We have to express the following ratio
[tex]\frac{10}{415}[/tex]in simplest form.
We can see that the factors of 10 are: 1,2,5,10.
And the factors of 415 are: 1,5,83,415.
Then the greatest common factor is 5. This imply that our fraction can be written as
[tex]\begin{gathered} \frac{10}{415}=\frac{5\cdot2}{5\cdot83} \\ \frac{10}{415}=\frac{2}{83} \end{gathered}[/tex]Therefore, the simplest fraction form is
[tex]\frac{2}{83}[/tex]