Properties of Operations and Identities

Name: ______Date: ______

Properties of Equality

Properties of Equality / Property / Example(s)
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, then a/c = b/c
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
Substitution Property / If a = b, then b may be substituted for a in any expression containing a

Properties of Operations and Identities

Properties of Operations and Identities / Property / Example(s)
Commutative Property of Addition / a + b = b + a
Commutative Property of Multiplication / a ∙ b = b ∙ a
Associative Property of Addition / a + (b + c) = (a + b) + c
Associative Property of Multiplication / a ∙ (b ∙ c) = (a ∙ b) ∙ c
Distributive Property of Multiplication over Addition / a ∙ (b + c) = a ∙ b + a ∙ c
Additive Identity Property / a + 0 = a
Multiplicative Identity Property / a ∙ 1 = a
Additive Inverse Property / a + (-a) = 0
Multiplicative Inverse Property /
Multiplicative Property of Zero / a ∙ 0 = 0
Exponential Property of Equality /

Name ______Date ______

Properties of Equality Homework

1.  A football team is on the 35-yard time. The quarterback is sacked at the line of scrimmage. The team gains 0 yards. Which identity or property does this represent? Explain.

2.  Identify the sentence that does not belong with the other three. Explain.

Identify the sentence property.

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11. / If then 4 = x
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18. / If then x = 5