What Is a Partial Product in Fourth Grade Math?

Students raising hands in math class.
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In recent years, fourth-grade curricula have begun to expand on traditional methods of addition, subtraction, multiplication and division to give students a wide range of techniques. One such technique is the partial product method used for multiplication.

Finding Partial Products

The partial product method involves multiplying each digit of a number in turn with each digit of another where each digit maintains its place. (So, the 2 in 23 would actually be 20.) For instance, 23 x 42 would become (20 x 40) + (20 x 2) + (3 x 40) + (3 x 2).

Adding Partial Products

You add partial products together to get a final answer for the multiplication problem. For instance, 800 + 40 + 120 + 6 would give you a total product of 966.


Using the partial product method in fourth grade lets students visualize the manipulation of factors which helps them prepare for learning algebraic properties. Furthermore, it gives them a method that is easier to do in their head because partial sums usually end in zeros or are single-digit numbers.


In some cases, the partial products method saves students time in comparison with the traditional method, but in others it does not. It takes practice to figure out when to use which. Furthermore, when pencil and paper are available, the traditional method is usually faster.

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