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Chapter1 6 ½ –

Rational Numbers

Introduction Example 1. Express each one of the following
numbers in standard form:
We have already learnt about rational
36 +60
numbers in previous class. Let us revise a bit. (a) (b)
72 -96
All numbers, including whole numbers,
integers, fractions and decimal numbers, can Solution: (i) The HCF of 36 and 72 is 36.
be written in the Numerator and Denominator Dividing the numerator and denominator by
36 ¸
36
1
36
form as fractions. 36, we get: = =
72 72 ¸ 36 2
Rational number +60
(ii) The denominator of is negative. so we
A rational number is a number that can be -96
p
written in the form , where p and q are multiply and divide it by -1.
q 60 - 1 -60
integers and q ¹ 0. The denominator of a - 96 ´ - 1 = 96
rational number can never be zero. The HCF of 60 and 96 is 12. Dividing the
9 5 7 8
e.g. , , but not . numerator and denominator by 12 we get:
11 8 12 0
¸
60 -60 12 -5
A rational number is positive if its numerator = =
- 96 96 ¸12 8
and denominator are both, either positive
integers or negative integers. Comparing Rational Number
2 3 - 7 - 5
For example: , , , Rational Number can be compared in two
5 4 - 10 - 11 different ways:-
If either the numerator or the denominator of a
rational number is a negative integer, then it 1. By Representing on Number line:
is a negative rational number. Rational numbers can be compared easily
-2 3 7 5 when they are represented on a number line.
For example: , , ,
5 -4 -10 -11 Any number on a number line is greater than
any other number lying to the left of it and on
Standard Form of a Rational Number the other hand, any number on a number line
p is less than any other number lying to the right
A rational number is said to be in standard of it. This topic has been further described in
q
this chapter.
form if q is positive and the integers p and q 2 5
have no common divisor other than 1. To Example -2 Compare and .
3 3
express a given rational number into standard
form, we first convert if into a rational number Solution:
whose denominator is positive then divide the 0 2 1 5 2
3 3
numerator as well as the denominator by their
HCF. Therefore, from the above number line it
2 5
is clear that <
3 3

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Mathematics In Focus - 8