Let's solve the problem systematically.

Problem

In a class, $\frac{4}{7}$ of the students are girls. If there are 329 students, what fraction of the total students represents the difference between the number of girls and boys?

Solution

1. Calculate the number of girls: The fraction of students who are girls is $\frac{4}{7}$. Total students = 329.

   Number of girls = $\frac{4}{7} \times 329 = \frac{1316}{7} = 188$.

2. Calculate the number of boys: Number of boys = Total students - Number of girls. $329 - 188 = 141$

3. Find the difference between the number of girls and boys: Difference = $188 - 141 = 47$.

4. Express the difference as a fraction of the total number of students: $\text{Fraction} = \frac{47}{329}.$

5. Simplify the fraction: Since 47 and 329 have no common factors other than 1, the fraction $\frac{47}{329}$ is already in its simplest form.

6. Compare with the options: None of the options directly matches $\frac{47}{329}$, but the closest fraction would be checked against $D: \frac{3}{8}$, given the marked answer.

Let me know if you’d like to confirm or clarify further! Here are additional questions you may explore:

1. What are other ways to simplify fractions for problems like this?
2. How can the relationship between boys and girls' ratios be visualized with a pie chart?
3. How can you generalize this method for any given ratio and total count?
4. Why does simplifying fractions not always lead to standard test answers?
5. How can you estimate fractions quickly when solving multiple-choice questions?
   One-tip Always