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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

6.1 Rational Number Ideas and Symbols

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

sets of numbers
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
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
Modeling Fractions
  • Area Model
  • Linear Model
  • Discrete Model
definition of a rational number and fraction
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
Fraction Terminology
  • Numerator
  • Denominator
  • Proper fraction
    • |numerator| < |denominator|
  • Improper fraction
    • |numerator|  |denominator|
equivalent fractions
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
Fundamental Law of Fractions

Given a fraction and a number c  0,

simplest form of a fraction
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
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.
  • Reading a decimal (writing)
  • Writing a decimal in expanded notation
modeling decimals
Modeling Decimals
  • Base-Ten Blocks
  • Play Money
  • Decimal Grids
conversions
Conversions
  • Fraction  Decimal
  • Terminating Decimal
  • Repeating Decimal
  • Note - Every rational number can be expressed as a terminating or repeating decimal.