1. Properties of Real Numbers
N: Natural (1,2,3, …)
W: Whole (0,1,2,3,…)
Z: Integers (… -2,-1,0,1,2,…)
Q: Rationals (m/n; m,n integers)
I: Irrational ( , )
R: Real (all rational and irrational)

2. Real Numbers, R
IMAGINARY I Q Z W N

3. Properties of Real Numbers
For any real numbers a, b, and c
Addition
Multiplication
Commutative
Associative
Identity
a + 0 = a = 0 + a
Inverse
If a in note zero, then

4. Properties of Real Numbers
Distributive property
For all real numbers a, b, and c a(b+c) = ab + ac and (b+c)a = ba + ca

5. Solving Equations; 5 Properties of Equality
Reflexive
For any real number a, a=a
Symmetric Property
For all real numbers a and b, if a=b, then b=a
Transitive Property
For all reals, a, b, and c, if a=b and b=c, then a=c

6. Solving Equations; 5 Properties of Equality
Addition and Subtraction
For any reals a, b, and c, if a=b then a+c=b+c and a-c=b-c
Multiplication and Division
For any reals a, b, and c, if a=b then a*c=b*c, and, if c is not zero, a/c=b/c

7. Applications of Equations
Problem Solving Plan
Explore the Problem
Plan the solution
Solve the problem
Examine the solution

8. Absolute Value Equations
Absolute value: Distance from zero
For any real number a:
If , then