• Algebra
• Trigonometry
• Geometry
• Calculus

Commutative property of Addition

Formula

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

The addition of two quantities is equal to their sum in reverse order. It is called the commutative property of addition.

Introduction

$a$ and $b$ are two operands in algebraic form and their sum is written in mathematical form as $a+b$. Now, add them in reverse order and it is expressed as $b+a$. Mathematically, the two expressions are equal and it is called as the commutative law of addition.

Example

$2$ and $3$ are two quantities and add them.

$\implies$ $2+3 = 5$

Now, add the same two operands in reverse order.

$\implies$ $3+2 = 5$

$\,\,\, \therefore \,\,\,\,\,\,$ $2+3$ $\,=\,$ $3+2$ $\,=\,$ $5$

Thus, the commutative rule of addition can be verified in numerical system.

Proof

Learn how to derive the commutative law of addition in algebraic form by geometrical method.