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1. The Internet’s Guide to…
Algebra Properties
By Ethan Sutherland
If a+(-a)=0
Then (-a)+a=0?

2. Additive Identify Property
a+0=a
+0=

3. Additive Inverse Property
a+(-a)=0
+(- )=0

4. Multiplicative Identity Property
a·1=a
·1=

5. Multiplicative Property of Zero
a·0=0
·0=0

6. Multiplicative Property of -1
a·-1=-a -a·-1=a
·-1=- - ·-1=

7. Multiplicative Inverse Property
a/b·b/a=1
__ · __ =1

8. Commutative Property
a+b=b+a ab=ba
+ = + =

9. Associative Property
(a+b)+c=a+(b+c)
(ab)c=a(bc)
( + )+ = +( + )
( ) = ( )

10. Distributive Property
a(b+c)=ab+ac
a(b-c)=ab-ac
( + )= +
( - )= -

11. Symmetric Property
a=b, b=c, a=c
= , = , =

12. Reflexive Property
a=a
=

13. Transitive Property
a=b, b=a
= =

14. Addition Property of Equality
a+c=b+c
+ = +

15. Subtraction Property of Equality
a-c=b-c
- = -

16. Multiplication Property of Equality
ac=bc
=

17. Division Property of Equality
a/c=b/c c≠0
__ = __ ≠0