Comparing numbers directly,
without using a number line,
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
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Compare the fractions
Convert the fractions so that both fractions have the same (common) denominator, and then
compare the numerators with one another.
(1) Computing the