Grade 3: Properties of Multiplication

Properties of Multiplication — Quick Reference

1 Commutative Property

Changing the order of the factors does not change the product.

Example: 3 × 4 = 4 × 3

a × b = b × a

2 Associative Property

Changing the grouping of the factors does not change the product.

Example: (2 × 3) × 4 = 2 × (3 × 4)

(a × b) × c = a × (b × c)

3 Identity Property

Any number multiplied by 1 equals itself.

Example: 7 × 1 = 7

a × 1 = a

4 Zero Property

Any number multiplied by 0 equals 0.

Example: 9 × 0 = 0

a × 0 = 0

Examples of Each Property

Commutative

3 × 4 = 4 × 3

Order of factors does not matter

Associative

(2 × 3) × 4 = 2 × (3 × 4)

Grouping of factors does not matter

Identity

7 × 1 = 7

Any number × 1 = itself

Zero

9 × 0 = 0

Any number × 0 = 0

Test Yourself

Grade 3 Math Lessons