ of the original amount of money.

Q: What if there are more or fewer friends?

A: If there are more friends, the fraction of money each friend receives will be smaller. For example, if there are $10$ friends instead of $5$, each friend will receive $\frac{2}{50}$ of the original amount of money. If there are fewer friends, the fraction of money each friend receives will be larger.

Q: How does the amount of money given to the friends affect the fraction of money each friend receives?

A: The amount of money given to the friends does not affect the fraction of money each friend receives. The fraction of money each friend receives is determined by the fraction of the money given to the friends and the number of friends.

Q: Can we use this problem to solve other problems involving fractions and division?

A: Yes, this problem can be used to solve other problems involving fractions and division. By applying the concepts learned from this problem, you can solve problems involving fractions and division in a variety of contexts.

Q: What are some real-world applications of this problem?

A: This problem has real-world applications in finance, economics, and other fields. For example, when a company distributes dividends to its shareholders, the fraction of the dividend each shareholder receives is determined by the number of shares they own.

Q: Can we extend this problem to include other variables?

A: Yes, this problem can be extended to include other variables. For example, we can add a variable to represent the interest rate on the money given to the friends. This would allow us to explore how the interest rate affects the fraction of money each friend receives.

Conclusion

In conclusion, this Q&A guide provides answers to some frequently asked questions related to the problem of Kwame giving $\frac{2}{5}$ of his money to his friends to share equally. By applying the concepts learned from this problem, you can solve problems involving fractions and division in a variety of contexts.

Key Takeaways

• The fraction of money each friend receives is determined by the fraction of the money given to the friends and the number of friends.
• The amount of money given to the friends does not affect the fraction of money each friend receives.
• This problem can be used to solve other problems involving fractions and division.
• This problem has real-world applications in finance, economics, and other fields.

Further Exploration

This problem can be extended to include other variables and real-world applications. By exploring these extensions, you can develop a deeper understanding of the concepts involved and develop problem-solving skills that can be applied to a wide range of mathematical problems.