1. **State the problem:** In the library, the number of fiction books is $\frac{2}{5}$ the number of nonfiction books. The total number of books is 56. We need to find how many books are fiction books. 2. **Set variables:** Let $x$ be the number of nonfiction books. Then the number of fiction books is $\frac{2}{5}x$. 3. **Write the total books equation:** $$x + \frac{2}{5}x = 56$$ 4. **Combine like terms:** $$\frac{5}{5}x + \frac{2}{5}x = 56$$ $$\frac{7}{5}x = 56$$ 5. **Solve for $x$:** Multiply both sides by $\cancel{\frac{5}{7}} \times \frac{7}{5}$ to isolate $x$: $$x = 56 \times \frac{5}{7}$$ 6. **Calculate $x$:** $$x = 56 \times \frac{5}{7} = 8 \times 5 = 40$$ So, there are 40 nonfiction books. 7. **Find fiction books:** $$\text{Fiction books} = \frac{2}{5} \times 40 = 16$$ **Answer:** There are 16 fiction books in the library.