We have to express the following ratio
![(10)/(415)](https://img.qammunity.org/2023/formulas/mathematics/college/xnmn00mlp3d3iebklq49h6u78k5i1or2j6.png)
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
![\begin{gathered} (10)/(415)=(5\cdot2)/(5\cdot83) \\ (10)/(415)=(2)/(83) \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/rwdw489muahegd90qxnfxa3ywexchislbo.png)
Therefore, the simplest fraction form is
![(2)/(83)](https://img.qammunity.org/2023/formulas/mathematics/college/w5yk02vreqh9b61d4ytc7ed5ijorljgvvp.png)