there's lot's of answers to your question, but I think you're just looking for an example of a fraction that is in between these two.
Let me give you some help here. Suppose I have 1 pizza and I cut it in 4 equal slices then if I take 1 slice I'll have 1/4 pizza. However if I cut the pizza in 8 slices and take 2 slices I'll still have 1/4 pizza.
Now suppose I have 1 pizza and I cut it in 11 equal slices then if I take 1 slice I'll have 1/11 pizza. However if I cut the pizza in 22 slices and take 2 I'll still have 1/11 pizza. Therefore we can say 1/11 = 2/22.
With similar reasoning we can also say that 1/12 = 2/24 (try to think of this pizza experiment yourself.)
So the question 1/11<...<1/12 is actually the same question as 2/22<...<2/24.
Now, I can divide a pizza in 22 slices, I can divide a pizza in 24 slices, but I could also divide it in 23 slices (Don't ask me to actually do it though, it would be very cumbersome).
Now if I have 2 slices of the pizza that is cut in 22 pieces those pieces will be bigger than 2 slices of the pizza that is cut in 23 pieces and those will again be bigger than the 2 slices of the pizza that is cut in 24 pieces.
Therefore we can state 2/22<2/23<2/24.
Now remember that we found that 1/11=2/22 and 1/12=2/24.
Hence we can also write 1/11<2/23<1/12.
And there you have an answer to your question, note however that it is not the only answer.
Suppose I cut the pizza in 44 slices and take 4 for myself I'd also have 1/11th pizza.
Similarly as above we can therefore also reason that 4/44<4/45<4/46<4/47<4/48 and therefore that
1/11<4/45<4/46<4/47<1/12 (try to follow the reasoning above and do this for yourself.)
I hope this helped