Comparing
numbers
directly,
without using a
number line,
has
many
practical
advantages
because it
does not require a
physical
drawing.
Although a number
line provides a
visual model which
is easy to
understand, it is
not feasible to use
it in most
situations.
The following
limitations
make a number line
cumbersome and time
consuming to
use:
 There is
not enough
space to
physically plot
more than a few
numbers on the
same line graph
(number
line).
 Plotting
extremely small
numbers, or
extremely large
numbers, or
numbers with
completely
different
orders of
magnitude, or
numbers which
are almost
equal may each
require
dramatically
different
labeling of
scale marks. In
addition, each
situation may
require
completely
different
intervals
marked on the
number
line.
Comparing
numbers directly
eliminates the
problems listed
above.
Direct comparison
does not require a
physical
drawing.
Real Numbers are
sequential. By
comparing place
values, any two
numbers can be
compared directly 
once the numbers are
written in the same
standard
notation.
. . .
Fractions

Comparisons
without
using the
number
line:
Return
To
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Page"
click
here
Compare the
fractions
and
.
(1)
Convert the
fractions so
that both
fractions have
the same
(common)
denominator,
and then
(2)
compare the
numerators with
one
another.
(1) Computing
the
Common
Denominator
(2)
Comparing
the
Numerators
is
less
than
is
greater
than