Page 59 - ICSE Math 7

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: Compare the following rational numbers.
–3 2 4 5 –3 1 2 4
(a) and (b) and (c) and (d) –4 and –4
2 3 5 7 12 –3 7 5
–3 2 4 5
Solution: (a) , (b) ,
2 3 5 7
Since positive rational number is LCM of 5 and 7 = 35
7
4
4
greater than a negative rational ∴ = × = 28
number. 5 5 7 35
–3 2 5 5 5 25
∴ 2 < 3 7 = × = 35
5
7
–3 1 –3 –1  28 > 25
(c) , or ,
4
12 –3 12 3 ∴ > 5
LCM of 12 and 3 = 12 5 7
–3 –3 2 4 –30 –24
12 = 12 (d) –4 , –4 or 7 , 5
7
5
–1 = –1 × = –4 LCM of 7 and 5 = 35
4
3 3 4 12 –30 –30 5 –150
 –3 > –4 ∴ 7 = 7 × = 35
5
–3 1 –24 –24 7 –168
∴ > = × =
12 –3 5 5 7 35
2
 –150 > –168 ∴ –4 > –4 4
5
7
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
–4 –2 –1
Solution: (a) 5 < 5 < 5 ( Denominators are same)

–1 –5 –4 –3 3 –3
(b) , , (c) , ,
3 9 3 14 2 4
LCM of 3, 9 and 3 is 9. LCM of 14, 2 and 4 is 28.
2
–1 = –1 × = –3 –3 = –3 × = –6
3
3 3 3 9 14 14 2 28
3
–5 = –5 3 = × 14 = 42
9 9 2 2 14 28
7
3
–4 = –4 × = –12 –3 = –3 × = –21
3 3 3 9 4 4 7 28
–12 –5 –3 –21 –6 42
 9 < 9 < 9  28 < 28 < 28

–4 –5 –1 –3 –3 3
∴ < < ∴ 4 < 14 < 2
3 9 3

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