Answer key for a math addition worksheet with problems involving numbers 1 through 9.

The image you uploaded appears to be a multiplication worksheet focusing on the 0, 1, and 2 times tables. The task involves solving all the multiplication problems in the grid and filling in the answers. Below is an explanation of how to solve this type of problem and the solution for the worksheet.

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Understanding the Worksheet

1. Structure: The worksheet consists of a grid with rows and columns. Each cell in the grid represents a multiplication problem.
- The numbers along the top row (columns) are the multipliers.
- The numbers along the left column (rows) are the multiplicands.
- Each cell contains the product of the corresponding row and column numbers.

2. Objective: Solve each multiplication problem by multiplying the row number by the column number.

3. Example: If the row number is `3` and the column number is `2`, the product is `3 × 2 = 6`.

4. Total Problems: There are 100 problems in total (10 rows × 10 columns).

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Solving the Problems

Let’s break down how to solve one row as an example:

#### Row Example: Multiplying by 2
- Row: `2`
- Columns: `0, 1, 2, 3, ..., 9`

| Column | Calculation | Result |
|--------|-------------|--------|
| 0 | \(2 \times 0\) | 0 |
| 1 | \(2 \times 1\) | 2 |
| 2 | \(2 \times 2\) | 4 |
| 3 | \(2 \times 3\) | 6 |
| 4 | \(2 \times 4\) | 8 |
| 5 | \(2 \times 5\) | 10 |
| 6 | \(2 \times 6\) | 12 |
| 7 | \(2 \times 7\) | 14 |
| 8 | \(2 \times 8\) | 16 |
| 9 | \(2 \times 9\) | 18 |

Repeat this process for all rows (multiplying by 0, 1, 2, ..., 9).

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General Rules for Multiplication

1. Multiplying by 0: Any number multiplied by 0 equals 0.
- Example: \(5 \times 0 = 0\)

2. Multiplying by 1: Any number multiplied by 1 equals the number itself.
- Example: \(7 \times 1 = 7\)

3. Multiplying by 2: Double the number.
- Example: \(4 \times 2 = 8\)

4. Patterns: Notice patterns in the results for each row. For example:
- Multiplying by 2 gives even numbers.
- Multiplying by 5 alternates between ending in 0 and 5.

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Solution Grid

Below is the completed grid for the worksheet. Each cell contains the product of the row number and the column number.

| × | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 1 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| 2 | 0 | 2 | 4 | 6 | 8 | 10 | 12 | 14 | 16 | 18 |
| 3 | 0 | 3 | 6 | 9 | 12 | 15 | 18 | 21 | 24 | 27 |
| 4 | 0 | 4 | 8 | 12 | 16 | 20 | 24 | 28 | 32 | 36 |
| 5 | 0 | 5 | 10 | 15 | 20 | 25 | 30 | 35 | 40 | 45 |
| 6 | 0 | 6 | 12 | 18 | 24 | 30 | 36 | 42 | 48 | 54 |
| 7 | 0 | 7 | 14 | 21 | 28 | 35 | 42 | 49 | 56 | 63 |
| 8 | 0 | 8 | 16 | 24 | 32 | 40 | 48 | 56 | 64 | 72 |
| 9 | 0 | 9 | 18 | 27 | 36 | 45 | 54 | 63 | 72 | 81 |

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Final Answer

The completed grid is as shown above. If you need the full numerical grid written out, here it is:

```
0 0 0 0 0 0 0 0 0 0
0 1 2 3 4 5 6 7 8 9
0 2 4 6 8 10 12 14 16 18
0 3 6 9 12 15 18 21 24 27
0 4 8 12 16 20 24 28 32 36
0 5 10 15 20 25 30 35 40 45
0 6 12 18 24 30 36 42 48 54
0 7 14 21 28 35 42 49 56 63
0 8 16 24 32 40 48 56 64 72
0 9 18 27 36 45 54 63 72 81
```

Thus, the final answer is:

\[
\boxed{
\begin{array}{cccccccccc}
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\
0 & 2 & 4 & 6 & 8 & 10 & 12 & 14 & 16 & 18 \\
0 & 3 & 6 & 9 & 12 & 15 & 18 & 21 & 24 & 27 \\
0 & 4 & 8 & 12 & 16 & 20 & 24 & 28 & 32 & 36 \\
0 & 5 & 10 & 15 & 20 & 25 & 30 & 35 & 40 & 45 \\
0 & 6 & 12 & 18 & 24 & 30 & 36 & 42 & 48 & 54 \\
0 & 7 & 14 & 21 & 28 & 35 & 42 & 49 & 56 & 63 \\
0 & 8 & 16 & 24 & 32 & 40 & 48 & 56 & 64 & 72 \\
0 & 9 & 18 & 27 & 36 & 45 & 54 & 63 & 72 & 81 \\
\end{array}
}
\]