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

Lesson 6: Mental Math Strategies for Multiplication

Property.

Section 1

Applying the Distributive Property

Property

The distributive property allows you to multiply a number by a sum or difference by multiplying each part of the sum or difference separately and then adding or subtracting the products.

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

a \times (b - c) = (a \times b) - (a \times c)

Examples

Section 2

Breaking Apart and Rearranging Factors

Property

To multiply mentally, you can break a factor into its own factors and then use the Commutative and Associative Properties to rearrange the multiplication into an easier problem.
$a \times (b \times c) = (a \times b) \times c$

Examples

To solve $25 \times 8$ , break apart $8$ into $4 \times 2$ . The problem becomes $25 \times 4 \times 2$ . Rearrange to get $(25 \times 4) \times 2$ , which simplifies to $100 \times 2 = 200$ .
To solve $5 \times 28$ , break apart $28$ into $2 \times 14$ . The problem becomes $5 \times 2 \times 14$ . Rearrange to get $(5 \times 2) \times 14$ , which simplifies to $10 \times 14 = 140$ .
To solve $5 \times 48$ , break apart $48$ into $4 \times 12$ . The problem becomes $5 \times 4 \times 12$ . Rearrange to get $(5 \times 4) \times 12$ , which simplifies to $20 \times 12 = 240$ .

Explanation

This mental math strategy involves breaking one of the numbers in a multiplication problem into its factors. Then, you can rearrange the factors to create an easier multiplication, often by making a multiple of 10 or 100. This uses the Associative Property of Multiplication, which allows you to group and multiply factors in any order. The goal is to transform a difficult problem into a series of simpler calculations.

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Applying the Distributive Property

Property

The distributive property allows you to multiply a number by a sum or difference by multiplying each part of the sum or difference separately and then adding or subtracting the products.

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

a \times (b - c) = (a \times b) - (a \times c)

Examples

Section 2

Breaking Apart and Rearranging Factors

Property

Examples

To solve $25 \times 8$ , break apart $8$ into $4 \times 2$ . The problem becomes $25 \times 4 \times 2$ . Rearrange to get $(25 \times 4) \times 2$ , which simplifies to $100 \times 2 = 200$ .
To solve $5 \times 28$ , break apart $28$ into $2 \times 14$ . The problem becomes $5 \times 2 \times 14$ . Rearrange to get $(5 \times 2) \times 14$ , which simplifies to $10 \times 14 = 140$ .
To solve $5 \times 48$ , break apart $48$ into $4 \times 12$ . The problem becomes $5 \times 4 \times 12$ . Rearrange to get $(5 \times 4) \times 12$ , which simplifies to $20 \times 12 = 240$ .

Explanation

Overview

Lesson overview

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

Overview

Section 1

Applying the Distributive Property

Property

The distributive property allows you to multiply a number by a sum or difference by multiplying each part of the sum or difference separately and then adding or subtracting the products.

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

a \times (b - c) = (a \times b) - (a \times c)

Examples

Section 2

Breaking Apart and Rearranging Factors

Property

Examples

To solve $25 \times 8$ , break apart $8$ into $4 \times 2$ . The problem becomes $25 \times 4 \times 2$ . Rearrange to get $(25 \times 4) \times 2$ , which simplifies to $100 \times 2 = 200$ .
To solve $5 \times 28$ , break apart $28$ into $2 \times 14$ . The problem becomes $5 \times 2 \times 14$ . Rearrange to get $(5 \times 2) \times 14$ , which simplifies to $10 \times 14 = 140$ .
To solve $5 \times 48$ , break apart $48$ into $4 \times 12$ . The problem becomes $5 \times 4 \times 12$ . Rearrange to get $(5 \times 4) \times 12$ , which simplifies to $20 \times 12 = 240$ .