There is one repeating digit, so we effectively multiply and divide by 10^1 -1 = 9. (The exponent of 10 here is the number of repeating digits.)
[tex]10 \times 3.1\overline{6} - 3.1\overline{6} = 31.6\overline{6} -3.1\overline{6} = 28.5 = 9 \times 3.1\overline{6}[/tex]
Then you have
[tex]3.1\overline{6} = \dfrac{28.5}{9} = \dfrac{285}{90} = \dfrac{19}{6}[/tex]
The equivalent fraction is 19/6.
