To express the fractions [tex]\( \frac{1}{2}, \frac{3}{16}, \text{and} \frac{7}{8} \)[/tex] with a common denominator, follow these steps:
1. Identify the denominators: The denominators are 2, 16, and 8.
2. Find the Least Common Denominator (LCD): The LCD of 2, 16, and 8 can be found by identifying the smallest number that all the denominators can divide evenly into. The LCD is 16.
3. Convert each fraction to the common denominator of 16:
- 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], the denominator is already 16:
[tex]\[
\frac{3}{16}
\][/tex]
- For [tex]\( \frac{7}{8} \)[/tex]:
[tex]\[
\frac{7}{8} = \frac{7 \times 2}{8 \times 2} = \frac{14}{16}
\][/tex]
4. List the fractions with the common denominator:
- [tex]\( \frac{8}{16} \)[/tex]
- [tex]\( \frac{3}{16} \)[/tex]
- [tex]\( \frac{14}{16} \)[/tex]
So the fractions [tex]\( \frac{1}{2}, \frac{3}{16}, \text{and} \frac{7}{8} \)[/tex] expressed with the Least Common Denominator of 16 are [tex]\( \frac{8}{16}, \frac{3}{16}, \text{and} \frac{14}{16} \)[/tex].
Therefore, the best answer is:
A. [tex]\( \frac{8}{16}, \frac{3}{16}, \text{and} \frac{14}{16} \)[/tex].
