Page 15 - Start Up Mathematics_8 (Non CCE)

4 3  3 
⇒ − = x  Transposingto RHSandx to LHS 
7 4  4 
LCM of 7 and 4 = 2 × 2 × 7 = 28
4 44× 16 3 37× 21 2 7, 4
= = = =
7 74× 28 4 47× 28 2 7, 2
4 3 7 7, 1
∴ − = x
7 4 1, 1
16 21 16 − 21 − 5
⇒ x = − = =
28 28 28 28
−5
Example 14: The sum of two rational numbers is . If one of the numbers is –4, find the other rational
number. 3
Solution: Let the other rational number be x.
 5
− 
Then (–4) + x =  
 3 
 5 −5 − ( ) 4
− 
4
⇒ x =   −− ( ) = − {Transposing (–4) to RHS}
 3  3 1
LCM of 3 and 1 = 3
−4 = −×43 = −12
×
1 13 3
−  
− 
So, x =  5  −−4( ) ⇒ x =  5   −12   = ( −5) − −12( ) = −+512 = 7
−


 3   3   3  3 3 3
7
The other rational number is .
3
EXERCISE 1.3
1. Subtract the first rational number from the second rational number.
−3 5 −4 5 4 2
(a) and (b) and (c) and
8 −7 21 14 5 3
2. Simplify the following.
15 6 2  9   − 6  1 5
(a) − (b) (− ) −4 (c)     (d) −
−
11 7 7  − 10   15  8 24

Properties of Subtraction of Rational Numbers
I. Closure Property
“The difference of two rational numbers is always a rational number.”
p r p r
So, if and are two rational numbers, then q − is also a rational number.
s
q
s
3  − 8  7 1
Example 15: Find: (a) −   (NCERT) (b) −
7  5  2 2
3  − 8  15 −−( 56) 15 56+ 71
Solution: (a) −   = = = which is a rational number.
7  5  35 35 35
7 1 71− 6 3
(b) − = = = 3 = which is a rational number.
2 2 2 2 1

7