Question

When a fraction of 17 is taken away from 17 , what remains exceeds one-third of seventeen by six.

Answer 1

The fraction is less than
`(17)/(18)`.

Explanation:

Let the fraction is
`(1)/(n)`.

Given that when the fraction of 17 is subtracted from 17 itself, then the remaining will be greater than one-third of 17 divided by six.

Therefore, by the given condition,

`17 - (17)/(n) > (1)/(3)((17)/(6) )`

⇒
`17 - (17)/(n) > (17)/(18)`

⇒
`1 - (1)/(n) > (1)/(18)`

⇒
`(1)/(n) < 1 - (1)/(18)`

⇒
`(1)/(n) < (17)/(18)`

Therefore, the fraction is less than
`(17)/(18)`. (Answer)