When to use worth vs worth while?

Question

I was going through this link - http://dictionary.cambridge.org/grammar/british-grammar/worth-or-worthwhile

However, I cannot find that the following sentence is wrong.

I wrote -

In conclusion, it all depends on the student whether taking a gap year is worth or not.

My teacher corrected -

In conclusion, it all depends on the student whether taking a gap year is worthwhile or not.

My question is why it is worthwhile and not worth. Here the gap year is like a noun. So, I am saying whether that noun is worth or not. For example - Do you think that buying a car (noun) is worth or not?

Answer 1

The adjective worth requires a complement: something which has worth must be worth something:

This book is worth $25.
This book is worth reading.
Reading this book is worth my time.

So "taking a gap year is worth" is ungrammatical, because there is no complement.

Worthwhile is formally an adjective, but it has the sense of worth plus the complement while, in the sense time.

Taking a gap year is worthwhile = Taking a gap year is worth the student's time.

Answer 2

Instead of "worth", you need the idiom worth it:

1) it is useful or important
2) it is rewarding despite the difficulties involved

Then you could use worth it or worthwhile:

In conclusion, it all depends on the student whether taking a gap year is worth it or not.
In conclusion, it all depends on the student whether taking a gap year is worthwhile or not.

The meaning of these is the same.