Let's break down the expression step by step:

1. First, evaluate the two mod operations separately:
   - \( 61 \mod 6 = 61 - (6 \times 10) = 1 \)
   - \( 33 \mod 6 = 33 - (6 \times 5) = 3 \)

2. Add the results:
   - \( 1 + 3 = 4 \)

3. Finally, take the result mod 6:
   - \( 4 \mod 6 = 4 \)

So, the result of \( [(61 \mod 6) + (33 \mod 6)] \mod 6 \) is **4**.

Would you like further clarification or details?

Here are some related questions to consider:
1. What does the modulo operation represent mathematically?
2. How do different moduli affect the results of a modular expression?
3. What are the properties of modular arithmetic in relation to addition and multiplication?
4. How can modular arithmetic be applied in cryptography?
5. How can you compute mod for very large numbers efficiently?

**Tip**: Modular arithmetic often comes in handy for solving problems in number theory, cryptography, and computer science!

Explore the step-by-step solution to the modular arithmetic expression [(61 mod 6) + (33 mod 6)] mod 6. This guide helps students understand how to break down and solve mod operations, focusing on key concepts of modular arithmetic. Ideal for Grades 8-10.

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