Page 37 - SM inner class 7.cdr

(b) Consider two rational numbers (iii) 7
p r 4
, with different denominators. The
q s So lu tion :
p r
difference - is as under :— (i) To find the additive inverse of 3,
q s
change its sign.
-
p r ps rq
- = Additive inverse of 3 is - 3
q s qs
-
Check : 3 + - 3 = 3 3 = 0
(
)
Ex am ple 5. Sim plify : (ii) To find the additive inverse of
4 æ 2ö 5 3 æ 1ö -1
(i) - - ÷ (ii) - - - ÷ change its sign.
ç
ç
3 è 9 ø 2 4 è 8 ø 2
-1 1
So lu tion : Additive inverse of is
4 æ 2ö 2 2
(i) - - ÷ -1 1 1 + 1 0
ç
3 è 9 ø Check : + = - = = 0
4 2 2 2 2 2
= + 7
3 9 (iii) To find the additive inverse of ,
12 + 2 14 5 4
= = =1 change its sign.
9 9 9
7 -7
5 3 æ 1ö Additive inverse of is
(ii) - - - ÷ 4 4
ç
2 4 è 8 ø
5 3 1 3. Multiplication of Rational Numbers
= - +
2 4 8 We can find the product of two or more rational
20 - 6 + 1 15 7 numbers by the given rule.
= = =1
8 8 8 Rule: Mul ti ply the nu mer a tor of one ra tio nal
num ber by the nu mer a tor of the other ra tio nal
Additive Inverse
num ber. Sim i larly, mul ti ply the de nom i na tors
p - p
Consider that and are any two rational of both ra tio nal numbers, i e. .
q q p r pr
numbers, then we can add them by the q ´ s = qs
following method.
Ex am ple 7. Find the prod uct of the fol low ing
p æ - pö
+ ç ÷ = 0 ra tio nal num bers.
q è q ø 2 11 1 - 2ö - 5ö
(i) ´ (ii) ´ ç æ ÷ ´ ç æ ÷
We can examine that the sum of these two rational 5 12 4 è 3 ø è 2 ø
p - p
numbers is zero. Hence, two and rational So lu tion :
q q
2 11
numbers are called additive inverse of each other (i) ´
and 0 is known as ad di tive iden tity. 5 12
1 1 -5 = 2 ´11 = 22 = 11
For ex am ple : and 3 , and -3 and and 5 ´12 60 30
2 - 2 11
5 1 æ 2ö æ 5ö
etc. all are ad di tive in verse of each other. (ii) ´ - ÷ ´ - ÷
ç
ç
11 4 è 3 ø è 2 ø
(
(
Ex am ple 6. Write the ad di tive in verse of the 1 ´ -2) ´ -5) 10 5
fol low ing ra tio nal num bers. = 4 ´ 3 ´ 2 = 24 = 12
1
(i) 3 (ii) -
2

37
Mathematics In Focus - 7