To express the fractions [tex]\( \frac{1}{2}, \frac{3}{16}, \frac{7}{8} \)[/tex] with a common denominator, we need to find the least common denominator (LCD) for the fractions.
1. Identify the denominators of the fractions: [tex]\(2\)[/tex], [tex]\(16\)[/tex], and [tex]\(8\)[/tex].
2. Determine the least common multiple (LCM) of these denominators to find the LCD.
- The multiples of [tex]\(2\)[/tex] are [tex]\(2, 4, 6, 8, 10, 12, 14, 16, \ldots\)[/tex]
- The multiples of [tex]\(16\)[/tex] are [tex]\(16, 32, 48, \ldots\)[/tex]
- The multiples of [tex]\(8\)[/tex] are [tex]\(8, 16, 24, 32, \ldots\)[/tex]
The LCM of [tex]\(2\)[/tex], [tex]\(16\)[/tex], and [tex]\(8\)[/tex] is [tex]\(16\)[/tex]. Therefore, the LCD is [tex]\(16\)[/tex].
3. Convert each fraction to have the denominator of [tex]\(16\)[/tex]:
- For [tex]\( \frac{1}{2} \)[/tex]:
[tex]\[
\frac{1}{2} = \frac{1 \times 8}{2 \times 8} = \frac{8}{16}
\][/tex]
- For [tex]\( \frac{3}{16} \)[/tex]:
[tex]\[
\frac{3}{16} \text{ is already in the desired form.}
\][/tex]
- For [tex]\( \frac{7}{8} \)[/tex]:
[tex]\[
\frac{7}{8} = \frac{7 \times 2}{8 \times 2} = \frac{14}{16}
\][/tex]
So, the fractions expressed with the LCD [tex]\(16\)[/tex] are:
[tex]\[
\frac{8}{16}, \frac{3}{16}, \frac{14}{16}
\][/tex]
Thus, the correct answer is:
A. [tex]\( \frac{8}{16}, \frac{3}{16}, \frac{14}{16} \)[/tex]
