A partial product multiplication algorithm is the process in which each part of one number is multiplied by each part of another number, after which the products are added together. An understanding of place value is necessary to use this algorithm, and the largest numbers are multiplied first.
The parts of each number are figured out by separating each number into the sum of ones, tens and hundreds. For example, 67 is broken up into 60 + 7, and 53 is broken up into 50 + 3. If these two numbers are being multiplied together, the partial product multiplication algorithm calls for multiplying 50 by 60, 60 by 3, 50 by 7 and 7 by 3. The answers to these multiplication problems are then added together to get the answer to the entire problem.
Another common multiplication algorithm is to multiply the number in the ones spot in the bottom factor by each of the numbers in the top factor, carrying any extra numbers and adding them to the next product. This is then repeated for the second number in the bottom factor, except the number in the ones column is always a zero. For each additional number in the bottom factor, an additional zero should be added to the end of the product. Once all numbers are multiplied, the products are added together.