The Internet’s Guide to…          Algebra Properties                 By Ethan Sutherland  If a+(-a)=0Then (-a)+a=0?
Additive Identify Property      a+0=a          +0=
Additive Inverse Property   a+(-a)=0    +(-         )=0
Multiplicative Identity Property         a·1=a            ·1=
Multiplicative Property of Zero         a·0=0              ·0=0
Multiplicative Property of -1a·-1=-a -a·-1=a·-1=-          -     ·-1=
Multiplicative Inverse Property     a/b·b/a=1    __ · __          =1
Commutative Propertya+b=b+a ab=ba+   =     +            =
Associative Property(a+b)+c=a+(b+c)  (ab)c=a(bc)(       +     )+     =    +(   +       )    (           )   =     (        )
Distributive Propertya(b+c)=ab+aca(b-c)=ab-ac(    +     )=        +(     -    )=         -
Symmetric Propertya=b, b=c, a=c=    ,    =       ,      =
Reflexive Property     a=a       =
Transitive Propertya=b, b=a=                =
Addition Property of Equality     a+c=b+c      +     =       +
Subtraction Property of Equality       a-c=b-c          -    =      -
Multiplication Property of Equality          ac=bc               =
Division Property of Equality a/c=b/c c≠0__ = __                  ≠0
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The Internet's Algebra Property Thingy

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The Internet's Algebra Property Thingy

  1. 1. The Internet’s Guide to… Algebra Properties By Ethan Sutherland If a+(-a)=0Then (-a)+a=0?
  2. 2. Additive Identify Property a+0=a +0=
  3. 3. Additive Inverse Property a+(-a)=0 +(- )=0
  4. 4. Multiplicative Identity Property a·1=a ·1=
  5. 5. Multiplicative Property of Zero a·0=0 ·0=0
  6. 6. Multiplicative Property of -1a·-1=-a -a·-1=a·-1=- - ·-1=
  7. 7. Multiplicative Inverse Property a/b·b/a=1 __ · __ =1
  8. 8. Commutative Propertya+b=b+a ab=ba+ = + =
  9. 9. Associative Property(a+b)+c=a+(b+c) (ab)c=a(bc)( + )+ = +( + ) ( ) = ( )
  10. 10. Distributive Propertya(b+c)=ab+aca(b-c)=ab-ac( + )= +( - )= -
  11. 11. Symmetric Propertya=b, b=c, a=c= , = , =
  12. 12. Reflexive Property a=a =
  13. 13. Transitive Propertya=b, b=a= =
  14. 14. Addition Property of Equality a+c=b+c + = +
  15. 15. Subtraction Property of Equality a-c=b-c - = -
  16. 16. Multiplication Property of Equality ac=bc =
  17. 17. Division Property of Equality a/c=b/c c≠0__ = __ ≠0

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