This image displays a partially filled multiplication table, also known as a times table. The task is to fill in all the empty cells with the correct products.
How to Solve It
The grid works like this:
- The top row (header) shows the numbers 1 through 10.
- The first column (leftmost) also shows the numbers 1 through 10.
- Each cell in the grid represents the product (result of multiplication) of the number in its row and the number in its column.
For example:
- The cell at the intersection of row `3` and column `4` should contain `3 × 4 = 12`.
- The cell at row `5` and column `7` should contain `5 × 7 = 35`.
The green shaded cells along the diagonal (from top-left to bottom-right) are where the row number equals the column number — these are the squares: `1×1`, `2×2`, `3×3`, etc. These are already highlighted, but we still need to calculate their values.
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Step-by-Step Solution
We’ll fill in the entire table by calculating each cell’s value.
Here is the complete multiplication table from 1 to 10:
```
X 1 2 3 4 5 6 7 8 9 10
------------------------------------------
1 1 2 3 4 5 6 7 8 9 10
2 2 4 6 8 10 12 14 16 18 20
3 3 6 9 12 15 18 21 24 27 30
4 4 8 12 16 20 24 28 32 36 40
5 5 10 15 20 25 30 35 40 45 50
6 6 12 18 24 30 36 42 48 54 60
7 7 14 21 28 35 42 49 56 63 70
8 8 16 24 32 40 48 56 64 72 80
9 9 18 27 36 45 54 63 72 81 90
10 10 20 30 40 50 60 70 80 90 100
```
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Explanation of Key Patterns
1.
Symmetry: The table is symmetric across the diagonal because multiplication is commutative: `a × b = b × a`. For example, `3 × 4 = 12` and `4 × 3 = 12`.
2.
Diagonal (Squares): The green diagonal cells represent perfect squares:
- `1×1 = 1`
- `2×2 = 4`
- `3×3 = 9`
- ...
- `10×10 = 100`
3.
Multiples:
- Row 1: All numbers 1–10 (multiples of 1)
- Row 2: Even numbers 2, 4, 6, ..., 20 (multiples of 2)
- Row 5: Ends in 0 or 5 (multiples of 5)
- Row 10: All end in 0 (multiples of 10)
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Final Answer
✔ The completed multiplication table is shown above. You can use it for reference or to check your work. Memorizing this table helps build a strong foundation for more advanced math!
*(Note: Since you uploaded an image, I’ve described the solution textually. If you want me to generate an image of the filled table, let me know!)*
Parent Tip: Review the logic above to help your child master the concept of printable multiplication table blank.
