Page 68 - Maths Skills - 7

66 Maths

− 5 2 11
Example 5: Arrange the rational numbers , and in ascending order.
7 − −15 3
2 2 ×−( 1) − 2
Solution: First, express the given rational numbers with positive denominators = =
− 15 − 15× −( 1) 15
11 11×−( 1) − 11
= = Now, LCM of 7, 15 and 3 is 105.
− 3 −× − 1) 3
3 (
Expressing, each rational number with the LCM as common denominator, we get
− 5 515 − 75 − 2 −×27 −14 −11 −11 35 − 385
×
×
= = ; = = ; = =
×
×
7 715 105 15 15 × 7 105 3 335 105
On comparing the numerators of the obtained rational numbers, we have – 385 < – 75 < – 14.
Therefore, − 385 < − 75 < −14 or 11 < − 5 < 2 .
105 105 105 − 3 7 −15

Example 6: Find seven rational numbers between – 3 and – 2.
−3 − 2
Solution: – 3 = and – 2 =
1 1
Multiplying both by 10
−×310 = −30 and − ×210 = − 20
×
×
110 10 110 10
− −21 −22 −23 −24 −25 26 −27
Hence, the required seven rational numbers are , , , , , , .
10 10 10 10 10 10 10

− − 4 2
Example 7: Find five rational numbers between and .
7 3
Solution: LCM of 7 and 3 is 21
−×43 = −12 and − ×27 = −14
×
×
73 21 37 21
Multiplying by 10, we get

−12 ×10 = −120 and −14 ×10 = −140
21 ×10 210 21 ×10 210
− −121 −122 −123 124 −125
Hence, the required five rational numbers are , , , , .
210 210 210 210 210

Exercise 4.2

1. Draw the number line and represent the following rational numbers on it.
5 − 3 2 13 23
(i) (ii) (iii) (iv) (v) − 4
7 8 5 3
2. In each of the following pairs of rational numbers, find the greater one.

8 − 21 7 4 − 5 8 7 − 5
(i) − , 0 (ii) , (iii) 0 , (iv) , (v) ,
7 35 8 7 13 − 3 19 38