Learn on PengienVision, Mathematics, Grade 4Chapter 3: Use Strategies and Properties to Multiply by 1-Digit Numbers

Lesson 3: Use Arrays and Partial Products to Multiply

Property.

Section 1

Find Partial Products from a Decomposed Array

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

Section 2

Calculate Partial Products

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.

a \times (b + c + d) = (a \times b) + (a \times c) + (a \times d)

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

Examples

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Find Partial Products from a Decomposed Array

Property

Examples

Section 2

Calculate Partial Products

Property

a \times (b + c + d) = (a \times b) + (a \times c) + (a \times d)

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

Examples

Overview

Lesson overview

Review the lesson summary and core properties without leaving the current page.

Overview

Section 1

Find Partial Products from a Decomposed Array

Property

Examples

Section 2

Calculate Partial Products

Property

a \times (b + c + d) = (a \times b) + (a \times c) + (a \times d)

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