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Fractions

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Simplest Form. A fraction is said to be in simplest (lowest) terms when its numerator and ... An improper fraction is one where the numerator is greater than ... – PowerPoint PPT presentation

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Title: Fractions

1
Chapter 6
• Fractions

2
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

3
Attributes of a Fraction
1. Number The amount describes the relative amount
shaded without regard to size, shape,
arrangement, orientation, etc.
2. Numeral Part to whole relationship

4
• Definition Fraction Equality
• if and only if
• Theorem Let be any fraction and n a
nonzero whole number. Then

5
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.

6
Ordering Fractions
• Definition of Less Than
• Theorem

7
The Set of Fractions is Dense
• Between any two fractions is another fraction.
• Gaps exist between whole numbers.
• Fractions appear in these gaps.

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8
• Theorem
• Let and be any fractions, where
.
• Then

9
• Definition
• Let and be any fractions. Then
• Theorem
• Let and be any fractions. Then

10
Properties of Fractions

11
Subtraction of Fractions
Definition Let and be any fractions
with . Then Theorem Let and
be any fractions with Then
12
6.3 Fractions Multiplication and Division
• Definition Let and be any fractions.
• Then

13
Properties of Fraction Multiplication
• Closure Property of Multiplication.
• Commutative Property of Multiplication.
• Associative Property of Multiplication
• Multiplicative Identity Property
• Multiplicative Inverse Property

14
• 6. Distributive Property of Fraction

15
Division of Fractions
• Definition
• Let and be any fractions with
.
• Then

16
Division of Fractions
• Theorem
• Let and be any fractions with
• Then