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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 | a, b I, b 0 } b 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 aof a integers, where b 0 and b b represents the quotient a b. a The symbol used in this definition is a b 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. a c Two fractions, b and d are equivalent fractions iff ad = bc. Fundamental Law of Fractions a Given a fraction and a number c 0, b a ac . b bc Simplest Form of a Fraction A fraction representing a rational number is in simplest form when: 1. The numerator and denominator are both integers and 2. The numerator and denominator are relatively prime and 3. 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. Reading a decimal (writing) Writing a decimal in expanded notation Modeling Decimals Base-Ten Blocks Play Money Decimal Grids Conversions Fraction Decimal Terminating Decimal Repeating Decimal Note - Every rational number can be expressed as a terminating or repeating decimal.