Select the best answer for the question.

Express the fractions [tex]\frac{1}{2}, \frac{3}{16},[/tex] and [tex]\frac{7}{8}[/tex] with a common denominator (LCD).

A. [tex]\frac{8}{16}, \frac{3}{16},[/tex] and [tex]\frac{14}{16}[/tex]
B. [tex]\frac{4}{8}, \frac{6}{8},[/tex] and [tex]\frac{14}{8}[/tex]
C. [tex]\frac{1}{4}, \frac{3}{4},[/tex] and [tex]\frac{7}{4}[/tex]
D. [tex]\frac{1}{32}, \frac{3}{32},[/tex] and [tex]\frac{7}{32}[/tex]



Answer :

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].