Final answer:
To find the fraction of all books that are historical fiction, multiply 23 2/3 percent (converted to 3/4) by 16 1/6 percent (converted to 1/6) to get 1/2. Hence, half of all the books are historical fiction.
Step-by-step explanation:
The question asks to find out what fraction of all your books are historical fiction if 23 2/3 percent of all your books are fiction and 16 1/6 percent of those are historical fiction. To find the fraction of all books that are historical fiction, we need to multiply the fraction representing fiction books by the fraction representing historical fiction books among the fiction books.
First, convert the percentages to fractions. 23 2/3 percent is equivalent to ⅓ or ¾, and 16 1/6 percent is equivalent to ⅗ or ⅟.
Next, multiply the fractions:
¾ (fraction of fiction books) × ⅟ (fraction of historical fiction among fiction books) = ½ (fraction of all books that are historical fiction).
Therefore, ½ of all the books are historical fiction.