Section 1-2

Properties of Real Numbers

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

Rational

Irrational

RealNumbers

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

Ratios

Rationa

l

0, 1, 2, 3 … Whole

… -3, -2, -1, 0, 1, 2, 3 …Integers

The Number System

1, 2, 3…Natural

Repeating decimals

Ratios

Real Numbers

Irrational

Rationa

l

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

a.) -32

b.) 21

c.) 0

d.) 5

3

Lets look at some of the properties ofReal Numbers

Property Addition MultiplicationAssociative (a + b) + c = a + (b + c) (a*b)*c = a*(b*c)Commutative a + b = b + a a*b = b*aIdentity a + 0 = a a*1 = aInverse a + (-a) = 0 a*(1/a) = 1Distributve a(b + c) = ab + ac

Properties of Real Numbers

This table is on page 14 in your book

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

2.) continued:

d.) Additive Identity

e.) 3(1) = 3 Multiplicative Identity

3

20

3

2

3.) What is the additive inverse of ? 3

2

4.) What is the multiplicative inverse of ? 5

3

Homework

Page 16

Problems: 10-18, 32-45, 52,53 and 56