# Section 6.1 Rational Number Ideas and Symbols Fractions ```Definition of a Rational Number
A number is a rational number if and only if it can be
a
a
represented by a pair of integers, , where b ≠ 0 and
b
b
represents the quotient a &divide; b.
Rational Number Ideas and Symbols
Section 6.1
Mathematics for Elementary School Teachers - 4th Edition
O’DAFFER, CHARLES, COONEY, DOSSEY, SCHIELACK
Linda Roper
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Fractions
! A fraction is a symbol,
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Definition of Equivalent Fractions
where a and b are numbers and b ≠ 0.
! Two fractions,
!
is the numerator of the fraction and b is the denominator of the
fraction.
!a
, are equivalent fractions if and only if ad = bc.
!
Example:
2
4
and
, are equivalent fractions since 2&middot; 8 = 4&middot; 4
4
8
!Proper Fraction: the numerator of a fraction is less than the
denominator.
!Improper Fraction: the numerator of a fraction is greater than or
equal to the denominator.
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4
Fractions (continued)
Example
Fundamental Law of Fractions
Given a fraction a/b and a number c ≠ 0, a/b = ac/bc.
Find two fractions equivalent to
Include its simplest form, and verify your choices.
Solution:
Description of the Simplest Form of a Fraction
A fraction representing a rational number is in simplest form
when the numerator and denominator are both integers that
are relatively prime and the denominator is greater than zero.
20
5
10
and are equivalent to
.
12
3
6
The fraction
5
is in simplest form.
3
5
Description of a Decimal
Expanded Notation
! A decimal is a symbol that uses a base-ten place-value
Example: Write the number 423.85 in expanded notation.
system with tenths and powers of tenths to represent a
number.
Thousands
1000
1
Hundreds
100
4
Tens
10
6
Ones
1
.
Tenths
Hundredths
Thousandths
0
.
4
5
8
6
5
.
2
5
3
.
8
7
9
(
) (
) (
) (
) (
423.85 = 4 !10 2 + 2 !101 + 3 !10 0 + 8 !10 &quot;1 + 5 !10 &quot;2
7
)
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Terminating and Repeating Decimals
Changing a fraction to decimal form
! Every rational number can be expressed as a
terminating or repeating decimal.
! We can translate any rational number in
fraction form into decimal form by dividing.
! Terminating Decimals: A decimal that has a fixed
number of places. The remainder eventually becomes 0.
The denominator of a fraction converted from a
terminating decimal will be a multiple of 2 and/or 5.
Examples .5 or .25
! Repeating Decimals: A decimal that has a digit or group
of digits that repeat.
Examples .333 or .3636
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The End
Section 6.1
Linda Roper
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10
```