https://file.aiquickdraw.com/mathbot/file/1722539952707u3x84gnq.PNG

To solve the problem in the image, we need to add the numbers \(453_6\) and \(345_6\), which are written in base 6.

### Steps to Solve:

1. **Convert Base 6 to Base 10:**
   - For \(453_6\):
     \[ 4 \times 6^2 + 5 \times 6^1 + 3 \times 6^0 = 4 \times 36 + 5 \times 6 + 3 \times 1 \]
     \[ 144 + 30 + 3 = 177_{10} \]

   - For \(345_6\):
     \[ 3 \times 6^2 + 4 \times 6^1 + 5 \times 6^0 = 3 \times 36 + 4 \times 6 + 5 \times 1 \]
     \[ 108 + 24 + 5 = 137_{10} \]

2. **Add the Base 10 Numbers:**
   \[ 177 + 137 = 314 \]

3. **Convert the Result Back to Base 6:**
   \[ 314 \div 6 = 52 \text{ R } 2 \quad \text{(2 is the least significant digit)} \]
   \[ 52 \div 6 = 8 \text{ R } 4 \quad \text{(4 is the next digit)} \]
   \[ 8 \div 6 = 1 \text{ R } 2 \quad \text{(2 is the next digit)} \]
   \[ 1 \div 6 = 0 \text{ R } 1 \quad \text{(1 is the most significant digit)} \]

So, the sum in base 6 is \(1242_6\).

### Final Answer:
\[ 453_6 + 345_6 = 1242_6 \]

Would you like more details on any of the steps, or do you have any other questions?

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**Follow-up Questions:**
1. How do you convert a number from base 6 to base 10?
2. What is the significance of the base in numeral systems?
3. Can you explain the division and remainder method in base conversion?
4. How can you verify the correctness of base conversion?
5. What is the difference between positional numeral systems and non-positional numeral systems?
6. How does base 6 (senary) compare to more common bases like decimal or binary?
7. What are some applications of different base systems in computing?
8. Can you solve another example of addition in a different base?

**Tip:** When working with different bases, ensure that you correctly interpret the digits and place values according to the base being used.

Learn how to solve the addition of numbers in base 6 step-by-step. This problem involves converting base 6 numbers to base 10, adding them, and converting the result back to base 6. Detailed explanations and examples provided.

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