From 1/1 we know that that is still greater than 5/6, and doesn't have as a denominator, but it is still a good place to start. Each time we can take away half until we get to something with a denominator of 8, which would take 1/1 to 1/2 and 1/2 to 1/4 and 1/4 to 1/8.... 1/8 is less than 5/6 and its denominator is 8.
Answer: 1/8