Page 43 - SM inner class 7.cdr

E xercise 4.3

1. Put the cor rect sign > , < or = be tween the fol low ing pairs of ra tio nal num bers.
1 15 2 1 -1 2 -1 -4
(a) , (b) , (c) , (d) ,
2 20 - 3 6 5 -10 9 3
-2 1 5 - 1 11 - 10
(e) -1, (f) 1 , (g) , (h) ,
3 2 7 2 - 10 11
4 - 1 -4 5 4 6 -8 3
(i) , (j) , (k) , (l)
- 100 25 7 -2 9 - 7 11, -10
2. Ar range the fol low ing ra tio nal num bers in de scend ing or der.
1 2 8 1 3 1 4 1 5
(a) , , (b) , , (c) , ,
2 3 9 6 4 2 7 3 6
3. Ar range the fol low ing ra tio nal num bers in as cend ing order.
1 1 1 4 1 2 3 1 5
(a) , , (b) , , (c) , ,
2 3 4 5 10 15 8 4 6
4. Prove that :
10 æ 5 ö æ 5 ö 10 2 æ7 9 ö æ 2 ö 7 9
(a) + ç ÷ = ç ÷ + (b) - ´ ç ´ ÷ = - ´ ÷ ´
ç
11 è - 44 ø è - 44 ø 11 3 è 8 14 ø è 3 ø 8 14
1 3 æ 1 ö æ 1 3ö 1 1 æ 8 12ö æ 1 8ö æ 1 12ö
(c) + ç + ÷ = ç + ÷ + (d) ´ ç - ÷ = ç ´ ÷ - ç ´ ÷
- 2 5 è 4 ø è - 2 5 ø 4 4 è 9 15 ø è 4 9 ø è 4 15 ø
24 7 æ 14ö æ 24 7ö æ 24 14ö
(e) ´ ç + ÷ = ç ´ ÷ + ç ´ ÷
49 8 è 6 ø è 49 8 ø è 49 6 ø

5. Find three rational num bers be tween -2 and -3.
6 -5
6. Find ten ra tio nal num bers be tween and .
7 7

Summary
m Every integer p can be divided by another non-zero integer q, the number obtained is called a rational number
p
and is written symbolically as .
q
m Addition of rational numbers with:
(i) Same denominator. (ii) Different denominators.
p q p + q p r ps + rq
+ = + =
s s s q s qs
m Subtraction of rational numbers with \
(i) Same denominator. (ii) Different denominators.
p q p - q p r ps - rq
- = - =
s s s q s qs
m To find the product of two rational numbers, multiply the numerator of one rational number by the numerator
of the other. Similarly, multiply the denominators.
p r pr
´ =
q s qs

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Mathematics In Focus - 7