Let's determine which fraction among the given options is equal to [tex]\(\frac{7}{8}\)[/tex]. Here are the steps to compare each option with [tex]\(\frac{7}{8}\)[/tex]:
1. Option A: [tex]\(\frac{49}{64}\)[/tex]
- Compare [tex]\(\frac{49}{64}\)[/tex] with [tex]\(\frac{7}{8}\)[/tex].
- To compare two fractions, convert them to a common denominator or convert them to decimal form.
- [tex]\(\frac{49}{64} \approx 0.765625\)[/tex]
- [tex]\(\frac{7}{8} = 0.875\)[/tex]
- Since [tex]\(0.765625 \neq 0.875\)[/tex], [tex]\(\frac{49}{64}\)[/tex] is not equal to [tex]\(\frac{7}{8}\)[/tex].
2. Option B: [tex]\(\frac{15}{8}\)[/tex]
- Compare [tex]\(\frac{15}{8}\)[/tex] with [tex]\(\frac{7}{8}\)[/tex].
- Convert [tex]\(\frac{15}{8}\)[/tex] to decimal form: [tex]\(\frac{15}{8} = 1.875\)[/tex]
- The decimal representation of [tex]\(\frac{7}{8}\)[/tex] is [tex]\(0.875\)[/tex].
- Since [tex]\(1.875 \neq 0.875\)[/tex], [tex]\(\frac{15}{8}\)[/tex] is not equal to [tex]\(\frac{7}{8}\)[/tex].
3. Option C: [tex]\(\frac{56}{8}\)[/tex]
- Compare [tex]\(\frac{56}{8}\)[/tex] with [tex]\(\frac{7}{8}\)[/tex].
- Convert [tex]\(\frac{56}{8}\)[/tex] to decimal form: [tex]\(\frac{56}{8} = 7\)[/tex]
- The decimal representation of [tex]\(\frac{7}{8}\)[/tex] is [tex]\(0.875\)[/tex].
- Since [tex]\(7 \neq 0.875\)[/tex], [tex]\(\frac{56}{8}\)[/tex] is not equal to [tex]\(\frac{7}{8}\)[/tex].
4. Option D: [tex]\(\frac{21}{24}\)[/tex]
- Compare [tex]\(\frac{21}{24}\)[/tex] with [tex]\(\frac{7}{8}\)[/tex].
- Simplify [tex]\(\frac{21}{24}\)[/tex] by dividing both the numerator and the denominator by their greatest common divisor, which is 3: [tex]\(\frac{21 \div 3}{24 \div 3} = \frac{7}{8}\)[/tex].
- Therefore, [tex]\(\frac{21}{24}\)[/tex] simplifies to [tex]\(\frac{7}{8}\)[/tex].
- Since [tex]\(\frac{21}{24} = \frac{7}{8}\)[/tex], Option D is equal to [tex]\(\frac{7}{8}\)[/tex].
In conclusion, the fraction equal to [tex]\(\frac{7}{8}\)[/tex] is Option D: [tex]\(\frac{21}{24}\)[/tex].
