Answer :
To solve the problem of expressing the fractions \(\frac{3}{4}\), \(\frac{7}{16}\), and \(\frac{5}{8}\) with a common denominator, follow these steps:
1. Identify the denominators of the given fractions:
- The denominators are \(4\), \(16\), and \(8\).
2. Find the Least Common Denominator (LCD):
- The LCD of the denominators \(4\), \(16\), and \(8\) is \(16\).
3. Express each fraction with the LCD:
- For \(\frac{3}{4}\):
- Convert the denominator \(4\) to \(16\). Multiply both the numerator and the denominator by \(4\):
[tex]\[ \frac{3}{4} = \frac{3 \times 4}{4 \times 4} = \frac{12}{16} \][/tex]
- For \(\frac{7}{16}\):
- The denominator is already \(16\).
[tex]\[ \frac{7}{16} = \frac{7}{16} \][/tex]
- For \(\frac{5}{8}\):
- Convert the denominator \(8\) to \(16\). Multiply both the numerator and the denominator by \(2\):
[tex]\[ \frac{5}{8} = \frac{5 \times 2}{8 \times 2} = \frac{10}{16} \][/tex]
4. Combine the results as fractions with the common denominator \(16\):
- The fractions \(\frac{3}{4}\), \(\frac{7}{16}\), and \(\frac{5}{8}\) are expressed as \(\frac{12}{16}\), \(\frac{7}{16}\), and \(\frac{10}{16}\), respectively.
So, the best answer is:
D. [tex]\(\frac{12}{16}, \frac{7}{16}, \frac{10}{16}\)[/tex]
1. Identify the denominators of the given fractions:
- The denominators are \(4\), \(16\), and \(8\).
2. Find the Least Common Denominator (LCD):
- The LCD of the denominators \(4\), \(16\), and \(8\) is \(16\).
3. Express each fraction with the LCD:
- For \(\frac{3}{4}\):
- Convert the denominator \(4\) to \(16\). Multiply both the numerator and the denominator by \(4\):
[tex]\[ \frac{3}{4} = \frac{3 \times 4}{4 \times 4} = \frac{12}{16} \][/tex]
- For \(\frac{7}{16}\):
- The denominator is already \(16\).
[tex]\[ \frac{7}{16} = \frac{7}{16} \][/tex]
- For \(\frac{5}{8}\):
- Convert the denominator \(8\) to \(16\). Multiply both the numerator and the denominator by \(2\):
[tex]\[ \frac{5}{8} = \frac{5 \times 2}{8 \times 2} = \frac{10}{16} \][/tex]
4. Combine the results as fractions with the common denominator \(16\):
- The fractions \(\frac{3}{4}\), \(\frac{7}{16}\), and \(\frac{5}{8}\) are expressed as \(\frac{12}{16}\), \(\frac{7}{16}\), and \(\frac{10}{16}\), respectively.
So, the best answer is:
D. [tex]\(\frac{12}{16}, \frac{7}{16}, \frac{10}{16}\)[/tex]
