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# Algebra 2 Properties

### Ch.1 Properties

Definition of Subtraction a - b = a + (-b)
Definition of Division a ÷ b = a/b = a ∙ 1/b, b≠0
Distributive Property for Subtraction a(b - c) = ab - ac
Multiplication by 0 0 ∙ a = -a
Multiplication by -1 -1 ∙ a = -a
Opposite of a Sum -(a + b) = -a + (-b)
Opposite of a Difference -(a -b) = b-a
Opposite of a Product -(ab) = -a ∙ b = a ∙(-b)
Opposite of an Opposite -(-a) = a
Reflexive Property of Equality a = a
Symmetric Property of Equality If a = b, then b = a
Transitive Property of Equality If a = b and b = c, then a = c
Addition Property of Equality If a = b, then a + c = b + c
Subtraction Property of Equality If a = b, then a - c = b - c
Multiplication Property of Equality If a = b, then ac = bc
Division Property of Equality If a = b and c ≠ 0, then a/c = b/c
Substitution Property of Equality If a = b, then b may be substituted for a in any expression to obtain an equivalent expression
Transitive Property of Inequality If a ≤ b and b ≤ c, then a ≤ c
Addition Property of Inequality If a ≤ b, then a + c ≤ b + c
Subtraction Property of Inequality If a ≤ b, then a - c ≤ b - c
Multiplication Property of Inequality If a ≤ b and c > 0, then ac ≤ bc. If a ≤ b and c < 0, then ac ≥ bc.
Division Property of Inequality If a ≤ b and c > 0, then a/c ≤ b/c. If a ≤ b and c < 0, then a/c ≥ b/c.
Closure of Addition a + b is a real number
Closure of Multiplication ab is a real number
Communtative of Addition a + b = b + a
Communtative of Multiplication ab = ba
Associative of Addition (a + b) + c = a + (b +c)
Associative of Multiplication (ab)c = a(bc)`
Identity of Addition a + 0 = a, 0 + a = a
Identity of Multiplication a ∙ 1 = a, 1∙ a = a
Inverse of Addition a + (-a) = 0
Inverse of Multiplication a ∙ 1/a = 1, a ≠ 0
Distributive a(b + c) = ab + ac
Created by: gnomealot