To solve this problem, let’s analyze the information step-by-step:

1. Understanding the Question:

   • Miles has $2 \frac{3}{4}$ berry granola bars.
   • He plans to break each whole bar into fourths.
   • The task is to find out how many fourths (quarters) he will have in total.

2. Breaking Down $2 \frac{3}{4}$ into Fourths:

   • $2 \frac{3}{4}$ can be broken down as follows: $2 + \frac{3}{4}$
   • Each whole (1) can be represented as $\frac{4}{4}$ in terms of fourths.
   • Therefore: $2 = \frac{4}{4} + \frac{4}{4} = \frac{8}{4}$
   • Adding the remaining $\frac{3}{4}$: $\frac{8}{4} + \frac{3}{4} = \frac{11}{4}$

3. Solution:

   • There are $\frac{11}{4}$ or 11 fourths in total.

The boxes should be filled in as:

• Numerator: 11
• Denominator: 4

Would you like further clarification on any part of the solution?

Here are five additional questions that relate to this problem:

1. What would the total be if Miles had $3 \frac{1}{4}$ granola bars instead?
2. If each fourth weighs 10 grams, what is the total weight of all the fourths Miles has?
3. How many granola bars are needed to make a total of $\frac{15}{4}$ pieces?
4. What is the process for converting any mixed number to an improper fraction?
5. If Miles shares the pieces equally among 5 friends, how many pieces does each friend get?

Tip: When working with mixed numbers, convert them to improper fractions for easier addition or multiplication.