1.1 properties

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Axiom or postulate

a statement that is assumed to be true

Reflexive Property

a=a
every real number equals itself

Symmetric property

if a=b then b=a
you can switch the sides of an equation
10=3x-5 or 3x-5=10

Transitive Property

if a=b and b=c then a=c
if 3y+22=m then m=3y+22

if a=b then a+c=b+c
you can add any real number to both sides of the equation 3x+=y then 3x+7=y+2

Multiplication property of equality

if a=b the ac=bc
here you are multiplying both sides by c
you can multiply both sides of an equation by any real number

Closure Property

a+b and ab are unique real numbers
whenever you add or multiply 2 real numbers together you get a real number
7+5=12 always

Commutative Property

a+b=b+a, ab=ba
you can change the order of numbers you are adding or multiplying
3+4=4+3
3(4)=4(3)

Associative Property

(a+b)+c=a(b+c)
(ab)c=a(bc)
you can change the grouping of numbers that are being added or multiplied
4+(5+6)=(4+6)+5

Identity Property

0+a=a
1(a)=a
adding 0 does not change the number neither does multiplying by 1

Inverse Property

a+(-a)=0
any number plus its opposite equals 0
x+ (-x)= 0

b)reciprocals or multiplicative inverses:
any number times its reciprocal = 1
mx1
- =1
m

Distributive Property

2(x+5)=2x+10
you must take the most out that you can
12m+18=6(2m+3)

Example: