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\ 06-Jan-2025 Bharat Arora Proof-7 Reader’s Sign _______________________ Date __________

• If the denominators are different, rewrite the rational numbers with a common denominator
by taking the LCM of the denominators, and then compare the numerators. For example, to
7 5
compare and , we first take the LCM of 24 and 16, that is 48. Now, we will rewrite the
24 16
given rational numbers with denominator 48 as:

7 = 72 = 14 , 5 = 53 = 15 . Since 15 > 14, therefore, 14 < 15 , and hence 7 < 5 .
×
×
24 24 2 48 16 16 3 48 48 48 24 16
×
×
• To compare two negative rational numbers, compare them ignoring their signs and then reverse
the order. For example, to compare −7 and −5 , we first compare 7 and 5 as compared in
24 16 24 16
the previous example and then reverse the order. So, −7 > −5 .
24 16
• A positive rational number is always greater than a negative rational number. For example,
1 > − 7 .
2 24
Comparison of Rational Numbers by Cross-multiplication Method

To compare two rational numbers, we can also use the cross-multiplication method. For example,
−4 −3 −4 −3
to compare and , cross multiply
5 7 5 7
(–4) × 7 = – 28 and (–3) × 5 = –15

Since, – 28 < – 15. So, −4 < −3 .
5 7
Comparison of Rational Numbers using Number Line

For any two rational numbers represented on a
number line, the rational number on the left is –1 −3 −2 −1 0 1 2 3 4 1
smaller than the rational number on its right. For 4 4 4 5 5 5 5
1 2 3 4
example, look at the rational numbers –1, −3 , −2 , −1 , 0, ,, , and 1 represented on the same
number line. 4 4 4 5 5 5 5

Comparing them, we have: –1 < −3 , −3 < −2 , −2 < −1 , …
4 4 4 4 4
−2 −3
Example 4: Compare and using a number line.
3 4

Solution: Here, LCM of 3 and 4 is 12. So, −2 = −×24 = −8 and −3 = −×33 = −9 .
×
×
3 34 12 4 43 12
Plot these rational numbers on the number line as shown below.
–1 Q P 1

−12 −9 −8 0
12 12 12

Point P  −  8   is right of point Q  −  9  . So, −9 < −8 ⇒ −3 < −2 .



4
3
 12
12
 12
12
11 Rational Numbers