To express the fractions [tex]\( \frac{3}{4}, \frac{7}{16}, \frac{5}{8} \)[/tex] with the Least Common Denominator (LCD), follow these steps:
1. Identify the fractions:
- [tex]\(\frac{3}{4}\)[/tex]
- [tex]\(\frac{7}{16}\)[/tex]
- [tex]\(\frac{5}{8}\)[/tex]
2. Determine the denominators of each fraction:
- The denominators are 4, 16, and 8.
3. Find the Least Common Denominator (LCD):
- The LCD of 4, 16, and 8 is 16.
4. Express each fraction with the LCD 16:
a. Convert [tex]\(\frac{3}{4}\)[/tex]:
- To express [tex]\(\frac{3}{4}\)[/tex] with a denominator of 16, multiply the numerator and the denominator by 4.
- [tex]\(\frac{3}{4} = \frac{3 \times 4}{4 \times 4} = \frac{12}{16}\)[/tex]
b. Convert [tex]\(\frac{7}{16}\)[/tex]:
- [tex]\(\frac{7}{16}\)[/tex] already has a denominator of 16, so it remains [tex]\(\frac{7}{16}\)[/tex].
c. Convert [tex]\(\frac{5}{8}\)[/tex]:
- To express [tex]\(\frac{5}{8}\)[/tex] with a denominator of 16, multiply the numerator and the denominator by 2.
- [tex]\(\frac{5}{8} = \frac{5 \times 2}{8 \times 2} = \frac{10}{16}\)[/tex]
5. Write the converted fractions:
- [tex]\(\frac{3}{4} = \frac{12}{16}\)[/tex]
- [tex]\(\frac{7}{16} = \frac{7}{16}\)[/tex]
- [tex]\(\frac{5}{8} = \frac{10}{16}\)[/tex]
Thus, the fractions [tex]\( \frac{3}{4}, \frac{7}{16}, \frac{5}{8} \)[/tex] when expressed with the LCD (Least Common Denominator) 16 are:
[tex]\[ \boxed{12 / 16, 7 / 16, 10 / 16} \][/tex]
So the correct answer is:
B) [tex]\( \frac{12}{16}, \frac{7}{16}, \frac{10}{16} \)[/tex]
