To determine the product of the fractions [tex]\(\frac{7}{16}\)[/tex], [tex]\(\frac{4}{3}\)[/tex], and [tex]\(\frac{1}{2}\)[/tex], we can follow these steps:
1. Multiply the numerators:
[tex]\[
\text{Numerators: } 7 \times 4 \times 1 = 28
\][/tex]
2. Multiply the denominators:
[tex]\[
\text{Denominators: } 16 \times 3 \times 2 = 96
\][/tex]
3. Form the initial fraction:
[tex]\[
\frac{28}{96}
\][/tex]
4. Simplify the fraction:
To simplify [tex]\(\frac{28}{96}\)[/tex], we need to find the greatest common divisor (GCD) of 28 and 96. The GCD of 28 and 96 is 4.
[tex]\[
\text{GCD of 28 and 96 is } 4
\][/tex]
Now, divide both the numerator and the denominator by their GCD:
[tex]\[
\frac{28 \div 4}{96 \div 4} = \frac{7}{24}
\][/tex]
5. Conclusion:
The simplified fraction is [tex]\(\frac{7}{24}\)[/tex].
Hence, the correct answer is [tex]\(\boxed{B}\)[/tex], [tex]\(\frac{7}{24}\)[/tex].
