Okay, let's go through the problem step-by-step to calculate the product of the fractions [tex]\(\frac{8}{15}\)[/tex], [tex]\(\frac{6}{5}\)[/tex], and [tex]\(\frac{1}{3}\)[/tex].
1. Write down the fractions to be multiplied:
[tex]\[
\frac{8}{15}, \quad \frac{6}{5}, \quad \frac{1}{3}
\][/tex]
2. Multiply the numerators together:
[tex]\[
8 \times 6 \times 1 = 48
\][/tex]
3. Multiply the denominators together:
[tex]\[
15 \times 5 \times 3 = 225
\][/tex]
4. Form the new fraction with the results from multiplications of numerators and denominators:
[tex]\[
\frac{48}{225}
\][/tex]
5. Simplify the fraction [tex]\(\frac{48}{225}\)[/tex] to its lowest terms:
- Find the greatest common divisor (GCD) of 48 and 225.
- The GCD of 48 and 225 is 3.
- Divide the numerator and the denominator by the GCD:
[tex]\[
\frac{48 \div 3}{225 \div 3} = \frac{16}{75}
\][/tex]
So, the simplified fraction is [tex]\(\frac{16}{75}\)[/tex].
Therefore, the correct answer is:
D. [tex]\(\frac{16}{75}\)[/tex]
