To find the product of the fractions [tex]\(\frac{7}{16}\)[/tex], [tex]\(\frac{4}{3}\)[/tex], and [tex]\(\frac{1}{2}\)[/tex], we will multiply them together step-by-step.
Firstly, let's write down the fractions:
[tex]\[
\frac{7}{16}, \quad \frac{4}{3}, \quad \text{and} \quad \frac{1}{2}
\][/tex]
To multiply these fractions, we multiply the numerators together and the denominators together:
[tex]\[
\frac{7 \times 4 \times 1}{16 \times 3 \times 2}
\][/tex]
Calculate the numerator:
[tex]\[
7 \times 4 \times 1 = 28
\][/tex]
Calculate the denominator:
[tex]\[
16 \times 3 \times 2 = 96
\][/tex]
Thus the product of the fractions is:
[tex]\[
\frac{28}{96}
\][/tex]
Next, we need to simplify this fraction. The greatest common divisor (GCD) of 28 and 96 is 4. Therefore, we divide both the numerator and the denominator by 4:
[tex]\[
\frac{28 \div 4}{96 \div 4} = \frac{7}{24}
\][/tex]
So the simplified product of [tex]\(\frac{7}{16}\)[/tex], [tex]\(\frac{4}{3}\)[/tex], and [tex]\(\frac{1}{2}\)[/tex] is:
[tex]\[
\frac{7}{24}
\][/tex]
Finally, the best answer for the question is:
[tex]\[
\boxed{\frac{7}{24}}
\][/tex]
