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

A. \(\frac{1}{4}, \frac{3}{4},\) and \(\frac{7}{4}\)

B. \(\frac{8}{16}, \frac{3}{16},\) and \(\frac{14}{16}\)

C. \(\frac{1}{32}, \frac{3}{32},\) and \(\frac{7}{32}\)

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



Answer :

GinnyAnswer
Certainly! Let's go through the steps to express the fractions \( \frac{1}{2}, \frac{3}{16}, \frac{7}{8} \), using the Least Common Denominator (LCD).

1. Identify the denominators of the given fractions: 2, 16, and 8.

2. Find the Least Common Denominator (LCD):
- The LCD of 2, 16, and 8 is 16.

3. Convert each fraction to an equivalent fraction with this LCD (16):
- For \( \frac{1}{2} \):
- To convert \( \frac{1}{2} \) to a fraction with a denominator of 16, multiply both the numerator and the denominator by 8.
- \( \frac{1 \times 8}{2 \times 8} = \frac{8}{16} \).
- For \( \frac{3}{16} \):
- The fraction already has the denominator of 16, so it remains the same.
- \( \frac{3}{16} \).
- For \( \frac{7}{8} \):
- To convert \( \frac{7}{8} \) to a fraction with a denominator of 16, multiply both the numerator and the denominator by 2.
- \( \frac{7 \times 2}{8 \times 2} = \frac{14}{16} \).

4. Thus, the fractions with the LCD of 16 are:
- \( \frac{1}{2} = \frac{8}{16} \),
- \( \frac{3}{16} \),
- \( \frac{7}{8} = \frac{14}{16} \).

Therefore, the correct answer is:
B. [tex]\( \frac{8}{16}, \frac{3}{16}, \frac{14}{16} \)[/tex].

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