What is partial products?

Partial products are the individual products that result from multiplying each digit of a multi-digit number by each digit of another multi-digit number. These partial products are then added together to find the final product of the two numbers.

For example, when multiplying 456 by 23, you would first multiply 456 by 3, then by 2, and then by 1 (before moving to the next place value). The individual products of these multiplications are the partial products.

Partial products can be written out in a vertical format, often used in long multiplication, where each partial product is written under the corresponding place value and then added up to find the final product. This method helps in breaking down the multiplication process into smaller, more manageable steps.