1. Lesson 1 – 2 Properties of Real Numbers
Pages 11 – 17

2. Objectives To graph and order real numbers
To identify properties of real numbers

3. Natural Numbers
{1, 2, 3, 4, 5, . . .}
Think of the natural numbers as the positive counting numbers.

4. Whole Numbers
{0, 1, 2, 3, 4, . . .}
The whole numbers are simply the natural numbers including 0.
This means that the natural numbers are a subset of the whole numbers.

5. Integers
{. . ., -3, -2, -1, 0, 1, 2, 3, . . .}
Think of the integers as the positive and negative counting numbers including 0.
This means that both the natural numbers and whole numbers are subsets of the integers.

6. Rational Numbers
A rational number is any number that can be written in the form:
This means that a rational number is any number that can be written as a fraction.
The natural numbers, whole numbers, and integers are all subsets of the rationals.

7. Irrational Numbers
Irrational numbers have decimal representations that neither terminate nor repeat.
This means that irrational numbers cannot be written as fractions.
Examples:

8. Venn Diagram Representation
Example:
Real Numbers
Rational
Irrational
Integers
Whole
Natural

9. Problem #1: Classifying a Variable
Your school is sponsoring a charity race. Which set of numbers best describes the number of people p who participate in the race?
Natural numbers
Integers
Rational numbers
Irrational numbers

10. Problem #1: Discussion
Would it make sense to use the set of integers to describe the number of people who participated in the race?
The set of rational numbers?

11. Got It?
In Problem #1, if each participant made a donation d of $15.50 to a local charity, which subset of real numbers best describes the amount of money raised?
Rational Numbers

12. Problem #2: The Number Line
What is the graph of the numbers below?

13. Got It?
Graph the numbers below:

14. Problem #3: Ordering Real Numbers
Compare the two numbers below by using “<“ or “>”.

15. Properties of Real Numbers
One property of real numbers excludes a single number, zero.
Zero is the additive identity for the real numbers, and zero is the one real number that has no multiplicative inverse.

16. Properties The opposite or additive inverse of any number a is –a.
Examples:
12 + (-12) = 0
= 0
-3x + 3x = 0

17. Properties
The reciprocal or multiplicative inverse of any nonzero number a is 1/a.
The product of a number and its reciprocal is 1, the multiplicative identity.
Examples:

18. Closure Property If a and b are real numbers, then
a + b is a real number
AND
ab is a real number

19. Commutative Property If a and b are real numbers, then a + b = b + a

20. Associative Property If a, b, and c are real numbers, then
(a + b) + c = a + (b + c)
AND
(ab)c = a(bc)

21. Distributive Property
If a, b, and c are real numbers, then
a(b + c) = ab + ac

22. Problem #4: Name the Property
(3 • 4) • 5 = (4 • 3) • 5
4(x + 2y) = 4x + 8y
7a + (-7a) = 0
(4 + 5) + 3 = 4 + (5 + 3)

23. SOL Question