Page 16 - ICSE Math 8

EXERCISE 1.1

3 6 7 11 −2 23
1. Add: (a) and (b) and (c) and
7 7 − 25 − 25 16 16
2. Simplify.
1 3 −5 4 2 4
(a) + (b) + (c) + − ( 4) (d) −+7
− 3 4 7 −5 3 13
13 4 3
(e) + 6 (f) +
− 8 − 15 − 25
3. Find the following sums and express your answer as mixed fraction.
27 25  − 11 18 62 9 − ( 46)
(a) + 15 (b) +   (c) + (d) +
20 4  4  − 5 4 10 5

Properties of Addition of Rational Numbers
p r
I. Closure Property: “The sum of two rational numbers is always a rational number.” Thus, if q and are
s
 p r 
two rational numbers, then   q + s   is also a rational number.

Example 4: Show that the sum of the following rational numbers is again a rational number.
2 3 ()−1 (−2 )
(a) + (b) +
7 5 2 3
2 3 10 + 21 31
Solution: (a) + = = is a rational number.
7 5 35 35
()−1 (−2 ) (−3 ) + (−4 ) −7
(b) + = = is a rational number.
2 3 6 6
Thus, rational numbers are closed under addition.
p r
II. Commutative Property: “Two rational numbers can be added in any order.” Thus, if q and (q, s ≠ 0)
s
p r r p
are two rational numbers, then + = + .
q s s q
(−6 ) (−8 ) (−8 ) (−6 )
Example 5: Show that + = + .
5 3 3 5
(−6 ) (−8 ) (−18 ) (+ −40 ) −58 (−8 ) (−6 ) (−40 ) (+ −18 ) −58
Solution: + = = and + = =
5 3 15 15 3 5 155 15
(6)−− (8)−− −− ( 8) (6)−−
So, ++ == ++
5 3 3 5
Thus, addition is commutative for rational numbers.
p r u
III. Associative Property: “Three rational numbers can be added in any order.” Thus, if q s v
, and are three
 p r u p r  u
rational numbers, then   q + s  + v = q +   s + v   .


3
3
− 
− 
Example 6: Show that  −  1  +  +  4  =     −  1  +  +  4  .



 2   7  3    2  7   3 
(
9
3
−   1
 =
Solution:  −  1  +  +  4  =  −   +  +−28)    −1  +   −19   = ( −21) + −38( ) = −−59


 2   7  3   2   21   2   21  42 42
6
  −  1 3   4 ( −7) +   4 −1  4 ( −3) + −56( ) −59
− 
− 
−  
=
and    +  +   =   +     +   = =
  2  7   3   14   3   14   3  42 42
4