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14 Properties

Commutative 5+2=2+5 or ab=ba
Additive Inverse 7+(-3)=7-3 or a-b=a+(-b)
Associative Property/Grouping Property (8+2)+3=8+(2+3) or (ab) c=a (bc)
Additive identity 6+0=6 or abc+0=abc
Multiplicative Identity 3*1 =3 or xyz*1 =xyz
Multiplicative Property of Zero 7*0 =0 or ab*0 =0
Distributive 5(6+2) = 5(6) + 5(2) or x(y-z) = xy - xz
Comparison Property given two numbers, x and y, either x >y, x <y, or x=y
Density Property The number line is forever dense. Given any two numbers x and y there is always a number between them.
Reflexive 8 = 8 or 2a +7= 2a+7. Anytime you check an equation you are seeking a true statement.
Symmetric If 3+8 =11 then 11= 3+8. or if a+b =c then c= a+b
Transitive Property of Equality If 5*2 =10 and 7+3 =10 then 5*2 = 7+3. or if a=b and b=c then a=c
Transitive Property of Order If a >b and b >c then a >c
Substitution Property Given (7-3) +5= 4+5. or Given a =b, then b may be substituted for a.
Created by: c.zervigon