A box in a college bookstore contains books, and each book in the box is a history book, an English book or a science book. If one-third of these books are history books and one-sixth are English books, what fraction of the books are science books?

what is 1-1/3-1/6?

To solve this problem, we need to use the information given about the fractions of the different types of books.

Let's assume that the total number of books in the box is represented by the variable 'x'.

We are told that one-third of these books are history books, which means (1/3)x books are history books.

We are also told that one-sixth of these books are English books, which means (1/6)x books are English books.

To find the fraction of books that are science books, we need to subtract the fractions of history books and English books from the total fraction of books.

Total fraction of books = 1 (since it represents the whole)
Fraction of history books = (1/3)x
Fraction of English books = (1/6)x

Fraction of science books = Total fraction - Fraction of history books - Fraction of English books

= 1 - (1/3)x - (1/6)x

Now, we can simplify the expression to find the fraction of science books:

= 1 - (2/6)x - (1/6)x

= 1 - (3/6)x

= 1 - (1/2)x

Therefore, the fraction of the books that are science books is (1 - (1/2)x).