https://file.aiquickdraw.com/mathbot/file/1729469181856c62cpc7r.jpg

Let's solve the problem step by step using the addition table provided.

We are asked to add \( 345_6 \) and \( 413_6 \) in base 6. We will use the addition table for this.

### Step 1: Align the numbers
Align the numbers like this:
```
  345_6
+ 413_6
```

### Step 2: Add the digits starting from the rightmost column
We add each column using the base 6 addition table.

#### Rightmost column (units place):
5 (from 345) + 3 (from 413):
- From the table, find the row labeled 5 and the column labeled 3. The sum is 10.
- In base 6, 10 means 0 with a carry of 1.

#### Middle column (tens place):
4 (from 345) + 1 (from 413) + 1 (carry):
- From the table, 4 + 1 = 5, and adding the carry makes it 6.
- In base 6, 6 means 0 with a carry of 1.

#### Leftmost column (hundreds place):
3 (from 345) + 4 (from 413) + 1 (carry):
- From the table, 3 + 4 = 10, and adding the carry makes it 11.
- In base 6, 11 means 1 with a carry of 1.

Since we still have a carry left, we append that to the result.

### Step 3: Final result
The final result is \( 1100_6 \).

Since the problem asks for the answer without the base 6 subscript, the answer is **1100**.

Would you like more details on any part of the solution?

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Here are 5 related questions for further practice:
1. How would you subtract \( 245_6 \) from \( 513_6 \) using a base 6 subtraction table?
2. How do you multiply two numbers in base 6, for example, \( 34_6 \times 12_6 \)?
3. Convert \( 1100_6 \) into base 10.
4. How can you convert a base 10 number like 100 into base 6?
5. What would the result of \( 515_6 + 321_6 \) be in base 6?

**Tip:** When working with different bases, always keep track of the carry-over, as it differs from base 10!

Use the addition table for base 6 to add 345_6 + 413_6. Do not include the subscript in your answer.

Learn how to add the base 6 numbers 345_6 and 413_6 using a step-by-step approach with the base 6 addition table. This guide includes a detailed breakdown of the carry-over process and is suitable for students in Grades 5-7.

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