arrays with an expanded algorithm for 31*19

What is 31x 19 in expanded algorithm?

To find the product of 31 and 19 using an expanded algorithm, we can break down the multiplication into smaller steps. Here's how you can do it:

Step 1: Set up the arrays
Create two arrays, each representing one of the numbers to be multiplied. In this case, we have:
Array A: [3, 1]
Array B: [1, 9]

Step 2: Multiply each digit by the corresponding digits in the other array.
Start by multiplying the last digit of Array A (1) by each digit in Array B:
1 * 9 = 9

Now, multiply the first digit of Array A (3) by each digit in Array B:
3 * 9 = 27
3 * 1 = 3

Step 3: Add the products together.
Write down the products of the multiplication step horizontally, with each product shifted one place to the left compared to the previous one:
0, 0, 9, 3, 2, 7

Step 4: Sum up the products.
Starting from the rightmost digit, sum up the digits within the result:
0 + 0 + 9 + 3 + 2 + 7 = 21

Step 5: Carry over if necessary.
If there are digits greater than 9 in the sum, carry them over to the next place on the left:
Carrying over the 2 from 21, we write down the digit 1 and carry over the remaining digit 1.

Step 6: Write down the final result.
Write down the carried over digit (1) followed by the digits in the sum:
191

Therefore, 31 multiplied by 19 equals 591.

Note: The expanded algorithm is useful for understanding the step-by-step process of multiplication, but for larger numbers, a more efficient method like the standard algorithm or using a calculator is recommended.