To convert the mixed number $8 \frac{315}{3}$ into an improper fraction:

Step 1: Simplify the fractional part.

$\frac{315}{3} = 105$

So, the mixed number becomes $8 \frac{105}{1}$, which is essentially $8 + 105$.

Step 2: Combine the whole number and the simplified fraction.

$8 + 105 = 113$

Thus, the improper fraction is simply $\frac{113}{1}$.

Would you like more details or have any questions?

Here are 5 related questions for further exploration:

1. How do you convert a mixed fraction with a larger denominator?
2. What is the process for adding or subtracting improper fractions?
3. How can you simplify fractions that are not initially obvious?
4. What are the benefits of converting between improper fractions and mixed numbers?
5. How do improper fractions work in multiplication and division?

Tip: Always simplify the fractional part of a mixed number before converting it to an improper fraction.