## Algebra Properties

##### Created by:

highschoolrox1  on December 14, 2010

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# Algebra Properties

 Symmetric PropertyIf a=b, then b=a ex: If 3=2x+5 then 2x+5=3
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#### Definitions

Symmetric Property If a=b, then b=a
ex: If 3=2x+5 then 2x+5=3
Reflexive Property For any a, a=a
ex: 4=4 ex: 3x+5=3x+5
Transitive Property If a=b, and b=c, then a=c
If 4x+5=2y+9 and 2y+9=10 then 4x+5=10
(3 equal signs to demonstrate)
Multiplicative Property Given a, the product of a and one is a
ex: a times 1=a
-8 times 1=-8
Associative Property of Multiplication (ab)c=a(bc)
ex: (2 times 3)4=2(3 times 4)
ex: (2+3)+5=2+(3+5)
Multiplication Property of Zero Given a,a times 0=0
ex: 5 times 0=0
Substitution Given a=b, you can put in b for a in an expression
ex: 4x+3y=10 and 4=y then 4x+3(4)=10
Additive Inverse For any a, a+(-a)=0 (opposite-what do I add to "undo it?")
ex: 4+(-4)=0
-2+(2)=0
Multiplicative Inverse For any a, a times 1 over a=1 (reciprocal!)
ex: 4 times one over 4=1
2 thirds times three halves=1
Distributive Property *Hint: Use Order of Operations
a(b+c)=ab+ac
This is what allows you to combine terms.
ex: -6 times 5 and a half=6(5+a half)
-3(x-2)=-3x-6
Commutative Multiplication a times b=b times a
ex: 7 times 3=3 times 7
x times 3=3x
Definition of Subtraction is used quite often with commutative property
Definition of Subtraction Add the opposite
ex: 7-5 Algebra-7+(-5)
*All signs attach to coefficient
Additive Identity Given a, the sum of a and zero is a
ex: a+0=a
4+0=4
Commutative Property of Addition Commute---> move it around
a+b=b+a
ex: 3+7=7+3
5+x=x+5

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