DUE TODAY Springboard Practice 7 Question 11 USING THESE PROOFS Reflexive Property of Equality For all real numbers a, a = a.
Symmetric Property of Equality For all real numbers a and b, if a = b, then b = a.
Transitive Property of Equality For all real numbers a, b, and c, if a = b and b = c, then a = c.
Substitution Property of Equality For all real numbers a and b, if a = b, then a may be replaced by b.
Additive Identity For all real numbers a, a + 0 = 0 + a = a.
Multiplicative Identity For all real numbers a, a ⋅ 1 = 1⋅ a = a.
Commutative Property of
Addition

For all real numbers a and b, a + b = b + a.

Commutative Property of
Multiplication

For all real numbers a and b, a ⋅ b = b ⋅ a.

Associative Property of Addition For all real numbers a, b, and c, (a + b) + c = a + (b + c).
Associative Property of
Multiplication

For all real numbers a, b, and c, (a ⋅ b) ⋅ c = a ⋅ (b ⋅ c).

Distributive Property of
Multiplication over Addition

For all real numbers a, b, and c, a(b + c) = a ⋅ b + a ⋅ c.
Additive Inverse For all real numbers a, there is exactly one real number -a

such that a + (-a) = 0 and (-a) + a = 0.

Multiplicative Inverse For all real numbers a and b where a ≠0, b ≠ 0, there is exactly

one number b
a
such that b
a
a
b⋅ = 1 and a
b
b
a⋅ = 1.
Multiplication Property of Zero For all real numbers a, a ⋅ 0 = 0 and 0 ⋅ a = 0.
Addition Property of Equality For all real numbers a, b, and c, if a = b, then a + c = b + c.
Subtraction Property of Equality For all real numbers a, b, and c, if a = b, then a − c = b − c.
Multiplication Property of
Equality

For all real numbers a, b, and c, if a = b, then a ⋅ c = b ⋅ c.
Division Property of Equality For all real numbers a, b, and c, c ≠ 0 if a = b, then a
c
b
c = .
Zero Product Property of Equality For all real numbers a and b, if a ⋅ b = 0 then a = 0 or b = 0 or

both a and b equal 0.

Addition Property of Inequality* For all real numbers a, b, and c, if a > b, then a + c > b + c.
Subtraction Property of
Inequality*

For all real numbers a, b, and c, if a > b, then a − c > b − c.

Multiplication Property of
Inequality *

For all real numbers a, b, and c, c > 0, if a > b, then a ⋅ c > b ⋅ c.
For all real numbers a, b, and c, c b, then a ⋅ c 0 if a > b, then a
c
b
c
> .
For all real numbers a, b, and c, c b, then a
c
b
c
< .