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13 terms

Algebra Properties of Real Numbers

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Commutative
Addition
For all real a, b

a + b = b + a
Associative
Addition
For all real a, b, c

a + (b + c) = (a + b) + c
Identity Addition
the sum of any number and zero is the original number
a+0=a
Additive Inverse
(Opposite)
For every real number a there exist a real number, denoted (-a), such that

a + (-a) = 0
Distributive Law
For all real a, b, c

a(b + c) = ab + ac, and (a + b)c = ac + bc
Commutative
Multiplication
Changing the order of the factors does not change the product; for example 10 x 9 = 9 x 10; a b = b a
Associative Multiplication
changing the grouping of factors will not change the product, (ab)c = a(bc)
Reflexive
a=a
Inverse Multiplication
states that a number multiplied by its reciprocal is equal to one
Identity Multiplication
the product of any number times 1 is that number
Ax1=A
Symmetric
if a=b then b=a
Transitive
If a=b and b=c then a=c
Multiplication by Zero
a x 0 = 0; also, if a x b = 0, then at least one of a or b must equal 0