To determine which of the given fractions is equal to [tex]\( \frac{7}{8} \)[/tex], let's analyze each option step by step:
Option A: [tex]\( \frac{21}{24} \)[/tex]
To see if [tex]\( \frac{21}{24} \)[/tex] is equal to [tex]\( \frac{7}{8} \)[/tex], we need to simplify [tex]\( \frac{21}{24} \)[/tex]. We do this by finding the greatest common divisor (GCD) of 21 and 24 and dividing both the numerator and the denominator by this GCD.
- The GCD of 21 and 24 is 3.
- Dividing 21 by 3, we get 7.
- Dividing 24 by 3, we get 8.
So, [tex]\( \frac{21}{24} = \frac{7}{8} \)[/tex].
Option B: [tex]\( \frac{15}{8} \)[/tex]
We will compare [tex]\( \frac{15}{8} \)[/tex] directly to [tex]\( \frac{7}{8} \)[/tex]:
- [tex]\(\frac{15}{8}\)[/tex] has a larger numerator than [tex]\(\frac{7}{8}\)[/tex].
Therefore, [tex]\( \frac{15}{8} \neq \frac{7}{8} \)[/tex].
Option C: [tex]\( \frac{49}{64} \)[/tex]
To check if [tex]\( \frac{49}{64} \)[/tex] is equal to [tex]\( \frac{7}{8} \)[/tex], we need to find a common basis. However, since their denominators (64 and 8) are different, we can compare their cross-products:
- [tex]\( 7 \times 64 = 448 \)[/tex]
- [tex]\( 8 \times 49 = 392 \)[/tex]
Since 448 [tex]\(\neq\)[/tex] 392, [tex]\( \frac{49}{64} \neq \frac{7}{8} \)[/tex].
Option D: [tex]\( \frac{56}{8} \)[/tex]
We simplify [tex]\( \frac{56}{8} \)[/tex]:
- Dividing 56 by 8, we get 7.
So, [tex]\( \frac{56}{8} = 7 \)[/tex].
Since 7 is an integer and [tex]\( \frac{7}{8} \)[/tex] is a fraction, [tex]\( \frac{56}{8} \neq \frac{7}{8} \)[/tex].
Given these calculations, the fraction that is equal to [tex]\( \frac{7}{8} \)[/tex] is:
A. [tex]\( \frac{21}{24} \)[/tex]
