To find the product of the fractions [tex]\(\frac{8}{15}\)[/tex], [tex]\(\frac{6}{5}\)[/tex], and [tex]\(\frac{1}{3}\)[/tex], we will multiply the fractions together step by step.
First, let’s recall the process for multiplying fractions:
[tex]\[
\frac{a}{b} \times \frac{c}{d} \times \frac{e}{f} = \frac{a \times c \times e}{b \times d \times f}
\][/tex]
Now, apply this to our fractions:
[tex]\[
\frac{8}{15} \times \frac{6}{5} \times \frac{1}{3}
\][/tex]
Multiply the numerators together:
[tex]\[
8 \times 6 \times 1 = 48
\][/tex]
Next, multiply the denominators together:
[tex]\[
15 \times 5 \times 3 = 225
\][/tex]
This gives us the fraction:
[tex]\[
\frac{48}{225}
\][/tex]
To simplify [tex]\(\frac{48}{225}\)[/tex], we need to find the greatest common divisor (GCD) of 48 and 225. The GCD of 48 and 225 is 3. Divide both the numerator and the denominator by their GCD:
[tex]\[
\frac{48 \div 3}{225 \div 3} = \frac{16}{75}
\][/tex]
Therefore, the simplified product of [tex]\(\frac{8}{15}\)[/tex], [tex]\(\frac{6}{5}\)[/tex], and [tex]\(\frac{1}{3}\)[/tex] is:
[tex]\[
\frac{16}{75}
\][/tex]
Hence, the correct answer is:
A. [tex]\(\frac{16}{75}\)[/tex]
