1. Real Numbers and their Properties
5.5
Real Numbers and their Properties

2. Real Numbers
The set of real numbers is formed by the union of the rational and irrational numbers.
The symbol for the set of real numbers is

3. Relationships Among Sets
Irrational numbers
Rational numbers
Integers
Whole numbers
Natural numbers
Real numbers

4. Properties of the Real Number System
Closure
If an operation is performed on any two elements of a set and the result is an element of the set, we say that the set is closed under that given operation.

5. Commutative Property Addition a + b = b + a
for any real numbers a and b.
Multiplication
a • b = b • a
for any real numbers a and b.

6. Example 8 + 12 = 12 + 8 is a true statement.
Note: The commutative property does not hold true for subtraction or division.

7. Associative Property Addition (a + b) + c = a + (b + c),
for any real numbers a, b, and c.
Multiplication
(a • b) • c = a • (b • c),
for any real numbers a, b, and c.

8. Example (3 + 5) + 6 = 3 + (5 + 6) is true.
Note: The associative property does not hold true for subtraction or division.

9. Distributive Property
Distributive property of multiplication over addition
a • (b + c) = a • b + a • c
for any real numbers a, b, and c.
Example: 6 • (r + 12) = 6 • r + 6 • 12
= 6r + 72

10. Homework
P. 256 # 2 – 80 even