1. **State the problem:** We need to determine which fraction is larger: $\frac{7}{8}$ or $\frac{8}{9}$.\n\n2. **Find a common denominator:** To compare fractions, we convert them to have the same denominator. The denominators are 8 and 9. The least common denominator (LCD) is the least common multiple (LCM) of 8 and 9.\n\n3. **Calculate the LCM:**\n$$\text{LCM}(8,9) = 72$$\n\n4. **Convert each fraction to have denominator 72:**\n$$\frac{7}{8} = \frac{7 \times 9}{8 \times 9} = \frac{63}{72}$$\n$$\frac{8}{9} = \frac{8 \times 8}{9 \times 8} = \frac{64}{72}$$\n\n5. **Compare the numerators:** Since $63 < 64$, we have\n$$\frac{63}{72} < \frac{64}{72}$$\nwhich means\n$$\frac{7}{8} < \frac{8}{9}$$\n\n**Final answer:** $\frac{8}{9}$ is larger than $\frac{7}{8}$.