Question

3/4 of your books are fiction. 2/3 of those are historical fiction.
what fraction of your books is historical fiction?
answers:
3/12
1/12
5/7
1/2

Answer 1

To find the fraction of books that are historical fiction, we can follow these steps:

1. Start with the fraction of books that are fiction: \( \frac{3}{4} \).
2. Next, take \( \frac{2}{3} \) of those fiction books that are historical fiction.

So, we calculate:

\[
\text{Fraction of historical fiction} = \left( \frac{3}{4} \right) \times \left( \frac{2}{3} \right)
\]

Now perform the multiplication:

\[
= \frac{3 \times 2}{4 \times 3} = \frac{6}{12}
\]

This reduces to:

\[
\frac{6}{12} = \frac{1}{2}
\]

Therefore, the fraction of your books that is historical fiction is \( \frac{1}{2} \).

Thus, the answer is \( \frac{1}{2} \).