Select the best answer for the question.

Express the fractions [tex]$\frac{1}{2}, \frac{3}{16}$, and $\frac{7}{8}$[/tex] with an LCD.

A. [tex][tex]$\frac{8}{16}, \frac{3}{16}$[/tex], and $\frac{14}{16}$[/tex]

B. [tex][tex]$\frac{1}{32}, \frac{3}{32}$[/tex], and $\frac{7}{32}$[/tex]

C. [tex][tex]$\frac{1}{4}, \frac{3}{4}$[/tex], and $\frac{7}{4}$[/tex]

D. [tex][tex]$\frac{4}{8}, \frac{6}{8}$[/tex], and $\frac{14}{8}$[/tex]



Answer :

To express the fractions [tex]\( \frac{1}{2}, \frac{3}{16}, \frac{7}{8} \)[/tex] with a common denominator, we need to find the least common denominator (LCD) for the fractions.

1. Identify the denominators of the fractions: [tex]\(2\)[/tex], [tex]\(16\)[/tex], and [tex]\(8\)[/tex].

2. Determine the least common multiple (LCM) of these denominators to find the LCD.
- The multiples of [tex]\(2\)[/tex] are [tex]\(2, 4, 6, 8, 10, 12, 14, 16, \ldots\)[/tex]
- The multiples of [tex]\(16\)[/tex] are [tex]\(16, 32, 48, \ldots\)[/tex]
- The multiples of [tex]\(8\)[/tex] are [tex]\(8, 16, 24, 32, \ldots\)[/tex]

The LCM of [tex]\(2\)[/tex], [tex]\(16\)[/tex], and [tex]\(8\)[/tex] is [tex]\(16\)[/tex]. Therefore, the LCD is [tex]\(16\)[/tex].

3. Convert each fraction to have the denominator of [tex]\(16\)[/tex]:

- 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]\[ \frac{3}{16} \text{ is already in the desired form.} \][/tex]

- For [tex]\( \frac{7}{8} \)[/tex]:
[tex]\[ \frac{7}{8} = \frac{7 \times 2}{8 \times 2} = \frac{14}{16} \][/tex]

So, the fractions expressed with the LCD [tex]\(16\)[/tex] are:

[tex]\[ \frac{8}{16}, \frac{3}{16}, \frac{14}{16} \][/tex]

Thus, the correct answer is:

A. [tex]\( \frac{8}{16}, \frac{3}{16}, \frac{14}{16} \)[/tex]