Let's solve this problem step by step.

Let the numerator of the fraction be $x$.

Since the denominator exceeds the numerator by 25, the denominator will be $x + 25$.

The value of the fraction is given as $\frac{3}{8}$.

Thus, we can set up the equation as: $\frac{x}{x + 25} = \frac{3}{8}$

To solve for $x$, cross-multiply: $8x = 3(x + 25)$

Now, distribute the 3 on the right side: $8x = 3x + 75$

Next, subtract $3x$ from both sides to isolate $x$ on one side: $5x = 75$

Now, divide both sides by 5 to solve for $x$: $x = 15$

So, the numerator of the fraction is 15.

The denominator, which is $x + 25$, will be: $15 + 25 = 40$

Thus, the fraction is: $\frac{15}{40}$

We can simplify this fraction by dividing both the numerator and denominator by their greatest common divisor, which is 5: $\frac{15 \div 5}{40 \div 5} = \frac{3}{8}$

Therefore, the fraction is $\frac{15}{40}$.

Would you like to go over any details, or do you have any questions?

Here are 5 related questions you might find interesting:

1. How do you find the least common denominator between two fractions?
2. What is the process for adding fractions with different denominators?
3. How do you simplify complex fractions?
4. Can a fraction be greater than 1? If so, give an example.
5. How do you convert an improper fraction to a mixed number?

Tip: When working with fractions, always check if the final answer can be simplified by finding the greatest common divisor of the numerator and denominator.