Sure! Let's calculate the product of the fractions [tex]\(\frac{8}{15}\)[/tex], [tex]\(\frac{6}{5}\)[/tex], and [tex]\(\frac{1}{3}\)[/tex] step by step.
First, let's write down each of the fractions:
[tex]\[
\frac{8}{15}, \quad \frac{6}{5}, \quad \frac{1}{3}
\][/tex]
Now, to find the product of these fractions, we need to multiply the numerators together and the denominators together.
Step 1: Multiplying the numerators:
[tex]\[
8 \times 6 \times 1 = 48
\][/tex]
Step 2: Multiplying the denominators:
[tex]\[
15 \times 5 \times 3 = 225
\][/tex]
Step 3: Putting the results together, we get:
[tex]\[
\frac{48}{225}
\][/tex]
Now, let's simplify the fraction [tex]\(\frac{48}{225}\)[/tex].
To simplify, we look for the greatest common divisor (GCD) of 48 and 225.
Dividing the numerator and the denominator by their GCD (which is 3), we get:
[tex]\[
\frac{48 \div 3}{225 \div 3} = \frac{16}{75}
\][/tex]
Therefore, the simplified product of the fractions [tex]\(\frac{8}{15}\)[/tex], [tex]\(\frac{6}{5}\)[/tex], and [tex]\(\frac{1}{3}\)[/tex] is:
[tex]\[
\frac{16}{75}
\][/tex]
So, the correct answer is:
[tex]\[
\boxed{\frac{16}{75}}
\][/tex]
Thus, the correct choice from the given options is:
C. [tex]\(\frac{16}{75}\)[/tex]
