** ** Algebra is the subdivision of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts
arising from them, including terms, polynomials, equations and algebraic structures. Simultaneously with geometry, analysis, topology, combinatory, and number theory, algebra is one of the main
branches of pure mathematics.** **

** ** The part of algebra is called elementary algebra is often part of the
curriculum in secondary education and introduces the concept of variables representing numbers, such as addition.

The property refers to rules that designate a standard procedure or method to be followed. A proof is a expression of the truth of a statement in mathematics. The property or rules in mathematics are the result from testing the truth or validity of something by experiment or trial to establish a proof.

The commutative property is one of the essential properties of numbers. The word “commute” means “exchange” or “swap over”. Commutative property states that numbers may be added or multiplied in any order.

The Commutative means change the order in which you add or subtract numbers does not change the sum or product.

Commutative Property of Addition describes that changing the order of addends doesn’t change the sum. Commutative can be described more formally. If + stands for an operation and A,B are elements from a given set, then + is commutative if, for all such elements.

a + b = b + a

** ** Commutative Property of Multiplication defines
that changing the order of factors doesn’t change the product. Commutative can be described more formally. If * stands for an operation and A,B are elements from a given set, then * is
commutative if, for all such elements.

a * b = b * a

**Example 1:**

** a =10, b = 12 **

a + b = b + a a * b = b * a

10 + 12 = 12 + 10 10 * 12 = 12 * 10

22 = 22 120 = 120

**Example 2:**

** a = 18, b = 26**

a + b = b + a a * b = b * a

18 + 26 = 26 + 18 18 * 26 = 26 * 18

44 = 44 468 = 468.