Page 63 - Maths Skills - 7

Rational Numbers 61

Example 4: Express each of the following rational numbers in standard form.

− 28 60
(i) (ii)
− 42 − 225

Solution: (i) The denominator of the rational number − 28 is negative.
− 42
We first make it positive by multiplying both numerator and denominator with (–1).
− 28 − 28 × −1( ) 28
Thus, = =
− 42 − 42 × −1( ) 42 The H.C.F. of 28 and 42 is 14.
28 28 14÷ 2
So, = = .
42 42 14÷ 3
60
(ii) The denominator of the rational number − 225 is negative.

Multiply both numerator and denominator by (– 1) to make it positive.

60 60 ×−( 1) − 60
Thus, = =
− 225 − 225× −( 1) 225 The H.C.F. of 60 and 225 is 15.

÷
So, − 60 = − 60 15 = − 4 .
225 225 ÷ 15 15
Example 5: Are the following rational numbers equivalent?

− 7 14 5 − 15
(i) , (ii) ,
8 −16 − 3 18

Solution: (i) – 7 × (– 16) = 112 ; 8 × 14 = 112 (ii) 5 × 18 = 90; (– 3) × (– 15) = 45

Since, – 7 × (– 16) = 8 × 14 = 112. Since 5 × 18 ≠ (– 3) × (– 15).

− 7 14 So, 5 ≠ − 15 .
So, = . − 3 18
8 −16

− 8 x x − 8
Example 6: Find the value of x, such that: (i) = (ii) =
20 5 13 39
− 8 x x − 8
Solution: (i) = (ii) =
20 5 13 39

⇒ – 8 × 5 = x × 20 ⇒ x × 39 = – 8 × 13
−×85 −×813 − 8
⇒ x = =− 2 ⇒ x = =

20 39 3

Exercise 4.1

1. Write the numerator and the denominator of each of the following rational numbers.
−148 7 −3 2
(i) (ii) (iii) (iv)
−249 13 13 − 29