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...}