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Absolute Value of a Rational Number
1 1
The absolute value of a rational number is the quantitative value of it. 2 2

The absolute value of a rational number is the distance of the rational –1 − 1 0 1 1
number from zero on the number line, irrespective of the direction. 2 2
1 1 1
Consider the position of and – on a number line. Both are units apart from 0.
2 2 2

p p p
If is a rational number, then its absolute value is or .
q q q

Maths Talk
1 1 1
Therefore, the absolute value of = = , and the absolute How many rational
2 2 2 numbers in the lowest
1 1 1
value of − = − = . form have the same
2 2 2 absolute value? Discuss.
Representation of Rational Numbers on a Number Line

We have already learnt that like natural numbers, whole numbers and integers, we can also
represent rational numbers on a number line. To do this, we divide each unit length into equal
parts based on the denominator of the rational number. Then, we place the rational number at
the correct point on the line based on the numerator of the rational number.

In this class, let us learn to represent rational numbers with different denominators on the same
number line.

4 −3
Example 3: Represent and on the same number line.
5 4
4
Solution: We know that lies between 0 and 1. Draw a number line and divide the unit length
5
4
between 0 and 1 into 5 equal parts. Since is positive, move right from 0 by 4 steps, and mark
5
4 −3
the position of . Since is negative, divide the unit length between –1 and 0 into 4 equal parts
5 4
−3
move left from 0 by 3 steps, and mark . Think and Answer
4

Look at the number line given here and
write the rational numbers that correspond
to the points P, Q and R.
–1 −3 0 4 1 R P Q
4 5 –3 –2 –1 0 1 2
Comparison of Rational Numbers

We have learnt that, we can compare two rational numbers as follows:
• If the denominators are the same, the rational number with the greater numerator is the greater
4 −3
one. For example, to compare the rational numbers and , we compare the numerators
5 5
only. Since 4 > (–3), therefore 4 > − 3 .
5 5

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