Chapter 6
Rational Number
Operations and Properties
Comparing Rational Numbers
Using Models
y Using Common Denominators
y Using Place Value
y Using Definition of Less Than
y
Section 6.5
Comparing, Ordering, and
Connecting Rational Numbers
Using Models
Fraction Wall
Using Common Denominators
When the denominators of two fractions are the
same, the one with the greater numerator
represents the larger rational number.
Using Models
Number Line
If Denominators are Unlike
Th Fundamental
The
F d
lL
Law off F
Fractions
i
can b
be used
d
to write equivalent fractions with the same
denominator if the denominators of the fractions
to be compared are different.
The Cross-Product can also be used to compare
fractions that have different denominators.
1
Using Place Value
y
y
Same procedure for comparing whole
numbers: we start on the left with the
place with the largest value and compare
each place as we move to the right.
Rationale for this process is based on the
use off common d
denominators.
i t
Denseness of Rational Numbers
y
y
y
Using Definition of Less Than
Between any two rational number there
exists an infinite number of other
rational numbers.
We can find rational numbers between
any two rational numbers using common
denominators and place value (much like
we do when comparing rational
numbers).
A discussion of denseness is important in
elementary classrooms to help students
understand, for example, that 2/5 is NOT
the only rational number between 1/5
and 3/5.
y
Whenever a positive rational number is
added to a first rational number to get a
second rational number, the first number
is less than the second.
y
For example, 3/7 + 1/7 = 4/7, so we know
that 3/7 < 4/7
Example
y
Find three rational numbers
between 5/6 and 8/9.
Repeating Decimals and Fractions
Examples
Recall that every rational number in
fraction form can be written as a
terminating or repeating decimal.
y By
y cchoosing
oos g an
a appropriate
app op ate power
powe of
o 100
and subtracting to eliminate the repeating
numerals leads to an integer numerator
and denominator of the fraction that is
equal to the repeating decimal.
y
y
Write each repeating decimal as a
simplified fraction.
1) 0.11111…
0 11111
2) 0.2222…
2
Scientific Notation
When numbers are extremely large or
extremely small, an easier way to write
them is to use scientific notation.
y A rational number is expressed in scientific
notation when it is written as a product
where one factor is a decimal greater than
or equal to 1 and less than 10 and the
other factor is a power of 10.
y Example: 127, 000, 000 = 1.27 x 108
y Example: 0.000089 = 8.9 x 10-5
y
3