### Addition property of equality

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

### Inverse Property

a) opposites or additive inverses:

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