<p> What are the "Grammar Rules" in the Language of Algebra?</p><p>The "Grammar Rules" of Algebra: Arithmetic follows the basic "grammar rules" or properties of Algebra. The following are the names of the more well known properties [or laws]. </p><p>Commutative Properties: </p><p> for Addition: A + B = B + A </p><p> for Multiplication: A x B = B x A </p><p>Associative Properties: </p><p> for Addition: A + (B + C) = (A + B) + C </p><p> for Multiplication: A(B x C) =(A x B)C </p><p>Distributive Properties: </p><p> for Addition: A(B + C) = AB + AC </p><p> for Multiplication: (A + B)C = AC + BC </p><p>Identities: </p><p> for Addition: A + 0 = A = 0 + A </p><p> for Multiplication: A x 1 = A = 1 x A </p><p>Inverses: </p><p> for Addition: for every real number A, there is a real number denoted by –A such that: A + (–A) = 0 = (–A) + A </p><p> for Multiplication: for every real number A not equal to zero, there is a real number denoted by 1/A such that: A(1/A) = 1 = (1/A)A </p><p>The Academic Support Center at Daytona State College (Math 52 pg 1 of 1)</p>