The task is to fill in the multiplication table shown in the image. A multiplication table is a grid that shows the results of multiplying two numbers together. The rows and columns are labeled with numbers from 0 to 9, and each cell in the grid represents the product of the row number and the column number.
Step-by-Step Solution:
1.
Understand the Structure:
- The top row (header) contains the numbers 0 through 9.
- The leftmost column (header) also contains the numbers 0 through 9.
- Each cell in the grid will contain the product of the corresponding row number and column number.
2.
Fill in the Table:
- For each cell at the intersection of row \( r \) and column \( c \), the value is \( r \times c \).
3.
Complete the Table:
- Start with the first row (row 0): Every product in this row will be 0 because any number multiplied by 0 is 0.
- Move to the second row (row 1): Every product in this row will be the same as the column number because any number multiplied by 1 is the number itself.
- Continue this process for all rows up to row 9.
Here is the completed multiplication table:
\[
\begin{array}{c|ccccccccc}
& 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\
\hline
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
1 & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\
2 & 0 & 2 & 4 & 6 & 8 & 10 & 12 & 14 & 16 & 18 \\
3 & 0 & 3 & 6 & 9 & 12 & 15 & 18 & 21 & 24 & 27 \\
4 & 0 & 4 & 8 & 12 & 16 & 20 & 24 & 28 & 32 & 36 \\
5 & 0 & 5 & 10 & 15 & 20 & 25 & 30 & 35 & 40 & 45 \\
6 & 0 & 6 & 12 & 18 & 24 & 30 & 36 & 42 & 48 & 54 \\
7 & 0 & 7 & 14 & 21 & 28 & 35 & 42 & 49 & 56 & 63 \\
8 & 0 & 8 & 16 & 24 & 32 & 40 & 48 & 56 & 64 & 72 \\
9 & 0 & 9 & 18 & 27 & 36 & 45 & 54 & 63 & 72 & 81 \\
\end{array}
\]
Explanation:
- The first row and first column are all zeros because any number multiplied by 0 is 0.
- The second row (row 1) is simply the numbers 0 through 9 because any number multiplied by 1 is the number itself.
- As you move down the rows, each cell's value is calculated by multiplying the row number by the column number.
Final Answer:
\[
\boxed{
\begin{array}{c|ccccccccc}
& 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\
\hline
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
1 & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\
2 & 0 & 2 & 4 & 6 & 8 & 10 & 12 & 14 & 16 & 18 \\
3 & 0 & 3 & 6 & 9 & 12 & 15 & 18 & 21 & 24 & 27 \\
4 & 0 & 4 & 8 & 12 & 16 & 20 & 24 & 28 & 32 & 36 \\
5 & 0 & 5 & 10 & 15 & 20 & 25 & 30 & 35 & 40 & 45 \\
6 & 0 & 6 & 12 & 18 & 24 & 30 & 36 & 42 & 48 & 54 \\
7 & 0 & 7 & 14 & 21 & 28 & 35 & 42 & 49 & 56 & 63 \\
8 & 0 & 8 & 16 & 24 & 32 & 40 & 48 & 56 & 64 & 72 \\
9 & 0 & 9 & 18 & 27 & 36 & 45 & 54 & 63 & 72 & 81 \\
\end{array}
}
\]
Parent Tip: Review the logic above to help your child master the concept of desktop multiplication chart printable.
