Mixed-Up Multiplication Table Worksheet for Math Practice

Let's solve the Mixed-Up Multiplication Table puzzle step by step.

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🔍 Understanding the Problem

We have a grid where:
- The top row (horizontal) contains numbers:
`2, 5, 9, 12, 0, 6, 7, 10, 3, 8, 1, 11, 4`
- The left column (vertical) contains numbers:
`12, 1, 5, 0, 8, 2, 4, 11, 7, 10, 3, 9, 6`

These are the multipliers. Each cell in the grid is the product of the corresponding row and column numbers.

Our goal: Fill in the empty squares using multiplication.

We’re given some products already filled in to help us verify or deduce others.

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🧩 Step-by-step Strategy

We’ll go through each row and use known values to deduce missing ones.

Let’s label the columns (top row) as:

| Col | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
|-----|---|---|---|---|---|---|---|---|---|---|----|----|----|
| | 2 | 5 | 9 |12 | 0 | 6 | 7 |10 | 3 | 8 | 1 | 11 | 4 |

And rows (left column):

| Row | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |10 |11 |12 |
|-----|---|---|---|---|---|---|---|---|---|---|---|---|---|
| |12 | 1 | 5 | 0 | 8 | 2 | 4 |11 | 7 |10 | 3 | 9 | 6 |

Now we can compute any cell as:
Row number × Column number

But note: the order is scrambled! So we need to match the position.

Let’s create a table with correct positions.

We'll denote:
- Rows: from top to bottom: R0 = 12, R1 = 1, R2 = 5, ..., R12 = 6
- Columns: from left to right: C0 = 2, C1 = 5, C2 = 9, ..., C12 = 4

So cell at row i, column j = R_i × C_j

Let’s fill in the entire grid based on this.

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✔ Let's fill in the grid systematically

We'll go row by row.

#### Row 0: R0 = 12

Multiply 12 by each column value:

- C0: 12×2 = 24
- C1: 12×5 = 60
- C2: 12×9 = 108
- C3: 12×12 = 144
- C4: 12×0 = 0
- C5: 12×6 = 72
- C6: 12×7 = 84
- C7: 12×10 = 120
- C8: 12×3 = 36 → Already given!
- C9: 12×8 = 96
- C10: 12×1 = 12 → Given!
- C11: 12×11 = 132
- C12: 12×4 = 48

So Row 0: [24, 60, 108, 144, 0, 72, 84, 120, 36, 96, 12, 132, 48]

Wait — but look: in the original table, C8 = 3, so 12×3=36 → matches given value.
Also, C10 = 1 → 12×1 = 12 → matches.

✔ Good.

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#### Row 1: R1 = 1

1 × anything = that number.

So:
- C0: 1×2 = 2
- C1: 1×5 = 5
- C2: 1×9 = 9
- C3: 1×12 = 12 → Given!
- C4: 1×0 = 0
- C5: 1×6 = 6
- C6: 1×7 = 7
- C7: 1×10 = 10
- C8: 1×3 = 3
- C9: 1×8 = 8
- C10: 1×1 = 1
- C11: 1×11 = 11
- C12: 1×4 = 4 → Given!

So Row 1: [2, 5, 9, 12, 0, 6, 7, 10, 3, 8, 1, 11, 4] → matches the top row!

This confirms our setup.

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#### Row 2: R2 = 5

5 × each column:

- C0: 5×2 = 10
- C1: 5×5 = 25
- C2: 5×9 = 45
- C3: 5×12 = 60
- C4: 5×0 = 0
- C5: 5×6 = 30
- C6: 5×7 = 35
- C7: 5×10 = 50
- C8: 5×3 = 15
- C9: 5×8 = 40 → Given!
- C10: 5×1 = 5 → Given!
- C11: 5×11 = 55
- C12: 5×4 = 20

So Row 2: [10, 25, 45, 60, 0, 30, 35, 50, 15, 40, 5, 55, 20]

Given values: C9 = 40, C10 = 5 → matches.

✔ Good.

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#### Row 3: R3 = 0

Any number × 0 = 0

So all entries in this row are 0

→ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

C4 is 0 → 0×0 = 0 → matches given.

✔ Done.

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#### Row 4: R4 = 8

8 × each column:

- C0: 8×2 = 16 → Given!
- C1: 8×5 = 40
- C2: 8×9 = 72
- C3: 8×12 = 96
- C4: 8×0 = 0
- C5: 8×6 = 48
- C6: 8×7 = 56 → Given!
- C7: 8×10 = 80
- C8: 8×3 = 24
- C9: 8×8 = 64
- C10: 8×1 = 8
- C11: 8×11 = 88 → Given!
- C12: 8×4 = 32

So Row 4: [16, 40, 72, 96, 0, 48, 56, 80, 24, 64, 8, 88, 32]

Given: 16, 56, 88 → matches.

✔ Good.

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#### Row 5: R5 = 2

2 × each column:

- C0: 2×2 = 4
- C1: 2×5 = 10
- C2: 2×9 = 18
- C3: 2×12 = 24
- C4: 2×0 = 0
- C5: 2×6 = 12
- C6: 2×7 = 14
- C7: 2×10 = 20
- C8: 2×3 = 6
- C9: 2×8 = 16
- C10: 2×1 = 2
- C11: 2×11 = 22
- C12: 2×4 = 8

So Row 5: [4, 10, 18, 24, 0, 12, 14, 20, 6, 16, 2, 22, 8]

No given values here, but let’s check if any clues match.

Wait — look at Row 7: has 66, 70, etc.

We’ll come back.

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#### Row 6: R6 = 4

4 × each column:

- C0: 4×2 = 8
- C1: 4×5 = 20
- C2: 4×9 = 36 → Given!
- C3: 4×12 = 48
- C4: 4×0 = 0
- C5: 4×6 = 24
- C6: 4×7 = 28
- C7: 4×10 = 40 → Given!
- C8: 4×3 = 12
- C9: 4×8 = 32
- C10: 4×1 = 4
- C11: 4×11 = 44
- C12: 4×4 = 16

So Row 6: [8, 20, 36, 48, 0, 24, 28, 40, 12, 32, 4, 44, 16]

Given: 36, 40 → matches.

✔ Good.

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#### Row 7: R7 = 11

11 × each column:

- C0: 11×2 = 22
- C1: 11×5 = 55
- C2: 11×9 = 99
- C3: 11×12 = 132
- C4: 11×0 = 0
- C5: 11×6 = 66 → Given!
- C6: 11×7 = 77
- C7: 11×10 = 110
- C8: 11×3 = 33
- C9: 11×8 = 88
- C10: 11×1 = 11
- C11: 11×11 = 121
- C12: 11×4 = 44

So Row 7: [22, 55, 99, 132, 0, 66, 77, 110, 33, 88, 11, 121, 44]

Given: 66, 33 → matches.

✔ Good.

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#### Row 8: R8 = 7

7 × each column:

- C0: 7×2 = 14
- C1: 7×5 = 35
- C2: 7×9 = 63 → Given!
- C3: 7×12 = 84
- C4: 7×0 = 0
- C5: 7×6 = 42
- C6: 7×7 = 49
- C7: 7×10 = 70 → Given!
- C8: 7×3 = 21
- C9: 7×8 = 56
- C10: 7×1 = 7
- C11: 7×11 = 77
- C12: 7×4 = 28

So Row 8: [14, 35, 63, 84, 0, 42, 49, 70, 21, 56, 7, 77, 28]

Given: 63, 70 → matches.

✔ Good.

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#### Row 9: R9 = 10

10 × each column:

- C0: 10×2 = 20
- C1: 10×5 = 50
- C2: 10×9 = 90
- C3: 10×12 = 120
- C4: 10×0 = 0
- C5: 10×6 = 60
- C6: 10×7 = 70
- C7: 10×10 = 100
- C8: 10×3 = 30
- C9: 10×8 = 80 → Given!
- C10: 10×1 = 10
- C11: 10×11 = 110
- C12: 10×4 = 40

So Row 9: [20, 50, 90, 120, 0, 60, 70, 100, 30, 80, 10, 110, 40]

Given: 80 → matches.

✔ Good.

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#### Row 10: R10 = 3

3 × each column:

- C0: 3×2 = 6
- C1: 3×5 = 15
- C2: 3×9 = 27
- C3: 3×12 = 36 → Given!
- C4: 3×0 = 0
- C5: 3×6 = 18
- C6: 3×7 = 21
- C7: 3×10 = 30
- C8: 3×3 = 9
- C9: 3×8 = 24
- C10: 3×1 = 3
- C11: 3×11 = 33 → Given!
- C12: 3×4 = 12

So Row 10: [6, 15, 27, 36, 0, 18, 21, 30, 9, 24, 3, 33, 12]

Given: 36, 33 → matches.

✔ Good.

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#### Row 11: R11 = 9

9 × each column:

- C0: 9×2 = 18
- C1: 9×5 = 45
- C2: 9×9 = 81
- C3: 9×12 = 108
- C4: 9×0 = 0
- C5: 9×6 = 54
- C6: 9×7 = 63 → Given!
- C7: 9×10 = 90
- C8: 9×3 = 27
- C9: 9×8 = 72 → Given!
- C10: 9×1 = 9
- C11: 9×11 = 99
- C12: 9×4 = 36

So Row 11: [18, 45, 81, 108, 0, 54, 63, 90, 27, 72, 9, 99, 36]

Given: 63, 72 → matches.

✔ Good.

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#### Row 12: R12 = 6

6 × each column:

- C0: 6×2 = 12
- C1: 6×5 = 30 → Given!
- C2: 6×9 = 54
- C3: 6×12 = 72 → Given!
- C4: 6×0 = 0
- C5: 6×6 = 36
- C6: 6×7 = 42
- C7: 6×10 = 60
- C8: 6×3 = 18
- C9: 6×8 = 48
- C10: 6×1 = 6
- C11: 6×11 = 66
- C12: 6×4 = 24

So Row 12: [12, 30, 54, 72, 0, 36, 42, 60, 18, 48, 6, 66, 24]

Given: 30, 72 → matches.

✔ Good.

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✔ Final Answer: Complete Grid

Now, we can write the full completed grid.

Here is the completed multiplication table:

```
2 5 9 12 0 6 7 10 3 8 1 11 4
-----------------------------------------------------
12 | 24 60 108 144 0 72 84 120 36 96 12 132 48
1 | 2 5 9 12 0 6 7 10 3 8 1 11 4
5 | 10 25 45 60 0 30 35 50 15 40 5 55 20
0 | 0 0 0 0 0 0 0 0 0 0 0 0 0
8 | 16 40 72 96 0 48 56 80 24 64 8 88 32
2 | 4 10 18 24 0 12 14 20 6 16 2 22 8
4 | 8 20 36 48 0 24 28 40 12 32 4 44 16
11 | 22 55 99 132 0 66 77 110 33 88 11 121 44
7 | 14 35 63 84 0 42 49 70 21 56 7 77 28
10 | 20 50 90 120 0 60 70 100 30 80 10 110 40
3 | 6 15 27 36 0 18 21 30 9 24 3 33 12
9 | 18 45 81 108 0 54 63 90 27 72 9 99 36
6 | 12 30 54 72 0 36 42 60 18 48 6 66 24
```

All given values are now verified.

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📌 Summary

The puzzle is solved by recognizing that:
- The row numbers are listed down the left side (12, 1, 5, ..., 6)
- The column numbers are across the top (2, 5, 9, ..., 4)
- Each cell is the product of its row and column numbers
- Use multiplication facts to fill in blanks
- Cross-check with given values for accuracy

✔ All empty cells are now correctly filled.

Let me know if you'd like this as a printable PDF or formatted table!