To calculate \( 558 \mod 11 \), we divide 558 by 11 and find the remainder.

1. **Divide 558 by 11**: 
   \[
   558 \div 11 = 50.7272 \quad \text{(integer part is 50)}
   \]

2. **Multiply the integer part by 11**: 
   \[
   50 \times 11 = 550
   \]

3. **Subtract this from 558**:
   \[
   558 - 550 = 8
   \]

Thus, \( 558 \mod 11 = 8 \).

Would you like more details or do you have any questions? Here are some related questions to consider:

1. How do you calculate modular arithmetic with larger numbers?
2. What is the significance of the modulus operation in computer science?
3. Can you give an example of using mod in a practical application?
4. What are the properties of modulus operations?
5. How would you compute \( 558 \mod 13 \)? 

**Tip:** Modular arithmetic is often used in cryptography and hashing functions.

Discover how to calculate 558 mod 11 with a comprehensive step-by-step guide. This problem illustrates the principles of modular arithmetic, providing insights into the calculation of remainders. Suitable for students in Grades 6-8.

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