To determine which fraction is equal to [tex]\( \frac{7}{8} \)[/tex], we need to compare each option to [tex]\( \frac{7}{8} \)[/tex].
Let's analyze each option:
Option A: [tex]\( \frac{49}{64} \)[/tex]:
[tex]\[
\frac{49}{64} \quad \text{can be simplified as} \quad \frac{49}{64} = \frac{7^2}{8^2} \text{, which is also equal to }\left(\frac{7}{8}\right)^2 \neq \frac{7}{8}
\][/tex]
Thus, [tex]\(\frac{49}{64} \neq \frac{7}{8}\)[/tex].
Option B: [tex]\( \frac{15}{8} \)[/tex]:
[tex]\[
\frac{15}{8} = \frac{15}{8}
\][/tex]
We can see this fraction is not equal to [tex]\( \frac{7}{8}\)[/tex].
Option C: [tex]\( \frac{56}{8} \)[/tex]:
[tex]\[
\frac{56}{8} = 7
\][/tex]
Clearly, this is not equal to [tex]\( \frac{7}{8} \)[/tex].
Option D: [tex]\( \frac{21}{24} \)[/tex]:
[tex]\[
\frac{21}{24} = \frac{21 \div 3}{24 \div 3} = \frac{7}{8}
\][/tex]
Here, we find that [tex]\( \frac{21}{24} \)[/tex] simplifies exactly to [tex]\( \frac{7}{8} \)[/tex].
Therefore, the fraction that is equal to [tex]\( \frac{7}{8} \)[/tex] is Option D: [tex]\( \frac{21}{24} \)[/tex].
