What is partial product?

Partial product refers to the intermediate products obtained when multiplying the digits of a multi-digit number step by step. It is commonly used in long multiplication to simplify the process of multiplying large numbers.

For example, when multiplying 456 by 23:

4 x 3 = 12 (partial product) 4 x 2 = 8 (partial product) 5 x 3 = 15 (partial product, but written as 50 since it is in the tens place) 5 x 2 = 10 (partial product, but written as 100 since it is in the hundreds place)

Adding all the partial products together gives the final product of 456 x 23 = 10488.

Using partial products can help break down the multiplication process into smaller, more manageable steps and reduce the likelihood of making errors while calculating. It is a useful technique to teach students when learning long multiplication.