Understanding the Ratio Problem

This problem involves understanding and solving ratios. We are given the ratio between two types of books in a library: fiction and non-fiction. We also know the exact number of fiction books and need to find the number of non-fiction books.

Ratio Definition

A ratio compares two or more quantities. The ratio of fiction books to non-fiction books is given as 4 : 3. This can be written as a fraction:

$ \frac{\text{Fiction Books}}{\text{Non-Fiction Books}} = \frac{4}{3} $

Applying the Given Information

We are told that the number of fiction books is 240. Let 'NF' represent the number of non-fiction books. We can substitute the known value into our ratio equation:

$ \frac{240}{NF} = \frac{4}{3} $

Calculating Non-Fiction Books

To find the number of non-fiction books (NF), we need to solve this equation. We can do this using cross-multiplication:

1. Multiply both sides by $NF$:

   $ 240 = \frac{4}{3} \times NF $

2. Multiply both sides by $3$:

   $ 240 \times 3 = 4 \times NF $

   $ 720 = 4 \times NF $

3. Divide both sides by $4$:

   $ NF = \frac{720}{4} $

   $ NF = 180 $

Alternatively, we can rearrange the equation $\frac{240}{NF} = \frac{4}{3}$ to solve for $NF$ directly:

$ NF = 240 \times \frac{3}{4} $

First, divide 240 by 4:

$ \frac{240}{4} = 60 $

Now, multiply the result by 3:

$ NF = 60 \times 3 $

$ NF = 180 $

Conclusion

Therefore, there are 180 non-fiction books in the school library.