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Algebraic Properties
for proofs
15
Other
9th Grade
11/18/2009

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Term
additive property of equality
Definition
if a=b and c=d, then a+c=b+d
Term
subtraction property of equality
Definition
if a=b and c=d, then a-c=b-d
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
additive identity
Definition
a+0=a (Zero is the additive identity)
Term
additive identity
Definition
a+0=a (Zero is the additive identity)
Term
multiplicative identity
Definition
a*1=a (One is the mult. identity)
Term
additive inverse
Definition
a+(-a)=0
Term
multiplicative inverse
Definition
a*(1/a)=1
a does not=0
Term
commutative property of addition
Definition
a+b=b+a
Term
associative property of addition
Definition
(a+b)+c=a+(b+c)
Term
associative property of multiplication
Definition
(ab)c+a(bc)
Term
distributive property
Definition
a(b+c)=a*b+a*c
Term
substitution principle
Definition
if a=b, then each may replace the other in any algebrai expression
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