Page 12 - Start Up Mathematics_8 (Non CCE)

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 −6 8 2 + − ( 4)
(a) + (b) + (c) + (d)
− 3 4 7 −5 5 3 3
5 2 4 13 4 3
(e) + (f) −+7 (g) + 6 (h) +
12 9 13 − 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
I. Closure Property
“The sum of two rational numbers is always a rational number.”

p r  p r 
So, if q and are two rational numbers, then   q + s   is also a rational number.
s
Example 6: 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

II. Commutative Property
“Two rational numbers can be added in any order.”
p r p r r p
So, if q and (q, s ≠ 0) are two rational numbers, then q + s = s + q .
s
Example 7: Show that:
3 2 2 3 (−6 ) (−8 ) (−8 ) (−6 )
(a) + = + (b) + = + (NCERT)
4 5 5 4 5 3 3 5

3 2 15 8+ 23 2 3 815+ 23
Solution: (a) + = = and + = =
4 5 20 20 5 4 20 20
3 2 2 3
So, + = +
4 5 5 4
(−6 ) (−8 ) (−18 ) (+ −40 ) −58 (−8 ) (−6 ) (−40 ) (+ −18 ) − 58
(b) + = = and + = =
5 3 15 15 3 5 155 15
(−6 ) (−8 ) (−8 ) (−6 )
So, + = +
5 3 3 5
III. Associative Property
“Three rational numbers can be added in any order.”

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