6.1 Rational Number Ideas and Symbols

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6.1 Rational Number Ideas and Symbols. Remember to Silence Your Cell Phone and Put It In Your Bag!. Sets of Numbers. The set of Natural Numbers N = {1, 2, 3, 4, . . . } The set of Whole Numbers W = {0, 1, 2, 3, 4, . . . } The set of Integers I = { . . . , -3, -2, -1, 0, 1, 2, 3, . . . }

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### 6.1 Rational Number Ideas and Symbols

Remember to Silence Your Cell Phone and Put It In Your Bag!

Sets of Numbers
• The set of Natural Numbers

N = {1, 2, 3, 4, . . . }

• The set of Whole Numbers

W = {0, 1, 2, 3, 4, . . . }

• The set of Integers

I = { . . . , -3, -2, -1, 0, 1, 2, 3, . . . }

• The set of Rational Numbers

Q = { | a, b  I, b  0 }

Representations of Fractions

What does ¾ mean?

• Parts of a whole
• Parts of a set
• Comparison of two sets
• Point on a number line
• Division of whole numbers
Modeling Fractions
• Area Model
• Linear Model
• Discrete Model
Definition of a Rational Number and Fraction
• A number is a rational number iff it can be represented by a pair of integers, where b  0 and represents the quotient a  b.
• The symbol used in this definition is a fraction.
Fraction Terminology
• Numerator
• Denominator
• Proper fraction
• |numerator| < |denominator|
• Improper fraction
• |numerator|  |denominator|
Equivalent Fractions
• Equivalent fractions
• Two fractions are equivalent if they represent the same rational number.
• Two fractions, are equivalentfractions iff ad = bc.
Fundamental Law of Fractions

Given a fraction and a number c  0,

Simplest Form of a Fraction

A fraction representing a rational number is in simplest form when:

• The numerator and denominator are both integers and
• The numerator and denominator are relatively prime and
• The denominator is greater than zero.
Definition of Decimal
• A decimal is a symbol that uses a base-ten place value system with tenths and powers of tenths to represent a number.