Transcript 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, . . . }
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.