Page 11 - Maths Skills - 8

Rational Numbers 9

COMPARISON OF RATIONAL NUMBERS
To compare or more rational numbers, we can choose any one method out of these given below.
p r
I. Let q and s be two rational numbers.

p r p r p r p r
⇒ If ps > qr, then > , and if ps < qr, then < and if ps = qr then = .
q s q s q s q s
p r u
II. Let ,, ,..., be rational numbers.
q s v
Follow these steps to compare three or more rational numbers:

Step 1: Take LCM of the denominators q, s, v,..., etc.
Step 2: Convert all rational numbers into equivalent rational numbers with LCM as the denominator.
Step 3: The rational number with the smallest numerator, amongst all the equivalent rational numbers, is the
smallest rational number and so on. 3 9, 12, 18, 3
− − 4 − 5 − 7 2 3 3, 4, 6, 1
Let’s compare , , ,
9 12 18 3 2 1, 4, 2, 1
Find the LCM of 9, 12, 18 and 3. 2 1, 2, 1, 1
LCM = 3 × 3 × 2 × 2 = 36 1, 1, 1, 1
Convert all the rational numbers into equivalent rational numbers with 36 (LCM) as the denominator.

4 44 16 5 53 15

9 94 36 12 12 3 36
7 72 14 2 212 24

18 18 2 36 3 312 36
Compare the numerators and arrange in ascending order.

24 16 15 14 or 2 4 5 7
36 36 36 36 3 9 12 18

STANDARD FORM OF A RATIONAL NUMBER
p
Standard form or lowest form of a rational number is q where p and q have no common divisor other than 1 and

q is always positive.

12
For example, is a rational number which is not in its standard or lowest form.
− 16
12 12 ÷ 4 3
Since, 12 and 16 have a common divisor 4, = =
− 16 − 16 ÷ 4 − 4
Now, 3 and 4 have no common divisor except 1. But the denominator is negative. To write in standard form, the
denominator should be positive.

So, 3 3 ( 1) 3
4 1) 4
4 (