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What are the "Grammar Rules" in the
Language of Algebra?
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].
Commutative Properties:
for Addition: A + B = B + A
for Multiplication: A x B = B x A
Associative Properties:
for Addition: A + (B + C) = (A + B) + C
for Multiplication: A(B x C) =(A x B)C
Distributive Properties:
for Addition: A(B + C) = AB + AC
for Multiplication: (A + B)C = AC + BC
Identities:
for Addition: A + 0 = A = 0 + A
for Multiplication: A x 1 = A = 1 x A
Inverses:
for Addition: for every real number A, there is a real number denoted by –A
such that: A + (–A) = 0 = (–A) + A
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
The Academic Support Center at Daytona State College (Math 52 pg 1 of 1)
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