Solution:
1. Convert both fractions to have a common denominator to compare them.
- The denominators are 8 and 4. The least common denominator is 8.
2. Convert \frac{7}{4} to a fraction with a denominator of 8:
\frac{7}{4} = \frac{7 \times 2}{4 \times 2} = \frac{14}{8}
3. Now compare \frac{15}{8} and \frac{14}{8}.
4. Since both fractions have the same denominator, compare the numerators:
- 15 > 14, so \frac{15}{8} > \frac{14}{8}.
5. Thus, \frac{15}{8} is greater than \frac{7}{4}.