Example 5: Identify the rational number shown A and B marked
on the following number line.
Any
A
repre
Notic
the
0
num
the e
Solution:
Here a unit, 0 to 1 is divided into 7 equal parts. Ther
is representing 3 out of 7 parts. So, A represents of th
3
5.
and B represents
7 this is the example
Answers
In representation of rational numbers on the number line are discussed here. We know how to represent integers on the number line.To represent the integers on the number line, we need to draw a line and take a point O on it. Call it 0 (zero).
Set of equal distances on the right as well as on the left of O. Such a distance is known as a unit length. Let A, B, C, D, etc. be the points of division on the right of 'O' and A',B', C', D', etc. be the points of division on the left of 'O'. If we take OA = 1 unit, then clearly, the point A, B, C, D, etc. represent the integers 1, 2, 3, 4, etc. respectively and the point A', B', C', D', etc. represent the integers -1, -2, -3, -4, etc. respectively.
Note: The point O represents integer 0.
Representation of Rational Numbers on the Number Line
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Thus, we may represent any integer by a point on the number line. Clearly, every positive integer lies to the right of O and every negative integer lies to the left of O.
We can represent rational numbers on the number line in the same way as we have learnt to represent integers on the number line.
In order to represent rational numbers on the number line, first we need to draw a straight line and mark a point O on it to represent the rational number zero. The positive (+ve) rational numbers will be represented by points on the number line lying to the right side of O and negative (-ve) rational numbers.
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.
Consider the following examples on representation of rational numbers on the number line;
1. Represent 12 and −12 on the number line.
Solution:
Draw a line. Take a point O on it. Let the point O represent 0. Set off unit lengths OA to the right side of O and OA' to the left side of O.
Then, A represents the integer 1 and A' represents the integer -1.
Represent 1/2 and -1/2 on the number line
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Now, divide the segment OA into two equal parts. Let P be the mid-point of segment OA and OP be the first part out of these two parts. Thus, OP = PA = 12. Since, O represents 0 and A represents 1, therefore P represents the rational number 12.
Again, divide OA' into two equal parts. Let OP' be the first part out of these two parts. Thus, OP' = PA' = −12. Since, O represents 0 and A' represents -1, therefore P' represents the rational number −12.
2. Represent 23 and −23 on the number line.
Solution:
Draw a line. Take a point O on it. Let it represent 0. From the point O set off unit distances OA to the right side of O and OA' to the left side of O respectively.
Divide OA into three equal parts. Let OP be the segment showing 2 parts out of 3. Then the point P represents the rational number 23.
Represent 2/3 and -2/3 on the number line
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Again, divide OA' into three equal parts. Let OP' be the segment consisting of 2 parts out of these 3 parts. Then, the point P' represents the rational number −23.