Question

find the rational number lies between 5/6 and11/12.

Answer 1

If you're given 3/4 and 1/3, convert them to 9/12 and 4/12. 
It should be obvious that the following fractions lie between 4/12 and 9/12: 
5/12 
6/12 = 1/2 
7/12 
8/12 = 2/3 

If the distance between them isn't big enough, you can always increase the denominator: 
Suppose you're asked to find 3 rational numbers between 1/2 and 2/3. 
Convert 1/2 and 2/3 to 3/6 and 4/6. Oops! Not enough room. 
Convert them to 4/12 and 8/12. Now you've got: 
5/12 
6/12 = 1/2 
7/12 

For decimal numbers, it really couldn't be easier. Any terminating decimal is rational so just list decimals between the two numbers: 

Answer 2

[tex] \frac{5 * 4}{6 * 4} = \frac{20}{24} , \frac{11 * 2}{12 * 2} = \frac{22}{24} [/tex]

Rational number between 22/24 and 20/24 is 21/24. If u need more than 1, try to multiply the denominator and numerator with same number then pick out the ones in between.