Find ten rational numbers between - 2 5 and 1 2 .

Given, rational numbers are - 2 5 and 1 2 . Here, LCM of 5 and 2 is 10 . So, - 2 5 = - 2 5 × 2 2 = - 4 10 Also, 1 2 = 1 2 × 5 5 = 5 10 Again, - 4 10 = - 4 10 × 2 2 = - 8 20 and 5 10 = 5 10 × 2 2 = 10 20 Hence, - 2 5 = - 8 20 and 1 2 = 10 20 ∴ Ten rational numbers between - 2 5 and 1 2 are - 7 20 , - 6 20 , - 5 20 , - 4 20 , - 3 20 , - 2 20 , - 1 20 , 0 , 1 20 , 2 20 . Note: There can be numerous rational numbers between - 2 5 and 1 2 .

Find a rational number between - 1 3 and 1 2

We have to find a rational number x between two rational numbers - 1 3 and 1 2 . We know that if p and q are two rational numbers such that p < q then 1 2 p + q is a rational number between p and q . So, required number x = 1 2 - 1 3 + 1 2 LCM of 3 and 2 = 6 ⇒ x = 1 2 - 2 + 3 6 = 1 2 × 1 6 = 1 12 Hence, 1 12 is a rational number lying between - 1 3 and 1 2 .

Write ten rational numbers between - 2 5 and 1 2

- 7 2 0 , - 6 2 0 , - 5 2 0 , - 4 2 0 , - 3 2 0 , - 2 2 0 , - 1 2 0 , 1 2 0 , 2 2 0 , 3 2 0

- 7 2 0 , - 6 2 0 , - 5 2 0 , - 4 2 0 , - 3 2 0 , - 2 2 0 , - 1 2 0 , 15 2 0 , 2 2 0 , 3 2 0

- 12 5 , - 7 2 0 , - 6 2 0 , - 5 2 0 , - 4 2 0 , - 3 2 0 , - 2 2 0 , 1 2 0 , 0, 1 2 0 , 2 2 0

- 7 2 0 , - 6 2 0 , - 5 2 0 , - 4 2 0 , - 3 2 0 , - 2 2 0 , - 1 2 0 , 15 2 0 , 2 2 0 , 17 2 0

Write four rational numbers between 1 3 and 1 2

1 1 3 0 , 1 2 3 0 , 1 3 3 0 , 1 4 3 0

5 1 2 , 2 9 2 4 , 1 1 2 4 , 2 1 2 8

5 1 2 , 11 2 4 , 29 2 4 , 2 1 2 8

1 1 3 0 , 1 2 3 0 , 1 3 3 0 , 1 7 3 0

Find two rational numbers lying between - 1 3 and 1 2

We have to find two rational number between - 1 3 and 1 2 First, r ational number between - 1 3 and 1 2 = 1 2 - 1 3 + 1 2 = 1 2 - 1 × 2 + 1 × 3 6 = 1 2 - 2 + 3 6 = 1 2 1 6 = 1 12 Now, rational number between 1 12 and 1 2 = 1 2 1 12 + 1 2 = 1 2 1 × 1 + 1 × 6 12 = 1 2 1 + 6 12 = 1 2 7 12 = 7 24 Hence, required numbers are 1 12 and 7 24 .

Find five rational numbers between - 3 5 and - 1 2 .

Given, − 3 5 , − 1 2 L.C.M of 5 , 2 is 10 . − 3 × 2 5 × 2 = − 6 × 4 10 × 4 = − 24 × 2 40 × 2 = − 48 80 − 1 × 5 2 × 5 = − 5 × 4 10 × 4 = − 20 × 2 40 × 2 = − 40 80 So, the rational numbers between − 48 80 , − 40 80 are − 45 80 , − 44 80 , − 43 80 , − 42 80 , − 41 80 .

Find 10 rational numbers between - 3 4 and 5 6 .

We have to find out 10 rational numbers between - 3 4 and 5 6 . LCM of 4 and 6 is 12 . Now, - 3 4 = - 3 × 3 4 × 3 = - 9 12 and 5 6 = 5 × 2 6 × 2 = 10 12 . Rational numbers lying between - 9 12 and 10 12 are - 8 12 , - 7 12 , - 6 12 , - 5 12 , - 4 12 , - 3 12 , - 2 12 , - 1 12 , 0 12 , 1 12 , 2 12 , 3 12 , 4 12 . Out of these any 10 can be taken. Therefore, 10 rational numbers between - 3 4 and 5 6 are - 8 12 , - 7 12 , - 6 12 , - 5 12 , - 4 12 , - 3 12 , - 2 12 , - 1 12 , 0 and 1 12 .

Find ten rational numbers between 3 5 and 3 4 .

Given, numbers are 3 5 and 3 4 . LCM of 5 and 4 = 20 . So, 3 5 = 3 5 × 4 4 = 12 20 and 3 4 = 3 4 × 5 5 = 15 20 Again, 12 20 = 12 20 × 8 8 = 96 160 and 15 20 = 15 20 × 8 8 = 120 160 Hence, ten rational numbers between 3 5 and 3 4 are 97 160 , 98 160 , 99 160 , 100 160 , 101 160 , 102 160 , 103 160 , 104 160 , 105 160 , 106 160 . There can be numerous rational numbers between 3 5 and 3 4 .

Find three rational numbers between 2 3 and 3 4 .

We have to find out three rational numbers between 2 3 and 3 4 . We know that if x and y be two rational numbers such that x < y then 1 2 x + y is a rational number between x and y . A rational number between 2 3 and 3 4 is 1 2 2 3 + 3 4 = 1 2 8 + 9 12 = 17 24 . Then, 2 3 < 17 24 < 3 4 . A rational number between 2 3 and 17 24 = 1 2 2 3 + 17 24 = 1 2 16 + 17 24 = 1 2 × 33 24 = 33 48 . A rational number between 17 24 and 3 4 = 1 2 17 24 + 3 4 = 1 2 17 + 18 24 = 1 2 35 24 = 35 48 . ∴ 4 < 33 48 < 17 24 < 35 48 < 5 . Hence, required numbers are 33 48 , 17 24 and 35 48 .

Find five rational numbers between 2 3 and 4 5

4 1 6 0 , 2 1 3 0 , 2 2 3 0 , 2 3 3 0 , 4 7 6 0

4 1 6 0 , 2 1 3 0 , 2 2 3 0 , 2 3 3 0 , 4 9 6 0

4 1 6 0 , 2 1 3 0 , 2 8 3 0 , 2 3 3 0 , 4 7 6 0

4 1 6 0 , 2 1 3 0 , 2 2 3 0 , 2 5 3 0 , 4 7 6 0

Find ten rational numbers between 3 5 and 3 4

4 9 8 0 , 5 0 8 0 , 5 1 8 0 , 5 2 8 0 , 5 3 8 0 , 5 4 8 0 , 5 5 8 0 , 5 6 8 0 , 5 7 8 0 , 5 8 8 0

4 9 8 0 , 5 0 8 0 , 6 1 8 0 , 5 2 8 0 , 5 3 8 0 , 5 4 8 0 , 5 5 8 0 , 5 6 8 0 , 5 7 8 0 , 5 8 8 0

4 9 8 0 , 5 0 8 0 , 5 1 8 0 , 5 2 8 0 , 5 3 8 0 , 5 4 8 0 , 5 5 8 0 , 5 6 8 0 , 5 7 8 0 , 7 8 8 0

5 9 8 0 , 6 0 8 0 , 6 1 8 0 , 6 2 8 0 , 5 3 8 0 , 5 4 8 0 , 5 5 8 0 , 5 6 8 0 , 5 7 8 0 , 5 8 8 0

Find a rational number between 1 4 and 1 3 .

We have to find a rational number x between two rational numbers 1 4 and 1 3 . We know that if p and q are two rational numbers such that p < q then 1 2 p + q is a rational number between p and q . So, required number x = 1 2 1 4 + 1 3 LCM of 4 and 3 = 12 ⇒ x = 1 2 3 + 4 12 = 1 2 × 7 12 = 7 24 Hence, 7 24 is a rational number lying between 1 4 and 1 3 .

Find five rational numbers between. - 3 2 and 5 3 .

Given, rational numbers are - 3 2 and 5 3 . LCM of 2 and 3 is 6 . So, - 3 2 = - 3 2 × 3 3 = - 9 6 and 5 3 = 5 3 × 2 2 = 10 6 Thus, - 3 2 = - 9 6 and 5 3 = 10 6 . ∴ Five rational numbers between - 3 2 and 5 3 are - 2 6 , - 1 6 , 0 , 1 6 , 2 6 . There can be numerous rational numbers between - 3 2 and 5 3 .