Addition Table (1-10) for learning basic math operations.

Problem Description:

The image shows an Addition Table (1 - 10), which is a grid where the rows and columns represent numbers from 1 to 10. Each cell in the grid contains the sum of the row number and the column number.

Task:

The task is to understand how the addition table works and verify or explain the entries in the table.

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Solution Explanation:

#### Step 1: Understanding the Structure
- The table has rows labeled with numbers from 1 to 10 on the left side.
- The table has columns labeled with numbers from 1 to 10 at the top.
- Each cell in the table represents the sum of the corresponding row number and column number.

For example:
- The cell in the first row and first column contains \( 1 + 1 = 2 \).
- The cell in the second row and third column contains \( 2 + 3 = 5 \).
- The cell in the fifth row and seventh column contains \( 5 + 7 = 12 \).

#### Step 2: Verifying the Entries
Let's verify a few entries to ensure the table is correct:

1. First Row (Row 1):
- \( 1 + 1 = 2 \)
- \( 1 + 2 = 3 \)
- \( 1 + 3 = 4 \)
- ...
- \( 1 + 10 = 11 \)

2. Second Row (Row 2):
- \( 2 + 1 = 3 \)
- \( 2 + 2 = 4 \)
- \( 2 + 3 = 5 \)
- ...
- \( 2 + 10 = 12 \)

3. Fifth Row (Row 5):
- \( 5 + 1 = 6 \)
- \( 5 + 2 = 7 \)
- \( 5 + 3 = 8 \)
- ...
- \( 5 + 10 = 15 \)

4. Tenth Row (Row 10):
- \( 10 + 1 = 11 \)
- \( 10 + 2 = 12 \)
- \( 10 + 3 = 13 \)
- ...
- \( 10 + 10 = 20 \)

#### Step 3: General Pattern
The value in any cell can be calculated using the formula:
\[
\text{Value} = \text{Row Number} + \text{Column Number}
\]

For example:
- In the cell at row 7 and column 9:
\[
7 + 9 = 16
\]
This matches the entry in the table.

#### Step 4: Observations
- The table is symmetric along the diagonal because addition is commutative (\(a + b = b + a\)).
- The diagonal entries (where row number = column number) are double the row/column number:
- \(1 + 1 = 2\)
- \(2 + 2 = 4\)
- \(3 + 3 = 6\)
- ...
- \(10 + 10 = 20\)

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Final Answer:

The addition table is correctly filled according to the rule:
\[
\boxed{\text{Each cell value is the sum of its row number and column number.}}
\]