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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. 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

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  1. 6.1 Rational Number Ideas and Symbols Remember to Silence Your Cell Phone and Put It In Your Bag!

  2. 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 }

  3. 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

  4. Modeling Fractions • Area Model • Linear Model • Discrete Model

  5. 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.

  6. Fraction Terminology • Numerator • Denominator • Proper fraction • |numerator| < |denominator| • Improper fraction • |numerator|  |denominator|

  7. Equivalent Fractions • Equivalent fractions • Two fractions are equivalent if they represent the same rational number. • Two fractions, are equivalentfractions iff ad = bc.

  8. Fundamental Law of Fractions Given a fraction and a number c  0,

  9. 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.

  10. 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

  11. Modeling Decimals • Base-Ten Blocks • Play Money • Decimal Grids

  12. Conversions • Fraction  Decimal • Terminating Decimal • Repeating Decimal • Note - Every rational number can be expressed as a terminating or repeating decimal.

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