Properties Flashcards
(a+b)+c=a+(b+c)
associative property of addition
a+b=real #
closure property of addition
a+b=b+a
commutative property of addition
a+0=a.
identity property of addition
a+(-a)=0
inverse property of addition
ab= real #
closure property of multiplication
(ab)c=a(bc)
associative property of multiplication
Ab=ba
commutative property of multiplication
a(1)=a
identity property of multiplication
a(1/a)=0
multiplicative inverse
a(b+c) = ab+av
distributive property
if a+b=c & x-y=z,
then (a+b)-y=x-y=z
substitution principle
a=a
reflexive
a=b, b=a
symmetric property
if a=b & b=c, then a=c
transitive property
a, | -(-a) = a
cancellation property of additive inverse
ac=bc, then a=b
cancellation property of multiplication
a+c=b+c, then a=b
cancellation property of addition
-(a+b)=(-a)+(-b)
property of opposites of a sum
a/b = a(1/b)
definition of division
ax=0
multiplicative property of zero
a(-1)=-a
multiplicative property of -1
(-a)b=-ab & (-a)(-b)=ab
property of opposites in products
a-b=a+(-b)
definition of subtraction
