Question

Find three rational numbers between 2/3 and 3/5

Answer 1

A rational number between 2/3 and 3/5 is 1/2 (2/3 + 3/5) = 1/2( [10+9]/15 ) = 1/2(19/15) = 19/30

Then, 2/3 < 19/30 < 3/5

A rational number between 2/3 and 19/30 = 1/2 {2/3 + 19/30} = 1/2 ([20+19]/30) = 1/2(39/30) = 39/60


A rational number between 19/30 and 3/5 = 1/2 {19/30 + 3/5} = 1/2 ([19+18]/30) = 1/2(37/30) = 37/60


Therefore, 2/3 < 39/60 < 19/30 < 37/60 < 3/5

Hence, 39/60, 19/30 and 37/60 are the three rational numbers lying between 2/3 and 3/5. 

Answer 2

Hence, 39/60, 19/30 and 37/60 are the three rational numbers lying between 2/3 and 3/5.