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The problem asks to add \(41_6 + 55_6\) in base 6 using the given addition table. Let's break it down step by step:

### Step 1: Adding the rightmost digits
The rightmost digits are 1 and 5. Using the base 6 addition table:
- Row 1, Column 5 gives the sum of \(1 + 5 = 10_6\). In base 6, \(10_6\) is written as 0 with a carry of 1.

### Step 2: Adding the leftmost digits
Now we move to the leftmost digits: 4 and 5. We must also add the carry of 1 from the previous step:
- First, find \(4 + 5 = 11_6\) from the table (Row 4, Column 5 gives 11).
- Add the carry of 1 to this sum: \(11_6 + 1 = 12_6\). The table shows that \(12_6\) is 2 with a carry of 1.

### Step 3: Final result
Since there is a final carry of 1, the result is \(102_6\).

Thus, the base 6 sum of \(41_6 + 55_6\) is \(102_6\), and the answer without the base suffix is:

\[
\boxed{102}
\]

Do you need any further details or have any questions? Here are some related questions:

1. How do you convert numbers between base 6 and base 10?
2. What are the rules for carrying over in base 6 arithmetic?
3. How do different base systems work in general?
4. Can you explain subtraction in base 6 using the same method?
5. How can you verify the base 6 addition by converting it to base 10 first?

**Tip**: When adding in any base system, always remember to adjust for overflow based on the base's value (in this case, 6), and carry the extra digits to the next higher place.

Use the addition table for base 6 to add: 41₆ + 55₆. Give your answer without the suffix.

Learn how to perform base 6 addition by adding 41₆ + 55₆ using an addition table. This example walks you through the steps, including handling carry-over and interpreting the final result. Suitable for students in Grades 6-8.

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