Question

insert two rational between 1/3 and 1/4

Answer 1

taking lcm first 
lcm =12
so we has to find rational no. between 4/12 and 3/12
multiply both no. with 10/10 (for more possible out comes)
so now the new 2 no. will be= 40/120 &30/120
so 2 rational no. are 31/120,32/120.

Answer 2

First of all take out the LCM of 3 & 4........ LCM = 12.......... Now make the denominators of both the fractions = 12.............. 1/3 ×4/4 =4/12........... 1/4×3/3= 3/12............... Now multiply both these fractions with any but same no., suppose 3.( as u want only 2 numbers ).......... 4/12×3/3= 12/36............. 3/12×3/3= 9/36.................... Now two rational numbers between 9/36 &12/36 or between. 3/12 & 4/12 or between 1/3 & 1/4 are ======> 10/36 and 11/36..............