Page 21 - ICSE Math 8

= (3 × 66) + {(–6) × 42} + (8 × 22) + {(–5) × 21}
462

= 198 + (–252) + 176 + (–105) = 374 – 357 = 17
462 462 462

EXERCISE 1.4

1. In each of the following, show that a – b ≠ b – a.
−3 −2 2 1 −6 10
(a) a = , b = (b) a = , b = (c) a = , b =
5 7 −9 3 15 25
2. In each of the following, show that a – (b – c) ≠ (a – b) – c.

−2 5 −1 5 11 −9 2 −7
(a) a = , b = , c = (b) a = , b = , c = (c) a =−1, b = , c =
3 7 6 3 2 4 3 6
3. Simplify.

2  − 5  7  7  6  13 1 2  3   − 5  21 10
− 
2
0
(a) +   + (b)   ++   − (c) − +   ++   (d) −+4 −
3  9  6  9   7 21 2 3  − 4   6  16 24
− 
4. The sum of two rational numbers is −3 . If one of the numbers is −9 , find the other rational number.
5 20
−13
5. The sum of two rational numbers is –8. If one of the numbers is 7 , find the other.
−3 3
6. What should be added to to get ?
5 7
−11 −3
7. What should be subtracted from to get ?
15 15

13 27 91
8. What should be added to the sum of and to get ?
15 20 60
7 4 9
9. What should be subtracted from the sum of and to get ?
8 15 40

Multiplication of Rational Numbers
p r p r pr×
“If and (q, s ≠ 0) are two rational numbers, then their product × = .
q s q s qs
×
Productofthe numerators
Product of two rational numbers =
Productofthe denominators
−5  3 −2 −15
− 
Example 17: Multiply: (a) and   (b) and
8  7  −3 8
−5  3 ( −× −5) ( 3) 15
− 
Solution: (a) ×   = =
8  7  87 56
×
−2 −15 2 − 15  −2 −× −1( )  2
2
(b) × = ×   = = 
3
−3 8 3 8  −3 −× −1( )  3
2×−( 15) − 30 − 30 6÷ −5
= = = =
38× 24 24 6÷ 4

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