For each real number a

a = a

Reflexive Property of
Equality

If a = b, then b = a

Symmetric Property of Equality

if a = b and b = c

then a = c

Transitive Property of Equality

For every real number a and b

a + b is a real number

Closure Property of Addition

For every real number a and b

ab is a real number

Closure Property of Multiplication

For every real number a and b

a + b = b + a

Commutative Property of Addition

For every real number a and b

ab = ba

Commutitive Property of Multiplication

For every real number a, b and c

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

Associative Property of Addition

For every real numbers a, b and c

(ab)c = a(bc)

Associative Property of Multiplication

Fore every real number a,

a + 0 = 0 + a = a

Identity Property of Addition

For every real number a,

a x 1 = 1 x a = a

a/a = 1

Identity Property of Multiplication

For every real number a, there is a real number ^-a such that,

a + ^-a = 0

Inverse Property of Addition

For every real number a, (a ≠ 0) there is a real number a^-1

such that,

a x a^-1 = a^-1 x a = 1

(a^-1 = 1/a)

Inverse Property of Multiplication

For every real number a, b and c

a(b + c) = ab + bc

Distributive Property

For every real number a, b and c

a - b = c if and only if b + c = a

a ÷ b = c if and only if bc = a

a - b = a + ^-b

a ÷ b = a x b^-1