Partial Products: What Is a Partial Product in Fourth Grade Math?

Students raising hands in math class.
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In recent years, 4th grade math 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. It uses place values to perform multi-digit multiplication, and it reinforces important tools of multiplication like the distributive property and order of operations.

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:

\begin{align*} (20 \times 40) + (20 \times 2)+ (3 \times 40) + (3 \times 2) \end{align*}.

This is a kind of expanded form of the multiplication method, but it allows for multi-digit numbers to be broken down into simpler numbers for multiplication. In this case we only used two-digit numbers, but this regrouping can apply to three-digit numbers, four-digit numbers, and beyond.


  • The partial products algorithm even works on decimal and mixed numbers, we just need to account for the additional decimal places in our final calculation.

Adding Partial Products

You add partial products together to get a final answer for the multiplication problem. Using our previous example:

\begin{align*} (20 \times 40) + (20 \times 2)+ (3 \times 40) + (3 \times 2) &=800 + 40 + 120 + 6 \\ &= 966 \end{align*}


Using the partial product multiplication 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. This allows students to use knowledge from basic multiplication tables to calculate extremely large sums – even with mental math.


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.

Partial products work very similarly to the standard algorithm of multiplication, but it simply expands the figures in a different way. There are other multiplication strategies that students might learn in 2nd or 3rd grade math. The area model of multiplication or representing multiplication as repeated addition might be a good starting point for some word problems and difficult worksheets.

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