To express the fractions [tex]\( \frac{1}{2} \)[/tex], [tex]\( \frac{3}{16} \)[/tex], and [tex]\( \frac{7}{8} \)[/tex] with a least common denominator (LCD), follow these steps:
1. Find the least common denominator (LCD):
- The denominators of the given fractions are 2, 16, and 8.
- The least common multiple (LCM) of 2, 16, and 8 is 16.
- Thus, the LCD is 16.
2. Convert each fraction to have the LCD:
- For [tex]\( \frac{1}{2} \)[/tex]:
- To convert [tex]\( \frac{1}{2} \)[/tex] to a fraction with the denominator of 16, multiply both the numerator and the denominator by 8:
[tex]\[
\frac{1}{2} \times \frac{8}{8} = \frac{8}{16}
\][/tex]
- For [tex]\( \frac{3}{16} \)[/tex]:
- The fraction [tex]\( \frac{3}{16} \)[/tex] already has the denominator of 16, so it remains the same:
[tex]\[
\frac{3}{16}
\][/tex]
- For [tex]\( \frac{7}{8} \)[/tex]:
- To convert [tex]\( \frac{7}{8} \)[/tex] to a fraction with the denominator of 16, multiply both the numerator and the denominator by 2:
[tex]\[
\frac{7}{8} \times \frac{2}{2} = \frac{14}{16}
\][/tex]
3. Verify the results:
- The fractions with the LCD are:
[tex]\[
\frac{1}{2} = \frac{8}{16}, \quad \frac{3}{16} = \frac{3}{16}, \quad \frac{7}{8} = \frac{14}{16}
\][/tex]
Therefore, when the fractions [tex]\( \frac{1}{2} \)[/tex], [tex]\( \frac{3}{16} \)[/tex], and [tex]\( \frac{7}{8} \)[/tex] are expressed with a least common denominator of 16, they become [tex]\( \frac{8}{16} \)[/tex], [tex]\( \frac{3}{16} \)[/tex], and [tex]\( \frac{14}{16} \)[/tex], respectively.
So, the correct answer is:
[tex]\[ \boxed{8 / 16, 3 / 16, and 14 / 16} \][/tex]
This corresponds to option B in the provided choices:
[tex]\[ \boxed{8 / 16, 3 / 16, and 14 / 16} \][/tex]
