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 equivalent fractions 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: 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.