Select the best answer for the question.

11. Calculate the product of [tex]\frac{8}{15}, \frac{6}{5},[/tex] and [tex]\frac{1}{3}[/tex].

A. [tex]\frac{16}{75}[/tex]

B. [tex]\frac{48}{15}[/tex]

C. [tex]\frac{16}{15}[/tex]

D. [tex]\frac{48}{30}[/tex]



Answer :

To determine the product of the fractions [tex]\( \frac{8}{15}, \frac{6}{5}, \text{ and } \frac{1}{3} \)[/tex], we need to multiply the numerators together and the denominators together.

1. Multiply the numerators:

The numerators of the fractions are 8, 6, and 1.

[tex]\[ 8 \times 6 \times 1 = 48 \][/tex]

2. Multiply the denominators:

The denominators of the fractions are 15, 5, and 3.

[tex]\[ 15 \times 5 \times 3 = 225 \][/tex]

3. Combine the results:

Putting together the multiplied numerators and denominators, we get:

[tex]\[ \frac{48}{225} \][/tex]

So, the product of [tex]\(\frac{8}{15}, \frac{6}{5}, \text{ and } \frac{1}{3}\)[/tex] is [tex]\(\frac{48}{225}\)[/tex].

Since none of the provided options match [tex]\(\frac{48}{225}\)[/tex], I will assume there must be a simplification expected. Checking the individual options:

A. [tex]\( \frac{16}{75} \)[/tex] is incorrect.
B. [tex]\( \frac{48}{15} \)[/tex] is incorrect.
C. [tex]\( \frac{16}{15} \)[/tex] is incorrect.
D. [tex]\( \frac{48}{30} \)[/tex] is incorrect.

None of the given choices seem to match the correct calculation of [tex]\(\frac{48}{225}\)[/tex]. Therefore, there is an error in the provided answer choices. The correct answer based on the calculations provided here should be [tex]\(\boxed{\frac{48}{225}}\)[/tex].