The Four Properties of Multiplication with Examples

There are four main properties of multiplication that can help us solve problems in algebra. These properties are the associative property, the commutative property, the distributive property, and the identity property.

Associative Property

The associative property tells us that the order that multiplied numbers are grouped by does not affect their product.

Example: (a×b)×c = b×(c×a)

Commutative Property

The commutative property tells us that changing the order of multiplied numbers does not affect their product.

Example: a×b = b×a

Distributive Property

The distributive property tells us that multiplying the sum of a quantity by a number is equivalent to multiplying that number by each of the numbers within the quantity and then summing them.

Example: a(b + c + d) = a×b + a×c + a×d

Identity Property

The identity property tells us that the product of any number and 1 is equal to the number.

Example: 1×a = a

Lesson Summary

These four properties are fundamental to algebra and all other math, science, and engineering topics that use algebra.

Although some of the properties may seem obvious, they are the foundation of being able to solve equations. You may have used these properties already, even if you never thought about their name or the property itself while using it!