• Algebra
• Trigonometry
• Geometry
• Calculus

Commutative property

The sum or product of any two operands equals to their corresponding sum or product in reverse order called the commutative property.

Introduction

Let $a$ and $b$ denote two quantities in algebraic form. The addition of them is written as $a+b$ and the multiplication of them is written as $a \times b$. Now, the commutative property is written in following two different forms in mathematics.

Addition

The sum of two operands equals to the sum of operands in reverse order is called the commutative property of addition.

$\large a+b \,=\, b+a$

Multiplication

The product of two operands equals to the product of operands in reverse order is called the commutative property of multiplication.

$\large a \times b \,=\, b \times a$

Usage

The commutative property is usually used in two different cases.

1. To replace the sum of any two quantities by the sum of the same quantities in reverse order.
2. To substitute the product of any two operands by the product of them in reverse order.