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The problem asks to add \( 53_6 + 35_6 \) (numbers in base 6) using the provided addition table for base 6.

Let's break this down step by step:

### Step 1: Breakdown of Base-6 Numbers
- \( 53_6 \) means:
  - \( 5 \times 6^1 + 3 \times 6^0 = 30 + 3 = 33_{10} \)
  
- \( 35_6 \) means:
  - \( 3 \times 6^1 + 5 \times 6^0 = 18 + 5 = 23_{10} \)

### Step 2: Add the Decimal Equivalents
Now add the decimal equivalents:
\[ 33_{10} + 23_{10} = 56_{10} \]

### Step 3: Convert the Result Back to Base 6
To convert \( 56_{10} \) to base 6, divide by 6:
- \( 56 \div 6 = 9 \) remainder \( 2 \)
- \( 9 \div 6 = 1 \) remainder \( 3 \)
- \( 1 \div 6 = 0 \) remainder \( 1 \)

So, \( 56_{10} = 132_6 \).

### Answer: \( 132_6 \)
Since the instruction asks to give the answer without the suffix, the answer is **132**.

Would you like a more detailed explanation or do you have any other questions?

Here are some related questions to further your understanding:

1. How does base conversion work in general?
2. What are the steps to add two numbers directly in a non-decimal base?
3. Can you explain how the addition table is constructed for any base?
4. How would subtraction work in base 6 using a similar table?
5. What are the practical applications of using base-6 (or other non-decimal) systems?

**Tip:** Always remember to carry over when the sum exceeds the base during addition in non-decimal systems, just like in base 10.

Use the addition table for base 6 to add: 53_6 + 35_6. Give your answer without the suffix.

Learn how to add two numbers in base 6 (53_6 and 35_6) using an addition table. This problem demonstrates key concepts like base conversion and handling carry-overs in non-decimal bases, suitable for students in Grades 6-9.

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