To express the fractions [tex]\( \frac{3}{4} \)[/tex], [tex]\( \frac{7}{16} \)[/tex], and [tex]\( \frac{5}{8} \)[/tex] with a common denominator, we need to find the Least Common Denominator (LCD) among their denominators.
Step-by-step solution:
1. Identify the denominators:
- The denominators are [tex]\(4\)[/tex], [tex]\(16\)[/tex], and [tex]\(8\)[/tex].
2. Find the Least Common Denominator (LCD) of [tex]\(4\)[/tex], [tex]\(16\)[/tex], and [tex]\(8\)[/tex]:
- The least common multiple of [tex]\(4\)[/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 common denominator [tex]\(16\)[/tex]:
- For [tex]\( \frac{3}{4} \)[/tex]:
[tex]\[
\frac{3}{4} = \frac{3 \times 4}{4 \times 4} = \frac{12}{16}
\][/tex]
- For [tex]\( \frac{7}{16} \)[/tex]:
[tex]\[
\frac{7}{16} \implies \text{It’s already with denominator} 16: \frac{7}{16}
\][/tex]
- For [tex]\( \frac{5}{8} \)[/tex]:
[tex]\[
\frac{5}{8} = \frac{5 \times 2}{8 \times 2} = \frac{10}{16}
\][/tex]
Thus, the fractions with the common denominator [tex]\(16\)[/tex] are:
[tex]\[ \frac{12}{16}, \frac{7}{16}, \frac{10}{16} \][/tex]
Now, we compare these fractions with the provided choices:
- A. [tex]\( \frac{12}{16}, \frac{7}{16}, \frac{10}{16} \)[/tex]
- B. [tex]\( \frac{24}{32}, \frac{14}{32}, \frac{44}{32} \)[/tex]
- C. [tex]\( \frac{3}{4}, \frac{2}{4}, \frac{3}{4} \)[/tex]
- D. [tex]\( \frac{9}{16}, \frac{49}{16}, \frac{36}{16} \)[/tex]
The correct answer is A. [tex]\( \frac{12}{16}, \frac{7}{16}, \frac{10}{16} \)[/tex].
