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

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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.

#### Tips

• 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*}

## Benefits

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.