TPE

Transitive Properity of Equality

If x=y and y=z, then x=z

If 1+7=8, and 8=2 to the third power, then 1+7= 2 to the third power

SubPE

Substitution Property of Equality

If x+7=10 and x=3, then 3+7=10

If 5+4=9 and x=4, then 5+x=9

SPE

Symmetric Property of Equality

If xy=8, then 8=xy

1+5=6, then 6=1+5

RPE

Reflexive Property of Equality

x=x

n+5=n+5-n+5

DPMA

1. Distributive Property of multiplication over addition

2. Undistribute

1. a(b+c)=ab+ac

1.5(x+2)=5x+10

2. (6ab)+(10a)= 2a(3b+5)

                               2a       2a

b-a=b+-a

8-12=8+-12

MIN

Mulitplicative Inverse Properity 

"Usually fractions"

b x 1= i

b

1 x 3 = 1

                                  b

AIN

Additive Inverse Property

a + -a= 0

-4 + 4 = 0

MP-(-1)

Mulitplication Property of -1

-1 x d = -d

12 x -1 = -12

MP - 0

Multiplication Property of 0

c x 0 = 0

0 x 6 = 0

MID

Multiplicative Identity Property

b x 1 = b

1 x 12 = 12

AID

Additive Idenity Property

a + 0 = a

0 + -8 = -8

APM

Associative Property of Mulitiplication

(d x e)f = d(e x f)

2 x (5 x 4) = (2 x 5) x 4

APA

Associative Property of Addition

a + (b + c) = (a + b) + c

(2 + 3) + 4 = 2 + (3 + 4)

CPA

Communitive Property of Addition

a + b = b + a

2 + 3 = 3 + 2

CPM

Communitive Property of Mulitplication 

c x d = d x c

8 x 2 = 2 x 8