Question

When n is divided by 14, the remainder is 9. what is the remainder when n is divided by 7?

Answer 1

If
`n\equiv9\mod14`, then there is some integer
`k` for which
`n=k+\frac9{14}` where
`k` would be a multiple of 14, i.e.
`k\equiv0\mod14`.

Because
`k` is a multiple of 14, it's also a multiple of 7, so
`k\equiv0\mod7`.

This then means that
`n\equiv9\equiv2\mod7`, so the remainder upon dividing by 7 is 2.