Page 25 - Maths Skills - 8

Rational Numbers 23

Example 2: Find a rational number between – 6 and 1 .
7
Solution: A rational number between – 6 and 1 is
7

1 1 1 42 1

6

2 7 2 7
1 41 41
2 7 14
41 1
ie.., 6
14 7

− 2 3
Example 3: Find three rational numbers between and .
3 5

− 2 3
Solution: To find the first rational number between and , we need to find
3 5

1 2 3 1 10 9 1 1 1

2 3 5 2 15 2 15 30
i.e., 2 1 3
3 30 5
− − 2 1
Second rational number can be found between and
3 30

1 2 1 1 2 1 1 20 1 21

i.e.,
2 3 30 2 3 30 2 30 60
2 21 1 3
i.e.,
3 60 30 5

1 3 1 1 3 1 118 1 17 17
Third rational number between and willbe
30 5 2 30 5 2 30 2 30 60
− 3 − 2 21 −1 17
Hence, the three rational numbers between and are , and .
3 5 60 30 60

Exercise 1.3

1. Find a rational number between −1 and 1 . 2. Find a rational number between 8 and 9.
3 4
3. Find two rational numbers between 5 and 6. 4. Find five rational numbers between 1 and 1 .
3 2
5. Find 10 rational numbers between −5 and 5 . 6. Find 20 rational numbers between – 3 and 2.
8 8
7. How many rational numbers can you find between the following?

(i) – 5 and – 4 (ii) 10 and 11