What is a partial product?

A partial product is the result of multiplying one digit of a number by each digit of another number, and then adding all of the products together. This method is often used in multiplication to break down the process into smaller, more manageable steps.

For example, when multiplying 23 by 45, the partial product for the digit 5 in the multiplier 45 would be 15 (5 x 3). The partial product for the digit 4 in the multiplier 45 would be 80 (4 x 20). These partial products are then added together to get the final product of 1035.

Partial products can be helpful in understanding the process of multiplication and can be useful for students learning to multiply larger numbers. They can also be used as a way to check the accuracy of multiplication calculations.