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Solution: (a) Divide both the numerator and denominator by 9 as the HCF of 27 and 144 is 9, we get
−27 9 = −3 .
÷
144 ÷ 9 16
Hence, the standard form of −27 is −3 .
144 16
(b) Divide both the numerator and denominator by 13 as the HCF of 78 and 169 is 13,
−78 13 −6
÷
we get =
−169 13 −13
÷
Here, the denominator is negative. So, multiply the numerator and denominator
by (–1), we get

6
−6 = −× − ( ) 1 = 6
−13 −13 × − ( ) 1 13 .
Hence, the standard form of −78 is 6 .
−169 13
(c) HCF of 4 and 11 = 1, and the denominator is negative.

4
So, to write the standard form of − 11 , multiply the numerator and denominator by (–1).
4 4 ×− ( 1) − 4 4 −4
\ = = . Hence, the standard form of is .
− 11 − 11 × − ( 1) 11 − 11 11

Life Skills
Three monkeys are climbing upstairs. They can only move ahead if they eat a banana with the common
factor of their numerator and denominator on it. Which of the three monkeys will be able to reach the end?
9 2 4
2 1 1
17 7 9
4 1 3

136 –112 –108
–124 224 405
Absolute Value of a Rational Number

The absolute value of a rational number is its quantative value. The symbol to show the absolute
value is two vertical lines (| |).

p p p
If is a rational number, then its absolute value is represented as or .
q q q
7 7 7 6 6 6
For example: The absolute value of + = + = and the absolute value of – = − =
8 8 8 7 7 7

p p
Thus, if is a positive rational number then its absolute value is and if it is a negative rational
q q
−p p
number i.e., then its absolute value is .
q q

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