Lesson 3: Use Arrays and Partial Products to Multiply

Property

The area of each smaller rectangle in a decomposed array represents a partial product. The total product is the sum of these partial products. For a problem like $a \times (b+c)$, the partial products are the areas of the two smaller rectangles: $(a \times b)$ and $(a \times c)$.

Examples

Property

The partial products algorithm uses the distributive property to solve multiplication.
A multi-digit number is broken into the sum of its place values (expanded form), and each part is multiplied separately before adding the results.

Each partial product can be represented as a section of an array, showing how the total product is composed of smaller, manageable parts.

Examples