A library has fiction and nonfiction books. 2/5 of the library 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) +(1-2/5)(1/3) = ?
1/5
To find the fraction of all the books that are mysteries, we need to add the fraction of fiction books that are mysteries to the fraction of nonfiction books that are mysteries.
Given:
- 2/5 of the library books are fiction.
- 1/5 of the fiction books are mysteries.
- 1/3 of the nonfiction books are mysteries.
Let's calculate the fraction of all the books that are mysteries step-by-step:
Step 1: Calculate the fraction of fiction books:
Out of all the library books, 2/5 are fiction. Therefore, the fraction of fiction books is 2/5.
Step 2: Calculate the fraction of fiction books that are mysteries:
Out of the fiction books, 1/5 are mysteries. Therefore, the fraction of fiction books that are mysteries is (2/5) * (1/5) = 2/25.
Step 3: Calculate the fraction of nonfiction books:
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 is 1).
Fraction of nonfiction books = 1 - 2/5 = 3/5.
Step 4: Calculate the fraction of nonfiction books that are mysteries:
Out of the nonfiction books, 1/3 are mysteries. Therefore, the fraction of nonfiction books that are mysteries is (3/5) * (1/3) = 1/5.
Step 5: Add the fractions of fiction books that are mysteries and nonfiction books that are mysteries to find the fraction of all the books that are mysteries:
Fraction of all books that are mysteries = (2/25) + (1/5)
= (2/25) + (5/25)
= 7/25.
Therefore, the fraction of all the books that are mysteries is 7/25.
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 those fractions together.
Let's start by calculating the fraction of fiction books that are mysteries. We are told that 1/5 of the fiction books are mysteries. Since fiction books make up 2/5 of the library books, we can find the fraction of fiction books that are mysteries by multiplying these two fractions: (2/5) * (1/5) = 2/25.
Next, let's calculate the fraction of nonfiction books that are mysteries. We are told that 1/3 of the nonfiction books are mysteries. Since nonfiction books make up 3/5 of the library books (since 2/5 are fiction), we can find the fraction of nonfiction books that are mysteries by multiplying these two fractions: (3/5) * (1/3) = 3/15 = 1/5.
Now, let's add the fractions together to find the total fraction of books that are mysteries: 2/25 + 1/5.
To add these fractions, we need a common denominator, which in this case is 25. So we can rewrite 1/5 as 5/25.
Now we can add the fractions: 2/25 + 5/25 = 7/25.
Therefore, the fraction of all the books that are mysteries is 7/25.