Theory:

A rational number is one that can be written as the ratio of two integers.
Example:
i) \(6 = 12/2\).
 
ii) \(9 = 27/3\).
 
iii) \(4 = 16/4\).
A number line is a way to visualize numbers by placing them along a line that shows their relative sizes.
numline.PNG
 
Order to represent the rational number on the number line:
  • We draw a line and mark a point \(O\) on it to represent the rational number \(0\).
  • The positive rational numbers will be represented on the number line to the right side of \(O\).
  • The negative rational numbers will be represented on the number line to the left side of \(O\).
  • If we mark a point \(A\) on the line to the right of \(O\) to represent \(1\), then \(OA =\) \(1\) unit.
  • Similarly, if we choose a point \(A'\) on the line to the left of \(O\) to represent \(-1\) then \(OA' =\) \(-1\) unit.
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Now, we are going to represent the rational number \(1/2\) on the number line.
 
For this, we divide the segment \(OA\) into equal parts. Let \(P\) be the midpoint of segment \(OA\). Then, \(OP = PA = 1/2\) and also we divide the segment \(OA'\) into equal parts. In this \(P'\) be the midpoint of segment \(OA'\), then \(OP'= P'A = -1/2\).
 
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