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 follow these steps:
1. First, multiply the numerators together:
[tex]\[
7 \times 4 \times 1 = 28
\][/tex]
2. Next, multiply the denominators together:
[tex]\[
16 \times 3 \times 2 = 96
\][/tex]
3. Now, we have:
[tex]\[
\frac{28}{96}
\][/tex]
4. To simplify this fraction, find the greatest common divisor (GCD) of 28 and 96. Here, the GCD is 4.
5. Divide both the numerator and the denominator by their GCD:
[tex]\[
\frac{28 \div 4}{96 \div 4} = \frac{7}{24}
\][/tex]
Therefore, the product of [tex]\(\frac{7}{16}\)[/tex], [tex]\(\frac{4}{3}\)[/tex], and [tex]\(\frac{1}{2}\)[/tex] is [tex]\(\frac{7}{24}\)[/tex].
The best answer choice is:
A. [tex]\(\frac{7}{24}\)[/tex]
