Question

Find five rational numbers between. (i) 2/3 and 4/5 (ii) -3/2 and 5/3 (iii) 1/4 and 1/2

Answer 1

(i) Five rational numbers between 2/3 and 4/5 The numbers 2/3 and 4/5 can be written as 30/45 and 36/45 Thus, five rational numbers are: 31/45, 32/45, 33/45, 34/45 and 35/45
(ii) Five rational numbers between -3/2 and 5/3 The numbers -3/2 and 5/3 can be written as -9/6 and 10/6 Thus, five rational numbers are: -8/6, -5/6, -2/6, 0 and 2/6

iii) Five rational numbers between 1/4 and 1/2 The numbers 1/4 and 1/2 can be written as 7/28 and 14/28 Thus, five rational numbers are: 8/28, 9/28, 10/28, 11/28 and 12/28

Answer 2

Similarly solve the rest
1.make the denominator equal
2.multiply it by (n+1) where n is no. of rationals required
3.then choose any n of them
**(Here n is 5)**