To solve the problem of multiplying the fractions [tex]\(\frac{5}{8}\)[/tex] and [tex]\(\frac{3}{5}\)[/tex], and then simplifying the result, we follow these steps:
1. Multiply the fractions:
To multiply two fractions, multiply the numerators together and then multiply the denominators together.
[tex]\[
\frac{5}{8} \cdot \frac{3}{5} = \frac{5 \times 3}{8 \times 5} = \frac{15}{40}
\][/tex]
2. Simplify the fraction [tex]\(\frac{15}{40}\)[/tex]:
To simplify a fraction, we look for the greatest common divisor (GCD) of the numerator and the denominator and then divide both by this number.
The GCD of 15 and 40 is 5.
[tex]\[
\frac{15 \div 5}{40 \div 5} = \frac{3}{8}
\][/tex]
3. Match the simplified answer with the given choices:
The choices provided are:
- [tex]\(1 \frac{9}{40}\)[/tex]
- [tex]\(\frac{3}{8}\)[/tex]
- [tex]\(\frac{8}{13}\)[/tex]
- [tex]\(\frac{15}{40}\)[/tex]
From our simplified result, [tex]\(\frac{3}{8}\)[/tex], we see that it matches the second choice.
Therefore, the simplified answer to the problem of multiplying [tex]\(\frac{5}{8}\)[/tex] and [tex]\(\frac{3}{5}\)[/tex] is [tex]\(\frac{3}{8}\)[/tex], which corresponds to the second choice provided.
