To find the product of the given fractions [tex]\( \frac{7}{16} \)[/tex], [tex]\( \frac{4}{3} \)[/tex], and [tex]\( \frac{1}{2} \)[/tex], follow these steps:
1. Write the fractions in their numerical form:
[tex]\[
\frac{7}{16}, \quad \frac{4}{3}, \quad \frac{1}{2}
\][/tex]
2. Multiply the fractions together:
[tex]\[
\frac{7}{16} \times \frac{4}{3} \times \frac{1}{2}
\][/tex]
3. Multiply the numerators and the denominators:
[tex]\[
\frac{7 \times 4 \times 1}{16 \times 3 \times 2}
\][/tex]
4. Simplify the multiplication in the numerator and the denominator:
[tex]\[
\frac{28}{96}
\][/tex]
5. Simplify the resulting fraction:
By dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 4:
[tex]\[
\frac{28 \div 4}{96 \div 4} = \frac{7}{24}
\][/tex]
Therefore, the product of the fractions [tex]\( \frac{7}{16} \)[/tex], [tex]\( \frac{4}{3} \)[/tex], and [tex]\( \frac{1}{2} \)[/tex] is [tex]\( \frac{7}{24} \)[/tex].
So, the best answer is:
D. [tex]\(\frac{7}{24}\)[/tex]
