REAL NUMBERS

Real

Integers Whole #’s Counting#’s

Rational

The Real Number system is a hierarchy of subsets. Each subset may be part of another subset.

Rational NumbersNumbers that can be written as the quotient of two integers.Can be in the form of integers, fractions, terminating or repeating decimals.(Ex. -5, -(2/3), 0, 1.75, 4.333)

Integers{…-3, -2, -1, 0, 1, 2, 3, …}

Whole #’s{0, 1, 2, 3, 4, 5, …}

Counting #’s{1, 2, 3, 4, 5, …}

Irrational Numbers ( “What is not rational is irrational !” )Numbers that cannot be written as the quotient of two integers.

(Ex. ,

Properties of Real Numbers. (Let a, b, c be real numbers)

PropertyClosure

Commutative

Associative

Distributive

Identity

Inverse

Addition or Subtractiona + b = real #

a + b = b + a

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

a + 0 = a

a + (-a) = 0

Multiplication or Divisionab = real #

ab = ba

(ab)c = a(bc)

a x 1 = a

a x (1/a) = 1

Reinterpretation of …

Subtraction

a – b can be written as addition

a + (-b)

Division

a can be written as multiplication

a

Think and Discuss with your elbow partner.

1. How does the set of whole numbers differ from the set of integers?

2. Which property of real numbers states that a number added to its opposite results in 0?

3. Think about a time in the past week that you added numbers. What type of numbers did you add?

Which two sets of numbers comprise the full set of real numbers?