Multiplication Grid | Times Table 1 to 10 | Multiplication Table |Math - Free Printable

Problem Analysis:

The image shows a multiplication table where the rows and columns are labeled from 1 to 10. The entries in the table represent the product of the row number and the column number. For example, the entry in row 3 and column 4 is \( 3 \times 4 = 12 \).

Some cells in the table are highlighted in yellow. The task is to identify a pattern or rule governing which cells are highlighted and explain the solution.

Observing the Highlighted Cells:

The highlighted cells in the table are:
- Row 1, Column 1: \( 1 \)
- Row 2, Column 2: \( 4 \)
- Row 3, Column 3: \( 9 \)
- Row 4, Column 4: \( 16 \)
- Row 5, Column 5: \( 25 \)
- Row 6, Column 6: \( 36 \)
- Row 7, Column 7: \( 49 \)
- Row 8, Column 8: \( 64 \)
- Row 9, Column 9: \( 81 \)
- Row 10, Column 10: \( 100 \)

Identifying the Pattern:

1. Position of Highlighted Cells: All highlighted cells are on the main diagonal of the table. The main diagonal consists of cells where the row number is equal to the column number.
- For example, the cell in row 3, column 3 is highlighted because \( 3 = 3 \).

2. Values in Highlighted Cells: The values in these cells are perfect squares.
- \( 1 = 1^2 \)
- \( 4 = 2^2 \)
- \( 9 = 3^2 \)
- \( 16 = 4^2 \)
- \( 25 = 5^2 \)
- \( 36 = 6^2 \)
- \( 49 = 7^2 \)
- \( 64 = 8^2 \)
- \( 81 = 9^2 \)
- \( 100 = 10^2 \)

Conclusion:

The highlighted cells are those where the row number equals the column number, and the value in each highlighted cell is a perfect square. Specifically, the value in the highlighted cell at row \( n \) and column \( n \) is \( n^2 \).

Final Answer:

\[
\boxed{\text{The highlighted cells are on the main diagonal, and their values are perfect squares.}}
\]