English: Unital associative algebra axioms, written as commutative diagrams (Photo credit: Wikipedia)

**Closure Property of Addition**

Sum (or difference) of 2 real numbers equals a real number

**Additive Identity**

a + 0 = a

**Additive Inverse**

a + (-a) = 0

**Associative of Addition**

(a + b) + c = a + (b + c)

**Commutative of Addition**

a + b = b + a

**Definition of Subtraction**

a – b = a + (-b)

**Closure Property of Multiplication**

Product (or quotient if denominator 0) of 2 reals equals a real number

**Multiplicative Identity**

a * 1 = a

**Multiplicative Inverse**

a * (1/a) = 1 (a 0)

**(Multiplication times 0)**

a * 0 = 0

**Associative of Multiplication**

(a * b) * c = a * (b * c)

**Commutative of Multiplication**

a * b = b * a

**Distributive Law**

a(b + c) = ab + ac

**Definition of Division**

a / b = a(1/b)

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Posted in Math

Tags: Associative property, Commutative property, Distributive property, Math, Real number, Recreations, Specific Numbers, Subtraction

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