A bookshop has some faction and nonfiction books. 2/5 of. The books are fiction. Of these, 1/5 are mysteries. 1/3 of the. Nonfiction books are mysteries. What fraction of all the books are mysteries?

(2/5)(1/5) + (3/5)(1/3)

Let's start solving this step by step.

We know that 2/5 of the books are fiction. Let's say there are a total of x books in the bookshop. So, the number of fiction books would be (2/5) * x.

Of the fiction books, we know that 1/5 are mysteries. So, the number of mystery fiction books would be (1/5) * (2/5) * x.

Next, we know that 1/3 of the nonfiction books are mysteries. So, the number of mystery nonfiction books would be (1/3) * (3/5) * x.

To find the fraction of all the books that are mysteries, we need to sum up the number of mystery fiction books and mystery nonfiction books, and divide it by the total number of books.

Total number of mystery books = (1/5) * (2/5) * x + (1/3) * (3/5) * x
= (2/25) * x + (3/25) * x
= (5/25) * x
= (1/5) * x

So, the fraction of all the books that are mysteries is 1/5.

To find the fraction of all the books that are mysteries, we need to determine the fraction of fiction books that are mysteries and the fraction of nonfiction books that are mysteries, and then add them together.

Let's start by finding the fraction of fiction books that are mysteries. We are given that 2/5 of the books are fiction, and out of these, 1/5 are mysteries.
So, the fraction of fiction books that are mysteries is (1/5) * (2/5) = 2/25.

Next, let's find the fraction of nonfiction books that are mysteries. We know that 1/3 of the nonfiction books are mysteries.

To calculate the fraction of nonfiction books, we need to subtract the fraction of fiction books from 1 (since the sum of fiction and nonfiction books should be equal to 1).
The fraction of nonfiction books is 1 - 2/5 = 5/5 - 2/5 = 3/5.

Now we can find the fraction of nonfiction books that are mysteries by multiplying the fraction of all nonfiction books by the fraction of nonfiction books that are mysteries.
The fraction of nonfiction books that are mysteries is (1/3) * (3/5) = 3/15 = 1/5.

Finally, we can add the fraction of fiction books that are mysteries to the fraction of nonfiction books that are mysteries to find the fraction of all the books that are mysteries:
2/25 + 1/5 = 2/25 + 5/25 = 7/25.

Therefore, the fraction of all the books in the bookshop that are mysteries is 7/25.