Explain how you can use an array to find partial products for 4x36.
To find partial products for 4x36 using an array, you can break down the multiplication into smaller steps by multiplying each digit of one number by each digit of the other number and placing the results in an array.
1. Create a 2D array with dimensions equal to the number of digits in each number. In this case, both numbers have two digits, so create a 2x2 array.
2. Write the two numbers, 4 and 36, vertically on the left side of the array. Place the 4 on top and the 36 beneath it.
| 3 6
--|----
| 4
3. Begin with the rightmost digit of the bottom number (6) and multiply it with each digit of the top number (4). Write the results in the first row from right to left.
| 3 6
--|----
| 4
| 2 4
Here, 6 x 4 = 24, so we write 24 in the first row of the array.
4. Move to the second digit from the right in the bottom number (3) and repeat step 3, but this time, write the results in the second row from right to left.
| 3 6
--|----
| 4
| 2 4
| 1 2
Here, 3 x 4 = 12, so we write 12 in the second row of the array.
5. Now, add up the values in each column of the array to find the partial products.
- In the rightmost column, we have 24 and 12. Add them up: 24 + 12 = 36. Write the result under the horizontal line in the rightmost column.
| 3 6
--|----
| 4
| 2 4
| 1 2
------
3 6
6. Finally, add up the values in each row of the array to find the final product.
- In the top row, we have 24 and 0 (empty space). Add them up: 24 + 0 = 24. Write the result above the horizontal line in the leftmost column.
| 3 6
--|----
| 4
| 2 4
| 1 2
------
2 4
3 6
The final product is 24 + 360 = 384.