Fractions

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Chapter 6

• Fractions

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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

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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

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

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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.

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Ordering Fractions

• Definition of Less Than
• Theorem

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

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6.2 Fractions Addition and Subtraction

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

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Properties of Fractions

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

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

• Definition Let and be any fractions.
• Then

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Properties of Fraction Multiplication

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

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• 6. Distributive Property of Fraction
  Multiplication over Addition

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Division of Fractions

• Definition
• Let and be any fractions with
  .
• Then

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Division of Fractions

• Theorem
• Let and be any fractions with
• Then