Write the missing numbers in this multiplication grid.
| x | 6 | |
| :---: | :--: | :---: |
| 8 | 48 | |
| -4 | | 20 |
Answer (1)
We identify the missing numbers as variables.
We set up the equation − 4 x = 20 to find the missing number in the first row.
We solve for x and find x = − 5 .
We calculate the missing value in the grid as 8 × − 5 = − 40 , so the missing numbers are − 5 , − 40 .
Explanation
Understanding the Problem We are given a multiplication grid with some missing values. Our goal is to find these missing numbers. The grid provides the products of the numbers in the first row and the first column.
Setting up the Equations Let's denote the missing number in the first row as x and the missing number in the second column as y . From the grid, we have the equation − 4 × x = 20 .
Solving for x To find x , we solve the equation − 4 x = 20 . Dividing both sides by -4, we get x = − 4 20 = − 5 .
Solving for the Missing Value Now, we need to find the missing value in the first row and second column. This value is the product of 8 and x , which we found to be -5. So, the missing value is 8 × − 5 = − 40 .
Final Answer Therefore, the missing numbers in the multiplication grid are -5 and -40.
Examples
Multiplication grids are useful in everyday life for calculating areas, determining quantities, or even planning schedules. For instance, if you're tiling a rectangular floor, a multiplication grid can help you quickly determine the number of tiles needed based on the length and width of the floor. Similarly, in scheduling, if you know the number of tasks and the time each task takes, a grid can help you calculate the total time required. These grids provide a visual and organized way to perform multiplication, making complex calculations easier to manage.
