A. Subsets of Real Numbers

whole numbers  positive numbers beginning with zero such as 0, 1, 2, 3, 4, . . .

integers  positive and negative whole numbers such as . . . 3, 2, 1, 0, 1, 2, 3, . . .

rational numbers  numbers when written as decimals either terminate OR repeat such as ¾, ½, 1/3, 2/3

irrational numbers  numbers when written as decimals do not terminate AND do not repeat such as 2, p
B. Definitions

zero  the origin of the number line

graphing or plotting  drawing the point

coordinate  the number corresponding to a point

opposites  numbers that are the same distance from zero, but on opposite sides of zero such as 5 and 5 OR ¾ and ¾.

reciprocal  to reciprocate a fraction, exchange the numerator and denominator and any number multiplied by its reciprocal is equal to 1.
C. Properties of Addition and Multiplication where a, b, c are Real Numbers
1. 
closure 
a + b is a real # 
a·b is a real # 
2. 
commutative 
a + b = b + a 
a·b = b·a 
3. 
associative 
(a+b)+c = a+(b+c) 
(ab)c = a(bc) 
4. 
identity 
a + 0 = a and 0 + a = a 
a·1 = a and 1·a = a 
5. 
inverse 
a + (a) = 0 
a·(1/a) =1, a¹0 
6. 
distributive 
a(b + c) = ab + ac 
D. The Four Basic Operations
 sum  means to add
 difference  means to subtract
 product  means to multiply
 quotient  means to divide
Practice Problems
