To express the fractions [tex]$\frac{1}{2}$[/tex], [tex]$\frac{3}{16}$[/tex], and [tex]$\frac{7}{8}$[/tex] with a common denominator or LCD (Least Common Denominator), let’s follow these steps:
1. Identify the denominators of all three fractions. The denominators are [tex]$2$[/tex], [tex]$16$[/tex], and [tex]$8$[/tex].
2. Determine the least common multiple (LCM) of the denominators [tex]$2$[/tex], [tex]$16$[/tex], and [tex]$8$[/tex]. Analyzing the numbers, it turns out that [tex]$16$[/tex] is the smallest number that is a multiple of all three denominators.
3. Convert each fraction to an equivalent fraction with [tex]$16$[/tex] as the new denominator:
- 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]\[
\frac{3}{16} = \frac{3}{16}
\][/tex]
(since the denominator is already [tex]$16$[/tex], it remains the same)
- For [tex]$\frac{7}{8}$[/tex]:
[tex]\[
\frac{7}{8} = \frac{7 \times 2}{8 \times 2} = \frac{14}{16}
\][/tex]
4. The equivalent fractions with the common denominator should now be:
- [tex]$\frac{8}{16}$[/tex]
- [tex]$\frac{3}{16}$[/tex]
- [tex]$\frac{14}{16}$[/tex]
Hence, the best answer that expresses the given fractions with the LCD is:
C. [tex]$\frac{8}{16}$[/tex], [tex]$\frac{3}{16}$[/tex], and [tex]$\frac{14}{16}$[/tex]
