A librarian put 39 books back on the shelves before lunch. Of the books, 13 were non-fiction. What is the ratio of the number of non-fiction books to the total number of books the librarian put away before lunch?

The number of fiction books is 39 - 13 = <<39-13=26>>26 books.

The ratio of non-fiction books to the total number of books is 13/39 = <<13/39=1/3>>1/3. Answer: \boxed{\frac{1}{3}}.

To find the ratio of non-fiction books to the total number of books put away before lunch, divide the number of non-fiction books by the total number of books and express it as a fraction.

Number of non-fiction books = 13
Total number of books put away before lunch = 39

Ratio of non-fiction books to total books = Number of non-fiction books / Total number of books
= 13 / 39

Simplifying the fraction, we get:
Ratio of non-fiction books to total books = 1/3

Therefore, the ratio of non-fiction books to the total number of books the librarian put away before lunch is 1:3.

To find the ratio of non-fiction books to the total number of books, we need to divide the number of non-fiction books by the total number of books.

In this case, the number of non-fiction books is 13 and the total number of books is 39.

So, the ratio of the number of non-fiction books to the total number of books can be calculated as follows:

Ratio = Number of non-fiction books / Total number of books
Ratio = 13 / 39

To simplify the ratio, we can divide both the numerator and denominator by their greatest common divisor, which in this case is 13.

Ratio = 1 / 3

Therefore, the ratio of non-fiction books to the total number of books is 1:3.