Multiplication Chart -Worksheets Library - Free Printable
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Step-by-step solution for: Multiplication Chart -Worksheets Library
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Show Answer Key & Explanations
Step-by-step solution for: Multiplication Chart -Worksheets Library
It looks like you've uploaded a multiplication chart for numbers 1 through 12, with some cells already filled in and others left blank. The goal of this worksheet is to complete the multiplication table up to 12 × 12, filling in the missing values.
Let’s go step by step to solve the missing entries in the chart.
---
This is a standard 12×12 multiplication table, where:
- The first row (top) and first column (left) are the multipliers.
- Each cell at row `a` and column `b` should contain `a × b`.
We’ll fill in all the blanks based on this rule.
---
We'll go row by row and fill in the missing entries.
#### Row 1: (1 × any number)
All entries are correct:
```
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12
```
#### Row 2:
- 2 × 1 = 2 → Already has 2
- 2 × 2 = 4 → Already has 4
- 2 × 3 = 6 → Missing → 6
- 2 × 4 = 8 → Already has 8
- 2 × 5 = 10 → Missing → 10
- 2 × 6 = 12 → Missing → 12
- 2 × 7 = 14 → Missing → 14
- 2 × 8 = 16 → Already has 16
- 2 × 9 = 18 → Missing → 18
- 2 × 10 = 20 → Missing → 20
- 2 × 11 = 22 → Missing → 22
- 2 × 12 = 24 → Missing → 24
✔ So far, Row 2 needs: 6, 10, 12, 14, 18, 20, 22, 24
#### Row 3:
- 3 × 1 = 3 → Already has 3
- 3 × 2 = 6 → Already has 6
- 3 × 3 = 9 → Missing → 9
- 3 × 4 = 12 → Already has 12
- 3 × 5 = 15 → Already has 15
- 3 × 6 = 18 → Already has 18
- 3 × 7 = 21 → Missing → 21
- 3 × 8 = 24 → Already has 24
- 3 × 9 = 27 → Already has 27
- 3 × 10 = 30 → Already has 30
- 3 × 11 = 33 → Missing → 33
- 3 × 12 = 36 → Already has 36
✔ Missing: 9, 21, 33
#### Row 4:
- 4 × 1 = 4 → Already has 4
- 4 × 2 = 8 → Missing → 8
- 4 × 3 = 12 → Missing → 12
- 4 × 4 = 16 → Already has 16
- 4 × 5 = 20 → Already has 20
- 4 × 6 = 24 → Missing → 24
- 4 × 7 = 28 → Already has 28
- 4 × 8 = 32 → Missing → 32
- 4 × 9 = 36 → Missing → 36
- 4 × 10 = 40 → Already has 40
- 4 × 11 = 44 → Already has 44
- 4 × 12 = 48 → Missing → 48
✔ Missing: 8, 12, 24, 32, 36, 48
Wait — let's double-check:
- 4×2 = 8 → Yes
- 4×3 = 12 → Yes
- 4×6 = 24 → Yes
- 4×8 = 32 → Yes
- 4×9 = 36 → Yes
- 4×12 = 48 → Yes
So yes, those are missing.
#### Row 5:
- 5 × 1 = 5 → Already has 5
- 5 × 2 = 10 → Missing → 10
- 5 × 3 = 15 → Already has 15
- 5 × 4 = 20 → Missing → 20
- 5 × 5 = 25 → Missing → 25
- 5 × 6 = 30 → Already has 30
- 5 × 7 = 35 → Already has 35
- 5 × 8 = 40 → Already has 40
- 5 × 9 = 45 → Missing → 45
- 5 × 10 = 50 → Missing → 50
- 5 × 11 = 55 → Already has 55
- 5 × 12 = 60 → Missing → 60
✔ Missing: 10, 20, 25, 45, 50, 60
#### Row 6:
- 6 × 1 = 6 → Missing → 6
- 6 × 2 = 12 → Already has 12
- 6 × 3 = 18 → Already has 18
- 6 × 4 = 24 → Missing → 24
- 6 × 5 = 30 → Already has 30
- 6 × 6 = 36 → Missing → 36
- 6 × 7 = 42 → Missing → 42
- 6 × 8 = 48 → Already has 48
- 6 × 9 = 54 → Missing → 54
- 6 × 10 = 60 → Already has 60
- 6 × 11 = 66 → Missing → 66
- 6 × 12 = 72 → Already has 72
✔ Missing: 6, 24, 36, 42, 54, 66
#### Row 7:
- 7 × 1 = 7 → Already has 7
- 7 × 2 = 14 → Already has 14
- 7 × 3 = 21 → Missing → 21
- 7 × 4 = 28 → Already has 28
- 7 × 5 = 35 → Already has 35
- 7 × 6 = 42 → Already has 42
- 7 × 7 = 49 → Missing → 49
- 7 × 8 = 56 → Already has 56
- 7 × 9 = 63 → Already has 63
- 7 × 10 = 70 → Missing → 70
- 7 × 11 = 77 → Already has 77
- 7 × 12 = 84 → Missing → 84
✔ Missing: 21, 49, 70, 84
#### Row 8:
- 8 × 1 = 8 → Missing → 8
- 8 × 2 = 16 → Missing → 16
- 8 × 3 = 24 → Already has 24
- 8 × 4 = 32 → Already has 32
- 8 × 5 = 40 → Missing → 40
- 8 × 6 = 48 → Missing → 48
- 8 × 7 = 56 → Already has 56
- 8 × 8 = 64 → Missing → 64
- 8 × 9 = 72 → Already has 72
- 8 × 10 = 80 → Already has 80
- 8 × 11 = 88 → Already has 88
- 8 × 12 = 96 → Missing → 96
✔ Missing: 8, 16, 40, 48, 64, 96
#### Row 9:
- 9 × 1 = 9 → Already has 9
- 9 × 2 = 18 → Already has 18
- 9 × 3 = 27 → Missing → 27
- 9 × 4 = 36 → Missing → 36
- 9 × 5 = 45 → Already has 45
- 9 × 6 = 54 → Missing → 54
- 9 × 7 = 63 → Missing → 63
- 9 × 8 = 72 → Already has 72
- 9 × 9 = 81 → Missing → 81
- 9 × 10 = 90 → Missing → 90
- 9 × 11 = 99 → Missing → 99
- 9 × 12 = 108 → Already has 108
✔ Missing: 27, 36, 54, 63, 81, 90, 99
#### Row 10:
- 10 × 1 = 10 → Missing → 10
- 10 × 2 = 20 → Missing → 20
- 10 × 3 = 30 → Already has 30
- 10 × 4 = 40 → Missing → 40
- 10 × 5 = 50 → Missing → 50
- 10 × 6 = 60 → Already has 60
- 10 × 7 = 70 → Already has 70
- 10 × 8 = 80 → Missing → 80
- 10 × 9 = 90 → Already has 90
- 10 × 10 = 100 → Already has 100
- 10 × 11 = 110 → Already has 110
- 10 × 12 = 120 → Missing → 120
✔ Missing: 10, 20, 40, 50, 80, 120
#### Row 11:
- 11 × 1 = 11 → Missing → 11
- 11 × 2 = 22 → Already has 22
- 11 × 3 = 33 → Missing → 33
- 11 × 4 = 44 → Already has 44
- 11 × 5 = 55 → Already has 55
- 11 × 6 = 66 → Missing → 66
- 11 × 7 = 77 → Already has 77
- 11 × 8 = 88 → Already has 88
- 11 × 9 = 99 → Missing → 99
- 11 × 10 = 110 → Already has 110
- 11 × 11 = 121 → Missing → 121
- 11 × 12 = 132 → Already has 132
✔ Missing: 11, 33, 66, 99, 121
#### Row 12:
- 12 × 1 = 12 → Already has 12
- 12 × 2 = 24 → Missing → 24
- 12 × 3 = 36 → Already has 36
- 12 × 4 = 48 → Already has 48
- 12 × 5 = 60 → Missing → 60
- 12 × 6 = 72 → Missing → 72
- 12 × 7 = 84 → Already has 84
- 12 × 8 = 96 → Already has 96
- 12 × 9 = 108 → Already has 108
- 12 × 10 = 120 → Missing → 120
- 12 × 11 = 132 → Already has 132
- 12 × 12 = 144 → Missing → 144
✔ Missing: 24, 60, 72, 120, 144
---
Here is the fully completed chart with all missing values filled in:
| × | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
|---|---|---|---|---|---|---|---|---|---|----|----|----|
| 1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
| 2 | 2 | 4 | 6 | 8 | 10 | 12 | 14 | 16 | 18 | 20 | 22 | 24 |
| 3 | 3 | 6 | 9 | 12 | 15 | 18 | 21 | 24 | 27 | 30 | 33 | 36 |
| 4 | 4 | 8 | 12 | 16 | 20 | 24 | 28 | 32 | 36 | 40 | 44 | 48 |
| 5 | 5 | 10 | 15 | 20 | 25 | 30 | 35 | 40 | 45 | 50 | 55 | 60 |
| 6 | 6 | 12 | 18 | 24 | 30 | 36 | 42 | 48 | 54 | 60 | 66 | 72 |
| 7 | 7 | 14 | 21 | 28 | 35 | 42 | 49 | 56 | 63 | 70 | 77 | 84 |
| 8 | 8 | 16 | 24 | 32 | 40 | 48 | 56 | 64 | 72 | 80 | 88 | 96 |
| 9 | 9 | 18 | 27 | 36 | 45 | 54 | 63 | 72 | 81 | 90 | 99 | 108 |
| 10 | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 | 110 | 120 |
| 11 | 11 | 22 | 33 | 44 | 55 | 66 | 77 | 88 | 99 | 110 | 121 | 132 |
| 12 | 12 | 24 | 36 | 48 | 60 | 72 | 84 | 96 | 108 | 120 | 132 | 144 |
---
The task was to complete the 12×12 multiplication chart. We identified all the missing entries by computing each product using the formula:
> Row × Column = Value
Now, every cell is filled correctly.
✔ This chart helps students memorize multiplication facts up to 12×12, which is essential for arithmetic fluency.
Let me know if you'd like a printable version or flashcards!
Let’s go step by step to solve the missing entries in the chart.
---
🔢 Understanding the Chart
This is a standard 12×12 multiplication table, where:
- The first row (top) and first column (left) are the multipliers.
- Each cell at row `a` and column `b` should contain `a × b`.
We’ll fill in all the blanks based on this rule.
---
✔ Step-by-step: Fill in Missing Values
We'll go row by row and fill in the missing entries.
#### Row 1: (1 × any number)
All entries are correct:
```
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12
```
#### Row 2:
- 2 × 1 = 2 → Already has 2
- 2 × 2 = 4 → Already has 4
- 2 × 3 = 6 → Missing → 6
- 2 × 4 = 8 → Already has 8
- 2 × 5 = 10 → Missing → 10
- 2 × 6 = 12 → Missing → 12
- 2 × 7 = 14 → Missing → 14
- 2 × 8 = 16 → Already has 16
- 2 × 9 = 18 → Missing → 18
- 2 × 10 = 20 → Missing → 20
- 2 × 11 = 22 → Missing → 22
- 2 × 12 = 24 → Missing → 24
✔ So far, Row 2 needs: 6, 10, 12, 14, 18, 20, 22, 24
#### Row 3:
- 3 × 1 = 3 → Already has 3
- 3 × 2 = 6 → Already has 6
- 3 × 3 = 9 → Missing → 9
- 3 × 4 = 12 → Already has 12
- 3 × 5 = 15 → Already has 15
- 3 × 6 = 18 → Already has 18
- 3 × 7 = 21 → Missing → 21
- 3 × 8 = 24 → Already has 24
- 3 × 9 = 27 → Already has 27
- 3 × 10 = 30 → Already has 30
- 3 × 11 = 33 → Missing → 33
- 3 × 12 = 36 → Already has 36
✔ Missing: 9, 21, 33
#### Row 4:
- 4 × 1 = 4 → Already has 4
- 4 × 2 = 8 → Missing → 8
- 4 × 3 = 12 → Missing → 12
- 4 × 4 = 16 → Already has 16
- 4 × 5 = 20 → Already has 20
- 4 × 6 = 24 → Missing → 24
- 4 × 7 = 28 → Already has 28
- 4 × 8 = 32 → Missing → 32
- 4 × 9 = 36 → Missing → 36
- 4 × 10 = 40 → Already has 40
- 4 × 11 = 44 → Already has 44
- 4 × 12 = 48 → Missing → 48
✔ Missing: 8, 12, 24, 32, 36, 48
Wait — let's double-check:
- 4×2 = 8 → Yes
- 4×3 = 12 → Yes
- 4×6 = 24 → Yes
- 4×8 = 32 → Yes
- 4×9 = 36 → Yes
- 4×12 = 48 → Yes
So yes, those are missing.
#### Row 5:
- 5 × 1 = 5 → Already has 5
- 5 × 2 = 10 → Missing → 10
- 5 × 3 = 15 → Already has 15
- 5 × 4 = 20 → Missing → 20
- 5 × 5 = 25 → Missing → 25
- 5 × 6 = 30 → Already has 30
- 5 × 7 = 35 → Already has 35
- 5 × 8 = 40 → Already has 40
- 5 × 9 = 45 → Missing → 45
- 5 × 10 = 50 → Missing → 50
- 5 × 11 = 55 → Already has 55
- 5 × 12 = 60 → Missing → 60
✔ Missing: 10, 20, 25, 45, 50, 60
#### Row 6:
- 6 × 1 = 6 → Missing → 6
- 6 × 2 = 12 → Already has 12
- 6 × 3 = 18 → Already has 18
- 6 × 4 = 24 → Missing → 24
- 6 × 5 = 30 → Already has 30
- 6 × 6 = 36 → Missing → 36
- 6 × 7 = 42 → Missing → 42
- 6 × 8 = 48 → Already has 48
- 6 × 9 = 54 → Missing → 54
- 6 × 10 = 60 → Already has 60
- 6 × 11 = 66 → Missing → 66
- 6 × 12 = 72 → Already has 72
✔ Missing: 6, 24, 36, 42, 54, 66
#### Row 7:
- 7 × 1 = 7 → Already has 7
- 7 × 2 = 14 → Already has 14
- 7 × 3 = 21 → Missing → 21
- 7 × 4 = 28 → Already has 28
- 7 × 5 = 35 → Already has 35
- 7 × 6 = 42 → Already has 42
- 7 × 7 = 49 → Missing → 49
- 7 × 8 = 56 → Already has 56
- 7 × 9 = 63 → Already has 63
- 7 × 10 = 70 → Missing → 70
- 7 × 11 = 77 → Already has 77
- 7 × 12 = 84 → Missing → 84
✔ Missing: 21, 49, 70, 84
#### Row 8:
- 8 × 1 = 8 → Missing → 8
- 8 × 2 = 16 → Missing → 16
- 8 × 3 = 24 → Already has 24
- 8 × 4 = 32 → Already has 32
- 8 × 5 = 40 → Missing → 40
- 8 × 6 = 48 → Missing → 48
- 8 × 7 = 56 → Already has 56
- 8 × 8 = 64 → Missing → 64
- 8 × 9 = 72 → Already has 72
- 8 × 10 = 80 → Already has 80
- 8 × 11 = 88 → Already has 88
- 8 × 12 = 96 → Missing → 96
✔ Missing: 8, 16, 40, 48, 64, 96
#### Row 9:
- 9 × 1 = 9 → Already has 9
- 9 × 2 = 18 → Already has 18
- 9 × 3 = 27 → Missing → 27
- 9 × 4 = 36 → Missing → 36
- 9 × 5 = 45 → Already has 45
- 9 × 6 = 54 → Missing → 54
- 9 × 7 = 63 → Missing → 63
- 9 × 8 = 72 → Already has 72
- 9 × 9 = 81 → Missing → 81
- 9 × 10 = 90 → Missing → 90
- 9 × 11 = 99 → Missing → 99
- 9 × 12 = 108 → Already has 108
✔ Missing: 27, 36, 54, 63, 81, 90, 99
#### Row 10:
- 10 × 1 = 10 → Missing → 10
- 10 × 2 = 20 → Missing → 20
- 10 × 3 = 30 → Already has 30
- 10 × 4 = 40 → Missing → 40
- 10 × 5 = 50 → Missing → 50
- 10 × 6 = 60 → Already has 60
- 10 × 7 = 70 → Already has 70
- 10 × 8 = 80 → Missing → 80
- 10 × 9 = 90 → Already has 90
- 10 × 10 = 100 → Already has 100
- 10 × 11 = 110 → Already has 110
- 10 × 12 = 120 → Missing → 120
✔ Missing: 10, 20, 40, 50, 80, 120
#### Row 11:
- 11 × 1 = 11 → Missing → 11
- 11 × 2 = 22 → Already has 22
- 11 × 3 = 33 → Missing → 33
- 11 × 4 = 44 → Already has 44
- 11 × 5 = 55 → Already has 55
- 11 × 6 = 66 → Missing → 66
- 11 × 7 = 77 → Already has 77
- 11 × 8 = 88 → Already has 88
- 11 × 9 = 99 → Missing → 99
- 11 × 10 = 110 → Already has 110
- 11 × 11 = 121 → Missing → 121
- 11 × 12 = 132 → Already has 132
✔ Missing: 11, 33, 66, 99, 121
#### Row 12:
- 12 × 1 = 12 → Already has 12
- 12 × 2 = 24 → Missing → 24
- 12 × 3 = 36 → Already has 36
- 12 × 4 = 48 → Already has 48
- 12 × 5 = 60 → Missing → 60
- 12 × 6 = 72 → Missing → 72
- 12 × 7 = 84 → Already has 84
- 12 × 8 = 96 → Already has 96
- 12 × 9 = 108 → Already has 108
- 12 × 10 = 120 → Missing → 120
- 12 × 11 = 132 → Already has 132
- 12 × 12 = 144 → Missing → 144
✔ Missing: 24, 60, 72, 120, 144
---
✔ Final Answer: Completed Multiplication Chart
Here is the fully completed chart with all missing values filled in:
| × | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
|---|---|---|---|---|---|---|---|---|---|----|----|----|
| 1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
| 2 | 2 | 4 | 6 | 8 | 10 | 12 | 14 | 16 | 18 | 20 | 22 | 24 |
| 3 | 3 | 6 | 9 | 12 | 15 | 18 | 21 | 24 | 27 | 30 | 33 | 36 |
| 4 | 4 | 8 | 12 | 16 | 20 | 24 | 28 | 32 | 36 | 40 | 44 | 48 |
| 5 | 5 | 10 | 15 | 20 | 25 | 30 | 35 | 40 | 45 | 50 | 55 | 60 |
| 6 | 6 | 12 | 18 | 24 | 30 | 36 | 42 | 48 | 54 | 60 | 66 | 72 |
| 7 | 7 | 14 | 21 | 28 | 35 | 42 | 49 | 56 | 63 | 70 | 77 | 84 |
| 8 | 8 | 16 | 24 | 32 | 40 | 48 | 56 | 64 | 72 | 80 | 88 | 96 |
| 9 | 9 | 18 | 27 | 36 | 45 | 54 | 63 | 72 | 81 | 90 | 99 | 108 |
| 10 | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 | 110 | 120 |
| 11 | 11 | 22 | 33 | 44 | 55 | 66 | 77 | 88 | 99 | 110 | 121 | 132 |
| 12 | 12 | 24 | 36 | 48 | 60 | 72 | 84 | 96 | 108 | 120 | 132 | 144 |
---
📌 Summary
The task was to complete the 12×12 multiplication chart. We identified all the missing entries by computing each product using the formula:
> Row × Column = Value
Now, every cell is filled correctly.
✔ This chart helps students memorize multiplication facts up to 12×12, which is essential for arithmetic fluency.
Let me know if you'd like a printable version or flashcards!
Parent Tip: Review the logic above to help your child master the concept of blank multiplication worksheet.