Find the best solutions to your questions at Westonci.ca, the premier Q&A platform with a community of knowledgeable experts. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.

5. 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{4}{8}, \frac{6}{8}[/tex], and [tex]\frac{14}{8}[/tex]
B. [tex]\frac{1}{32}, \frac{3}{32}[/tex], and [tex]\frac{7}{32}[/tex]
C. [tex]\frac{8}{16}, \frac{3}{16}[/tex], and [tex]\frac{14}{16}[/tex]
D. [tex]\frac{1}{4}, \frac{3}{4}[/tex], and [tex]\frac{7}{4}[/tex]


Sagot :

To express the fractions \( \frac{1}{2} \), \( \frac{3}{16} \), and \( \frac{7}{8} \) with a common denominator, we follow these steps:

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

2. Find the least common denominator (LCD) that all these denominators can divide into. The least common multiple (LCM) of 2, 16, and 8 is 16.

3. Convert each fraction so that they all have this common denominator (LCD = 16).

- For \( \frac{1}{2} \):
[tex]\[ \frac{1}{2} = \frac{1 \times 8}{2 \times 8} = \frac{8}{16} \][/tex]
- For \( \frac{3}{16} \):
[tex]\[ \frac{3}{16} = \frac{3}{16} \quad (\text{already has the denominator 16}) \][/tex]

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

4. The fractions with the common denominator 16 are:
[tex]\[ \frac{8}{16}, \frac{3}{16}, \frac{14}{16} \][/tex]

So, the correct answer is:

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