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The problem is asking to add two numbers in base 7 using the provided addition table. The numbers are \( 563_7 \) and \( 246_7 \).

Let's break down the process step by step:

### Step 1: Adding the digits column by column from right to left
We'll use the addition table provided in the image.

#### Rightmost digits (3 and 6 in base 7)
Using the addition table, we look at the intersection of row 3 and column 6. This gives us 12 in base 10, which corresponds to \( 12_7 \). In base 7, this means we write down the 2 and carry over the 1.

#### Middle digits (6 and 4 in base 7)
Now, we add 6 and 4 using the table. Row 6 and column 4 give us 12 in base 7, plus the carry of 1 makes it 13. So we write down 3 and carry over 1.

#### Leftmost digits (5 and 2 in base 7)
For the last column, we add 5 and 2. Row 5 and column 2 give us 7 in base 7, plus the carry of 1 makes it 10. So we write down 0 and carry over the 1.

Finally, the carried-over 1 becomes the leftmost digit.

### Step 2: Final Answer
The final result is \( 1032_7 \), but the problem asks for the answer without the base 7 suffix.

So the final answer is **1032**.

Would you like more details on the steps? Let me know if you have any questions!

Here are 5 related questions:
1. How do you perform addition in other bases, such as base 5 or base 9?
2. Can we convert base 7 numbers to base 10 before performing addition?
3. What is the process for subtraction in base 7?
4. How do you handle carries when adding numbers in other bases?
5. How does multiplication work in base 7?

**Tip**: Always verify carries when working with non-decimal bases, as they can significantly affect the final result!

Use the addition table for base 7 to add 563₇ + 246₇. Give your answer without the suffix.

Learn how to add two numbers in base 7 (563₇ and 246₇) using an addition table. Follow a detailed step-by-step process including handling carries. Suitable for Grades 5-8.

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