Properties Used in Algebra and Geometry/Complex Number System

Symmetric Property of Equality

2 equations involved (If 2+4=6 them 6=2+4) ****DO NOT CONFUSE WITH COMMUTATIVE****

Distributive Property

4 (x + 6) = 4x + 24 3 (2 + 5) = 6 + 15 2x (3 + 10) = 6x + 20x

Additive Inverse Property

Any number plus its opposite is equal to 0 (4+(-4)=0, 5x+(-5x)=0, 0xy+(-0xy)=0)

Multiplicative Inverse Property

Any number times its reciprocal is equal to 1 (4(1/4)=1, (3/4)(4/3)=1, (2x/y)(y/2x)=1

Additive Identity Property

Anything + 0 = that thing (3+0=3, 2x+0=2x, 5t+0=5t)

Reflexive Property of Equality

Anything equals itself (8=8, a=a)

Multiplicative Property of Zero

Anything times 0 is 0 (8(0)=0, (2x+5)(0)=0, (0y)(0)=0)

Multiplicative Identity Property

Anything times 1 = that thing (5(1)=5, 6x(1)= 6x, (2x+7)(1)= 2x+7y

Rational Number

Fraction, terminating decimal, repeating decimal

Irrational Number

Go on forever and do not repeat (Pie, 0.010010001, non perfect square)

Subtraction Property of Equality

If 2x + 3 = 9, then 2x = 6

Division Property of Equality

If 5x = -30, then x = -6

Transitive Property of Equality

If _____ and _____ then statement (If x=4 and 4=2+2, then x=2+2

Multiplication Property of Equality

If x/3 = 4, then x = 12

Substitution Property of Equality

Replacement (If 2x=6 and 3y+2x=7, them 3y+6=7)

Associative Property

The Grouping changes but the order does not (4+(5+6)=(4+5)+6) ****DO NOT CONFUSE WITH DISTRIBUTIVE BECAUSE OF ( )****

Commutative Property

The order changes and there is one equation (3+4=4+3, 2x+4=4+2x, 3y+7x+5c=7x+5c+3y) ****DO NOT CONFUSE WITH SYMMETRIC****

Imaginary Number

The square root of a negative number

Addition Property of Equality

When you add the same value to both sides of the equation (If 2x-5=15 then 2x=20)

Integers

{...-4, -3, -2, -1,0, 1, 2, 3, 4...}

Whole Number

{0, 1, 2, 3...}

Natural/Counting Number

{1, 2, 3...}