An infinite amount of fraction can come between 1/6 and 1/5. For example, we know that 1/6 = 10/60 and 1/5 = 12/60, so a fraction between them would be 11/60.
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it's 1/4 if you want the fraction exactly half way between them.
2/11ths is exactly between 1/5th and 1/6th. There are an infinite number of alternate answers to choose from, should you wish.
1/6
6/12 ÷ 5/6 = 3/5
5/6