To perform partial product multiplication, you use the distributive property of numbers, multiplying each digit of a number by each digit of the other number and adding the results while taking the place value of each digit into account. One of the most common types of multiplication problems involves a pair of two-digit numbers. When working with these problems, add a total of four partial products.
First, break each number down into its components by place value. Assuming as an example you're multiplying 23 and 14, the components are 20, 10, 3 and 4. If it helps, draw a chart to separate each partial product. First, multiply the digits in the tens place, which are 20 and 10 in this case, yielding a partial product of 200. Multiply the ones digits next, providing you with 12. Then, multiply each tens digit by its opposite ones digit. For the example, these are 20 multiplied by 4 and 10 multiplied by 3.
All the partial products in the example are 200, 80, 30 and 12, which add to 322. If you're unsure of the result, use a calculator or the standard method of multiplication to verify the results. The partial product method can extend to multiplying three-digit numbers as well.