Partial products let you use answers you already know. For example, if multiply 87 by 24, you should focus on the products you know, such as 8 times 4 and 8 times 2. By breaking down the factors, you work a series of partial products to get to the final number. You would start by doing 80 times 4 and 80 times 20. You would continue by doing 7 times 20 and 7 times 4. This breaks down the larger numbers into multiples of 10 or small equations.
By breaking down the numbers, you can use the zero method of 10s -- multiplying anything by 10 adds a zero to the solution. When you multiply 80 times 4, it is the same as 8 times 4 with a zero added to the end. For 80 times 20, it is just 8 times 2 with two zeros at the end. This process makes it simpler.
With the simplified version of the partial products, you should be able to do most of the steps in your head: 8 times 4 is 32, so 80 times 4 is 320; 80 times 20 is 1,600; 7 times 20 is 140; and 7 times 4 is 28. Now you just need to write down the series of these answers. By walking through all the steps, you have completed the multiplication problem. The process is called "partial products," because you are creating a series of "products," or multiplication solutions, that are added together for a total.
After you write down all the partial products, you must add them together. You can accomplish this with a calculator or by writing out the answer on your own. As with any other addition problem, be sure to line up the number on the right. In this case, the solution comes out to be 2,088. Adding 28, 320, 1,600 and 140 gives you 2,088. Often you will have to write out the final addition problem, but you can be secure in your multiplication, because you have used the algorithm to simplify the problem.