# Properties for Final 2

## 13 terms

### closure

any calculation that doesn't have a property name; the calculation is usually something assumed in math
ex) 5+6=11

### commutative property( of addition and multiplication)

the order doesn't matter
ex) a+b=b+a
ex) ab=ba

### associative property( of addition and multiplication)

the parenthesis can be moved around
ex) (a+b)+c= a+(b+c)
ex) (ab)c=a(bc)

any number added to zero is the same number
ex) a+0=a

### identity of multiplication

any number multiplied by one is itself
ex) a(1)=a

when opposites are added, the result is zero
ex) a+(-a)=0

### inverse property of multiplication

when reciprocals are multiplied, the result is one
ex) (a/b)(b/a)=1

### distributive property

ex) a(b+c)= ab+ac

### (addition and multiplication )axiom of equality

whatever you do to the right, you have to do to the left
ex) a+c=b→a=b-c
ex) x/2=a→x=2a

### substitution

ex) if a=2, then 3a is equal to 6

### factoring

ex) a²+2ax+x²=(a+x)²

ex) x/2= x(1/2)

ex) (-1)(x)=₋x
ex) (-1)(-x)=x
ex) 16(-1)=-16