To add the numbers \(4_{\text{base 7}}\) and \(6_{\text{base 7}}\) in base 7, we can proceed directly by treating them as base 10 values, then perform the addition and ensure the result is converted back to base 7.

### Steps:

1. **Convert each number to base 10**:
   - \(4_{\text{base 7}} = 4_{\text{base 10}}\)
   - \(6_{\text{base 7}} = 6_{\text{base 10}}\)

2. **Add the base 10 equivalents**:
   \[
   4 + 6 = 10_{\text{base 10}}
   \]

3. **Convert the sum back to base 7**:
   To convert 10 from base 10 to base 7, divide 10 by 7:
   \[
   10 \div 7 = 1 \text{ remainder } 3
   \]
   So, \(10_{\text{base 10}} = 13_{\text{base 7}}\).

### Final Answer:
The sum of \(4_{\text{base 7}} + 6_{\text{base 7}} = 13_{\text{base 7}}\).

Do you need more details on base arithmetic or have any other questions? Here are some related topics to explore:

1. How do you subtract numbers in base 7?
2. How can you multiply two numbers in base 7?
3. What is the process for dividing numbers in base 7?
4. How do you convert numbers from base 10 to base 7?
5. What are the rules for carrying over in base 7 addition?
6. How would you add larger numbers, like \(56_{\text{base 7}} + 32_{\text{base 7}}\)?
7. What happens when you add multiple numbers together in base 7?
8. How does addition in base 7 compare to addition in other bases?

**Tip:** Always double-check your results when adding numbers in different bases to ensure you're using the correct base system rules!

Learn how to add numbers in base 7 with a step-by-step solution. This problem involves converting base 7 numbers to base 10, performing addition, and converting the result back to base 7. Suitable for students learning about number systems and base arithmetic in Grades 6-8.

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