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Chapter 6

- Fractions

6.1 The Set of Fractions

- A fraction is a number than can be represented by
- an ordered pair of whole numbers
- The set of fractions is

Attributes of a Fraction

- Number The amount describes the relative amount

shaded without regard to size, shape,

arrangement, orientation, etc. - Numeral Part to whole relationship

- Definition Fraction Equality
- if and only if
- Theorem Let be any fraction and n a

nonzero whole number. Then

Simplest Form

- A fraction is said to be in simplest (lowest)

terms when its numerator and denominator have no

common prime factors. - An improper fraction is one where the numerator

is greater than the denominator.

Ordering Fractions

- Definition of Less Than
- Theorem

The Set of Fractions is Dense

- Between any two fractions is another fraction.
- Gaps exist between whole numbers.
- Fractions appear in these gaps.

0

1

2

3

10

4

5

6

7

8

9

- Theorem
- Let and be any fractions, where

. - Then

6.2 Fractions Addition and Subtraction

- Definition
- Let and be any fractions. Then
- Theorem
- Let and be any fractions. Then

Properties of Fractions

- Closure Property of Addition.
- Commutative Property of Addition
- Associative Property of Addition
- Additive Identity Property

Subtraction of Fractions

Definition Let and be any fractions

with . Then Theorem Let and

be any fractions with Then

6.3 Fractions Multiplication and Division

- Definition Let and be any fractions.
- Then

Properties of Fraction Multiplication

- Closure Property of Multiplication.
- Commutative Property of Multiplication.
- Associative Property of Multiplication
- Multiplicative Identity Property
- Multiplicative Inverse Property

- 6. Distributive Property of Fraction

Multiplication over Addition

Division of Fractions

- Definition
- Let and be any fractions with

. - Then

Division of Fractions

- Theorem
- Let and be any fractions with
- Then