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The problem is to add the numbers \( 315_6 \) and \( 255_6 \), where the subscript 6 indicates that these numbers are in base 6.

### Step 1: Convert to Base 10
First, convert both numbers from base 6 to base 10.

- \( 315_6 = 3 \times 6^2 + 1 \times 6^1 + 5 \times 6^0 \)
  \[
  = 3 \times 36 + 1 \times 6 + 5 \times 1 = 108 + 6 + 5 = 119_{10}
  \]

- \( 255_6 = 2 \times 6^2 + 5 \times 6^1 + 5 \times 6^0 \)
  \[
  = 2 \times 36 + 5 \times 6 + 5 \times 1 = 72 + 30 + 5 = 107_{10}
  \]

### Step 2: Add in Base 10
Now, add the two base 10 numbers.

\[
119_{10} + 107_{10} = 226_{10}
\]

### Step 3: Convert the Sum Back to Base 6
Finally, convert the result back to base 6.

To convert \( 226_{10} \) to base 6:
1. Divide 226 by 6, which gives a quotient of 37 and a remainder of 4.
2. Divide 37 by 6, which gives a quotient of 6 and a remainder of 1.
3. Divide 6 by 6, which gives a quotient of 1 and a remainder of 0.
4. Divide 1 by 6, which gives a quotient of 0 and a remainder of 1.

So, \( 226_{10} \) in base 6 is \( 1014_6 \).

### Final Answer:
\[
315_6 + 255_6 = 1014_6
\]

Would you like further details or have any questions?

### Related Questions:
1. How do you convert between different bases?
2. What are the steps to add numbers in a base other than 10 directly?
3. How do you subtract numbers in base 6?
4. Can you explain multiplication in different bases?
5. What is the importance of understanding base conversions in computer science?
6. How do you perform division in base 6?
7. What are the common base systems used in mathematics and computing?
8. Can you provide a step-by-step guide for base conversion?

**Tip:** When working with different bases, always ensure you correctly identify the base before performing operations, as this affects the interpretation of digits.

Learn how to add numbers in base 6, specifically how to add the numbers 315_6 and 255_6 step-by-step. This problem involves converting numbers from base 6 to base 10, performing addition in base 10, and converting the result back to base 6. Suitable for students in Grades 7-9.

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