What is a partial product in math?

A partial product is a method used in multiplication to break down a multiplication problem into smaller, more manageable parts. This method involves multiplying each digit of one number by each digit of the other number and then adding all the resulting products together to find the final answer.

For example, in the multiplication problem 23 x 45, the partial product method would involve multiplying 3 (the digit in the ones place of 23) by 5 (the digit in the ones place of 45) to get 15, then multiplying 3 by 4 (the digit in the tens place of 45) to get 12. Finally, you would add these two products together to get the partial product for the ones place.

You would then repeat this process for the tens place, multiplying 2 by both digits of 45 and adding the results together. The final answer is the sum of these two partial products.

The partial product method can be especially helpful for children learning multiplication as it breaks down the process into smaller, more manageable steps.