To solve the problem of expressing the fractions [tex]\( \frac{1}{2}, \frac{3}{16}, \text{and} \frac{7}{8} \)[/tex] with a common denominator, we need to follow these steps:
1. Identify the Least Common Denominator (LCD):
- The denominators of the given fractions are 2, 16, and 8.
- The least common denominator (LCD) is the smallest number that all the denominators can divide into. The LCD of 2, 16, and 8 is 16.
2. Convert each fraction to an equivalent fraction with the LCD:
- For [tex]\( \frac{1}{2} \)[/tex]:
- Multiply both the numerator and denominator by the factor needed to get the LCD (16).
- [tex]\( \frac{1}{2} = \frac{1 \times 8}{2 \times 8} = \frac{8}{16} \)[/tex].
- For [tex]\( \frac{3}{16} \)[/tex]:
- The denominator is already 16, so the fraction remains the same.
- [tex]\( \frac{3}{16} \)[/tex].
- For [tex]\( \frac{7}{8} \)[/tex]:
- Multiply both the numerator and denominator by the factor needed to get the LCD (16).
- [tex]\( \frac{7}{8} = \frac{7 \times 2}{8 \times 2} = \frac{14}{16} \)[/tex].
3. Combine the equivalent fractions:
- We have converted the fractions to:
- [tex]\( \frac{1}{2} = \frac{8}{16} \)[/tex]
- [tex]\( \frac{3}{16} \)[/tex]
- [tex]\( \frac{7}{8} = \frac{14}{16} \)[/tex]
4. Select the best answer from the given options:
- Option D states [tex]\( \frac{8}{16}, \frac{3}{16}, \text{and} \frac{14}{16} \)[/tex].
Therefore, the best answer is:
[tex]\[ \boxed{8 / 16, 3 / 16, and 14 / 16} \][/tex]
So, the correct option is:
[tex]\[ \text{Option D: } \frac{8}{16}, \frac{3}{16}, \text{and} \frac{14}{16} \][/tex]
