Choosing the index with the strictest constraint and solving the simplex algorithm

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Could someone provide an intuitive explanation as to why we choose our pivot element in the simplex algorithm to be the element whose index $\frac {b_i}{a_{ik}}$ is smallest?

EDIT: $a_{ik}$ is the coefficient for the non-basic variables and $b_i$ is the value for the $i^{th}$ constraint

After we have identified the 'Key column' from the objective function we must decide on the index and this calculation comes into place. Could someone explain why the minimum in this calculation is the deciding factor please.

What is the intuitive reason for doing so?

Thanks,

IS