To express the fractions [tex]\(\frac{1}{2}\)[/tex], [tex]\(\frac{3}{16}\)[/tex], and [tex]\(\frac{7}{8}\)[/tex] with a common denominator, we need to follow these steps:
1. Identify the denominators:
- The denominators of the given fractions are 2, 16, and 8.
2. Find the Least Common Denominator (LCD):
- The LCD is the smallest number that is a multiple of all the denominators.
- In this case, we find that the smallest number that 2, 16, and 8 all divide evenly into is 16.
3. Convert each fraction to an equivalent fraction with the LCD as the new denominator:
- For [tex]\(\frac{1}{2}\)[/tex]:
- We need to find a fraction equivalent to [tex]\(\frac{1}{2}\)[/tex] that has a denominator of 16.
- Multiply both the numerator and the denominator of [tex]\(\frac{1}{2}\)[/tex] by 8: [tex]\(\frac{1 \times 8}{2 \times 8} = \frac{8}{16}\)[/tex].
- For [tex]\(\frac{3}{16}\)[/tex]:
- This fraction already has 16 as the denominator, so it remains [tex]\(\frac{3}{16}\)[/tex].
- For [tex]\(\frac{7}{8}\)[/tex]:
- We need to find a fraction equivalent to [tex]\(\frac{7}{8}\)[/tex] that has a denominator of 16.
- Multiply both the numerator and the denominator of [tex]\(\frac{7}{8}\)[/tex] by 2: [tex]\(\frac{7 \times 2}{8 \times 2} = \frac{14}{16}\)[/tex].
So, the fractions [tex]\(\frac{1}{2}\)[/tex], [tex]\(\frac{3}{16}\)[/tex], and [tex]\(\frac{7}{8}\)[/tex] expressed with the least common denominator (LCD) of 16 are:
[tex]\[
\frac{8}{16}, \frac{3}{16}, \text{ and } \frac{14}{16}
\][/tex]
Therefore, the correct answer is:
B. [tex]\(\frac{8}{16}, \frac{3}{16}, \text{ and } \frac{14}{16}\)[/tex]
