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Properties (Mrs. Wood)
Properties of Real Numbers
27
Mathematics
Not Applicable
11/24/2004

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Cards

Term
Additiive Identity
Definition
the number 0
Term
Multiplicative Identity
Definition
the number 1
Term
Commutative Property of Addition
Definition
a + b = b + a
Term
Associative Property of Addition
Definition
a + (b + c) = (a + b) + c
Term
Property of Opposites
Definition
a + (-a) = 0
Term
Property of Reciprocals
Definition
a(1/a) = 1
Term
Reflexive Property of Equality
Definition
a = a
Term
Transitive Property of Equality
Definition
if a = b and b = c, then a = c
Term
Symmetric Property of Equality
Definition
if a = b, then b = a
Term
Closure Property
Definition
for all real numbers, a + b and ab is a unique real number
Term
Addition Property of Equality
Definition
if a,b, and c are any real numbers, and a = b, then a + c = b + c
Term
Distributive Property
Definition
a(b + c) = ab + ac
Term
Distributive Property
Definition
a(b + c) = ab + ac
Term
Division Property of Equality
Definition
if a = b, then a/c = b/c
Term
Identity Property of Addition
Definition
a + 0 = a
Term
Identity Property of Multiplication
Definition
a • 1 = a
Term
Multiplication Property of Equality
Definition
if a,b, and c are any real numbers, and a = b, then ac = bc
Term
Multiplicative Property of –1
Definition
(-1)a = -a
Term
Multiplicative Property of Zero
Definition
a(0) = 0
Term
Property of the Opposites of a Sum
Definition
-(a + b) = -a + -b
Term
Property of Opposites in Products
Definition
for all real numbers a(-b) = -ab,
(-a)b = -ab and
(-a)(-b) = ab
Term
Property of the Reciprocal of a Product
Definition
1/ab = 1/a • 1/b
Term
Property of the Reciprocal of the Opposite of a Number
Definition
1/-a = -(1/a)
Term
Substitution Principle
Definition
an expression may be replaced by another expression with the same value
Term
Subtraction Property of Equality
Definition
if a,b, and c are any real numbers, and a = b, then a - c = b - c
Term
Commutative Property of Multiplication
Definition
ab = ba
Term
Associative Property of Multiplication
Definition
a(bc) = (ab)c
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