Page 18 - ICSE Math 8

4. Write the name of the property that is illustrated in the following.
2 3 3 2  (−11 ) 5   5 −11  5 − ( 5 )
−  
=
(a) + = + (b)  +  +     +  + 
5 10 10 5  27 9   18   27  9 18 
2  − 2   − 2  2
(c) +   ==   + (d) 3 + 0 = 3 = 0 + 3
0
3  3   3  3
5. Fill in the blanks.
(a) The rational number which is its own additive inverse is ______________.
13
 +
+
(b)  −23   +−9( ) = _____ +  −23   (c)     −7 13   2  =(_____ )+  +  2 






 8   8    11 22   −5   22  −5 
16 16 16 3  − 3  3
0 (______
(d) + ____ = 0 + = (e) +   == ) +
31 31 31 4  4  4
Subtraction of Rational Numbers
p r r p
“If q and are two rational numbers, then subtraction of from q means addition of the additive inverse
s
s
r p p r p  r −  p r
of to q .” So, q − s = q +   s   = q + (additive inverse of ).
s
s
− −6 3
Example 9: Subtract from .
11 5
Solution: LCM of 5 and 11 = 5 × 11 = 55
−3 −×311 −33 −6 −×65 −30 5 5, 11
= = = =
×
5 511 55 11 11 × 5 55 11 1, 11
 3 −   −33  ( −30) ( −33) − −30( ) ( −333) + 30 −3 1, 1
−   6
=
−
So,       − = = =
 5   11   55  55 55 55 55
4 3 Try These
Example 10: What should be subtracted from to get ?
7 4 –7
4 3 1. What should be added to
11
4
Solution: Let a rational number x be subtracted from to get . to get ?
7 4 7
4 3 2. Find –3 – (–2).
So, −= –2
x
7 4
4 3  3 
⇒ − = x  Transposingto RHSandx to LHS 
7 4  4 
LCM of 7 and 4 = 2 × 2 × 7 = 28
2 7, 4
4 44× 16 3 37× 21
= = = = 2 7, 2
7 74× 28 4 47× 28
4 3 16 21 16 − 21 −5 7 7, 1
⇒ x = − = − = =
7 4 28 28 28 28 1, 1
−5
Example 11: 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  5 −− ( 4 ) = −5 − − ( 4 )
− 
Then (–4) + x =   ⇒ x =   {Transposing (– 4) to RHS}
 3   3  3 1
6