Page 36 - SM inner class 7.cdr

Operations on Rational Numbers p r
(v) If and are any two rational
In this section, we perform operation of addition, q s
subtraction, multiplication and division on numbers, where q ¹ 0, whose
rational numbers. denominators are different, then we
can add them by the following
1. Addition of Rational Numbers
formula.
p q
(a) If and are any two rational numbers p r ps + rq
s s + =
with the same denominators, then we q s qs
shall add them as given below. Ex am ple 3. Find the sum of the following
p q p + q ra tio nal num bers.
+ =
1
s s s (i) - 6 + 7 (ii)1 + 5 + 1
Ex am ple 2. Sim plify the fol low ing ra tio nal 5 12 3 2 4
num bers. So lu tion :
2 1 6 7
(i) + (i) - +
3 3 5 12
1 2 4 -72 + 35 37
(ii) - + + = = -
7 7 7 60 60
11 8 æ 14 ö 1 5 1
(iii) + + - ÷ (ii) 1 + +
ç
15 15 è 15 ø 3 2 4
a c 4 5 1
(iv) + = + +
b b 3 2 4
16 + 30 + 3 49 1
So lu tion : = = = 4
2 1 12 12 12
(i) +
3 3 2. Subtraction of Rational Numbers
2 + 1 (a) Consider two rational numbers with
=
3 the same denominators. The difference
3 p q
= =1 - is as under :
3 s s
-
1 2 4 p q p q
(ii) - + + - =
7 7 7 s s s
- + 2 + 4 Ex am ple 4. Sim plify the fol low ing.
1
=
7 1 2 8 1 æ - 4 ö
÷
5 (i) 5 - 5 (ii) 9 - 9 - ç è 9 ø
=
7
So lu tion :
11 8 æ - 14 ö
(iii) + + ç ÷ (i) 1 - 2
15 15 è 15 ø 5 5
-
11 + 8 14 1 - 2 1
= = = -
15 5 5
5 1 8 1 -
æ
= = (ii) - - ç 4 ö
÷
15 3 9 9 è 9 ø
a c
(iv) + = 8 - 1 + 4
b b 9 9 9
a + c
1
= 8 - + 4 11 2
b = = =1
9 9 9

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Mathematics In Focus - 7