Page 16 - SM inner class 8.cdr

The numbers q q, lie to the left of q .
2 3 1 Second Method :
Similarly, q q, are the rational numbers
4 5
between ‘a’ and ‘b’ lie to the right of q as Let ‘a’ and ‘b’ be two rational numbers.
1
follows: (i) Convert the denominator of both the
q 1 q 4
a b fractions into the same denominator by
q q q taking LCM. Now, if there is a number
1 4 5
a b between numerators there is a rational
1
b
q = (q + ) number between them.
4 1
2 (ii) If there is no number between their
1
b
q = (q + ) and so on. numerators, then multiply their
5 4
2
numerators and denominators by 10 to
Example 18. Find two rational numbers get rational numbers between them.
-3 1
between and . To get more rational numbers, multiply
5 2
by 100, 1000 and so on.
-3 1
Solution: Given: a = , b = So, we conclude that there are countless
5 2
rational numbers between any two
Let q and q be two rational numbers.
1 2 rational numbers.
1
b
q = (a + ) Example 19. Find nine rational numbers
1
2
between 3/4 and 4/5.
1 æ -3 1 ö
q = ´ ç + ÷ 3 4
1 Solution: a = , b =
2 è 5 2 ø
4 5
- + ö
1 æ 6 5 1 æ - ö 1 -1 3 5 15 4 4 16
= ´ ç ÷ = ´ ç ÷ = We can write a and b as ´ = and ´ =
2 è 10 ø 2 è10 ø 20 4 4 20 5 4 20
1 15
q = (a + q ) To find a rational number between and
2 1
2 20
- öö
1 æ -3 æ 1 16
= ´ ç + ç ÷÷ , we have to multiply the numerator and
2 è 5 è20 øø 20
denominator by 10.
(
1 æ -12 + - ö
1)
= ´ ç ÷ 15 10 150
2 è 20 ø ´ =
20 10 200
- ö
1 æ -12 1 16 10 160
= ´ ç ÷ ´ =
2 è 20 ø 20 10 200
1 æ -13 ö -13 150 160
= ´ ç ÷ = \ The rational numbers between and
2 è 20 ø 40 200 200
151 152 153 154 155 156 157 158
-1 -13 are , , , , , , ,
The two rational numbers are and . 200 200 200 200 200 200 200 200
20 40 159
and .
200

16
Mathematics In Focus - 8