Page 68 - Start Up Mathematics_7

Comparison of Rational Numbers
Case I: When one rational number is positive and the other is negative
Clearly, a positive rational number is greater than a negative rational number.

Case II: When both the rational numbers are positive
(i) Find the LCM of the denominators.

(ii) Find equivalent rational numbers with denominators equal to the LCM obtained.
(iii) Now compare their numerators. The number having greater numerator is greater.
Case III: When both the rational numbers are negative

(i) Express each rational number with positive denominator.
(ii) Find the LCM of the denominators.
(iii) Find equivalent rational numbers with denominators equal to the LCM obtained.

(iv) Now compare their numerators. The number having greater numerator is greater.
Example 7: Which is greater in each of the following:
–3 2 4 5
(a) (b)
2 3 5 7
–3 1 2 4
(c) (d) –4 –4
–12 –3 7 5

–3 2 4 5
Solution: (a) , (b) ,
2 3 5 7
Since positive rational number LCM of 5 and 7 = 35
is greater than a negative 4 4 7 28
rational number. ∴ = × = 35
5
5
7
5
5
–3 2 5 = × = 25
∴ < 35
2 3 7 7 5
–3 1 –3 –1  28 > 25
(c) , or , 4 5
12 –3 12 3 ∴ >
5
LCM of 12 and 3 = 12 2 7 4 –30 –24
–3 –3 (d) –4 , –4 or 7 , 5
5
7
=
12 12 LCM of 7 and 5 = 35
–1 –1 4 –4
= × = –30 –30 5 –150
3 3 4 12 ∴ 7 = 7 × =
5
 –3 > –4 35
7
–24 = –24 × = –168
–3 1 5 5 7 35
∴ >
2
12 –3  –150 > –168 ∴ –4 > –4 4
7 5
Example 8: Write the following rational numbers in ascending order:
–4 –2 –1 –1 –5 –4 –3 3 –3
(a) , , (b) , , (c) , ,
5 5 5 3 9 3 14 2 4

Solution: (a) –4 < –2 < –1 ( Denominators are same)
5 5 5

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