Properties Flashcards
Closure property of multiplication
a•b= a real # 5•2= 10
Closure Property of addition
a+b= a real #
2+3=5
Commutative property of addition
a+b= b+a 3+7= 7+3
Commutative property of multiplication
a•b= b•a 9•4= 4•9
Associative property of addition
(a+b)+c= a+(b+c) (2+3)+4= 2+(3+4)
Associative property of multiplication:
(ab)c= a(bc) (2•3)4= 2(3•4)
Reflexive property
x=x
2=2
Symmetric property
a=b, b=a
7=b, b=7
Transitive property
a=b and b=c, then a=c
2=b and b=c, then 2=c
Additive identity
a+0=a, 0+a=0
2+0=2, 0+2=2
Additive inverse
a+(-a)=0, -a+a=0
7+(-7)=0, -7+7=0
Property of opposites of a sum
- (a+b)= -a+(-b)
- (2+3)= -2+(-3)
Definition of subtraction
a-b= a+(-b)
3-2=3+(-2)
Distributive property with respect to addition
a(b+c)= ab+ac 2(3+4)= 2•3+2•4
Distributive property with respect to subtraction
a(b-c)= ab-ac 2(3-4)= 2•3-2•4
Multiplicative identity
a(1)=a
7(1)=7
Multiplicative property of zero
a(0)=0
7(0)=0
Multiplicative property of -1
a(-1)=-a
7(-1)=-7
Property of opposites
(-a)(b)= -ab, a(-b)= -ab, (-a)(-b)= ab (-2)(3)= -6
Multiplicative inverse
a•1/a= 1
2• 1/2= 1
Property of reciprocal products
1/ab= 1/a • 1/b 1/2•3= 1/2 • 1/3
Definition of division
a/b = a• 1/b 2/3 = 2• 1/3
