To find the product of 355 and 893 using the standard algorithm, follow these steps:
Step 1: Write down the two numbers vertically, aligning them by place value:
355
x 893
Step 2: Start with the ones digit (3), and multiply it by each digit in the second number (893).
3 multiplied by 3 = 9
3 multiplied by 9 = 27
3 multiplied by 8 = 24
The product of multiplying by the ones digit is: 9, 27, 24
Step 3: Move to the tens digit (5), and multiply it by each digit in the second number (893).
5 multiplied by 3 = 15
5 multiplied by 9 = 45
5 multiplied by 8 = 40
The product of multiplying by the tens digit is: 15, 45, 40
Step 4: Move to the hundreds digit (3), and multiply it by each digit in the second number (893).
3 multiplied by 3 = 9
3 multiplied by 9 = 27
3 multiplied by 8 = 24
The product of multiplying by the hundreds digit is: 9, 27, 24
Step 5: Add up the products from each step to get the final product.
Add up all the products: 9 + 27 + 24 (ones digit) + 15 + 45 + 40 + 9 + 27 + 24 (tens digit) + 9 + 27 + 24 (hundreds digit)
The product is 11,194.
So, the final product of multiplying 355 and 893 using the standard algorithm is 11,194.