Question

from a new order of books, \\(\frac{3}{8}\\) of the books will go in the adult section. of those \\(\frac{3}{8}\\) books, \\(\frac{2}{5}\\) will go in the mystery section within the adult section.

what fraction of the new books are going in the mystery section? provide your answer in the simplest form.

select one of four
\\(\frac{3}{20}\\)
\\(\frac{5}{13}\\)
\\(\frac{15}{16}\\)
\\(\frac{16}{15}\\)

Explanation:

Identify the given fractions

We are given the following:

• Fraction of books for the adult section:

$$\frac{3}{8}$$

• Fraction of those adult books for the mystery section:

$$\frac{2}{5}$$

Set up the multiplication

To find the fraction of the total books going to the mystery section, we multiply the two fractions:

$$\frac{2}{5} \times \frac{3}{8}$$

Calculate the product

Multiply the numerators and the denominators:

$$\frac{2 \times 3}{5 \times 8} = \frac{6}{40}$$

Simplify the fraction

Reduce the fraction to its simplest form by dividing both the numerator and the denominator by their greatest common divisor, which is 2:

$$\frac{6 \div 2}{40 \div 2} = \frac{3}{20}$$

Answer:

• (A) \(\frac{3}{20}\) (Correct answer)
• (B) \(\frac{5}{13}\)
• (C) \(\frac{15}{16}\)
• (D) \(\frac{16}{15}\)