1. Properties of Real Numbers
Section 1-2
Properties of Real Numbers

2. All real numbers can be classified as rational or irrational
Rational numbers can be expressed as a fraction:
Or a repeating decimal.
Otherwise the number is irrational

3. Rational Rational Numbers are subdivided into subsets Integers
0, 1, 2, 3 …
Whole
… -3, -2, -1, 0, 1, 2, 3 …
Integers
Rational Numbers are subdivided into subsets
1, 2, 3…
Natural
Repeating decimals
Rational
Ratios

4. Rational The Number System Real Numbers Integers
0, 1, 2, 3 …
Whole
… -3, -2, -1, 0, 1, 2, 3 …
Integers
The Number System
1, 2, 3…
Natural
Real Numbers
Repeating decimals
Rational
Irrational
Ratios

5. 1.) Name the sets of numbers to which each belongs.
d.)

6. Different kinds of numbers sometimes act differently!
Lets look at some of the properties of
Real Numbers

7. This table is on page 14 in your book
Properties of Real Numbers
This table is on page 14 in your book

8. ( ) 2.) Name the property illustrated by the equation:
a.) (3 + a) + 2b = 3 + (a + 2b)
( )
( )
Associative property of (+)
Grouping has changed
b.) 3(x + 8) = (x + 8)3
Commutative property of (•)
Order of elements is changed
c.) 3(x + 8)
= 3x + 24
Distributive property

9. 2.) continued: d.) e.) 3(1) = 3 Additive Identity
Multiplicative Identity

10. 3.) What is the additive inverse of ?
4.) What is the multiplicative inverse of ?

11. Homework
Page 16
Problems: 10-18, 32-45, 52,53 and 56