To solve the problem of calculating the product of the fractions [tex]\( \frac{8}{15}, \frac{6}{5}, \)[/tex] and [tex]\( \frac{1}{3} \)[/tex], we can follow these steps:
1. Multiply the Numerators:
- Multiply the numerators of the fractions together: [tex]\( 8 \times 6 \times 1 = 48 \)[/tex].
2. Multiply the Denominators:
- Multiply the denominators of the fractions together: [tex]\( 15 \times 5 \times 3 = 225 \)[/tex].
3. Form the Product of the Fractions:
- Combine the results from steps 1 and 2 into a single fraction:
[tex]\[ \frac{48}{225} \][/tex]
4. Simplify the Fraction:
- Determine the greatest common divisor (GCD) of the numerator (48) and the denominator (225). By simplifying the fraction:
- 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]
After simplifying, the final answer is [tex]\(\frac{16}{75}\)[/tex].
Thus, the correct choice is:
C. [tex]\(\frac{16}{75}\)[/tex]
