Download 6.1 Rational Number Ideas and Symbols

6.1 Rational Number Ideas
and Symbols
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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.