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Step 4: The rational number having greater numerator will be greater.
3 2
Let us compare and .
4 3
Here, LCM of 4 and 3 is 12. FACTS
(i) Every positive rational number is
Write the equivalent rational numbers of the given rational greater than 0 and also greater
numbers with denominator 12. than every negative rational number.
×
×
3 33 − 9 24 − 8 (ii) Every negative rational number is
Therefore, = = and =
×
4 43 12 34 12 less than 0.
×
Q –9 < –8
−9 −8 −3 −2
\ < ⇒ <
12 12 4 3
We can also use a number line to compare rational numbers as shown below:

 8   9  –1 Q P 1
The point P −  is right of the point Q −  .




 12
 12
–12 –9 –8 0
9 8 3 2 12 12 12
So, − < − ⇒ − < − .
12 12 4 3
Clearly, when two rational numbers have the same denominator, then the rational number with
greater numerator will be greater.
Example 5: Which is greater?
−7 12 −3 5
(a) or (b) or
23 −23 16 − 9
12
Solution: (a) Write the rational number into its standard form by converting the negative
− 23
12 − 1 − 12
denominator into positive. So, × =
− 23 − 1 23
−7 −12
Now, in and , since –7 > –12
23 23
−7 −12
Hence, >
23 23

(b) Write the rational number − 5 into its standard form by multiplying it (–1)
5 ×− ( 1) − 5 9
i.e., =
9 (
−× − 1) 9
Now, LCM of 16 and 9 is 144.

−3 −×39 −27 −5 −×516 −80

\ = = and = =
16 16 × 9 144 9 916 144
×
−27 −80
Clearly, –27 > –80 ⇒ >
−3 5 144 144
Thus, >
16 − 9

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