Page 39 - SM inner class 7.cdr

7 9 -9 -13
rational number . In general for any non-zero Likewise, or is the reciprocal of ,
3 - 13 13 9
p -105 113 -113
rational number we have another non-zero and is the reciprocal of or . We
q 113 - 105 105
q q
rational number . This number is called the observe from here that if is the reciprocal of
p p
p 7 p p q
reciprocal of . The number is the reciprocal , then , is the reciprocal of . In other words,
q 3 q q p
3 p q
of . and are reciprocals of each other.
7 q p

E xercise 4.2

1. Find the ad di tive in verse and multi pli ca tive in verse of the fol low ing ra tio nal numbers.
1 -2
(a) -7 (b) 23 (c) -11 (d) (e)
3 7
-6 1 18
(f) 6 (g) 1 (h) (i) (j)
13 100 27
99 102
(k) - (l)
100 117
2. Sim plify the fol low ing.
1 æ 5ö 99 77 3 4 1 3
(a) - - ÷ (b) - + (c) + (d) -
ç
8 è 8 ø 100 100 4 3 5 20
æ 49ö 11 1 æ - 5ö 10 13 10 4
(e) 1 + - ÷ (f) 1 + (g) + ç ÷ + (h) - +
ç
è 50 ø 100 11 è 11 ø 11 23 23 23
æ 1 ö æ 1 ö 9 1 1 15 3 5 æ 17 ö 1 11 æ 22ö
(i) ç - ÷ + - ÷ + (j) + - (k) - - - - ÷ (l) + + - ÷
ç
ç
ç
è 2 ø è 5 ø 10 8 9 18 4 6 è 8 ø 11 10 è 5 ø
3. Sim plify:
8 3 50 7 121 11 5 35
(a) ´ (b) ´ (c) ¸ (d) ¸
9 4 51 10 169 13 7 40
æ 15 ö 14 111 222 3 4 16 8 2 15
(e) ç - ÷ ´ (f) ¸ (g) ¸ ´ (h) ¸ ´
è 28 ø 30 100 300 2 9 81 9 3 28
8 16 1 æ 2ö æ - 100ö 1 æ 1 ö -1 3 æ -51 ö
(i) ¸ (j) ´ - ÷ ´ ç ÷ (k) ¸ - ÷ (l) ´ ¸ ç ÷
ç
ç
125 75 5 è 5 ø è 32 ø 1000 è 100 ø 2 5 è 40 ø
Properties of Rational Numbers Consider that p and r are any two rational
The rational numbers also obey commutative, q s
associative and distributive properties like numbers, then according to the commutative
whole numbers, fractions, integers, etc. Let us property of addition, we have.
verify it with examples. p r r p
+ = +
1. Commutative Property q s s q
(i) Com mu ta tive prop erty of ra tio nal Ex am ple 10. Prove that :
num bers with re spect to ad di tion 1 2 2 1
So lu tion : + = +
2 3 3 2
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Mathematics In Focus - 7