Converting each of the given fractions into decimal form, we get: $$\frac{15}{16}=0.9375, \frac{19}{20}=0.95, \frac{24}{25}=0.96, \frac{34}{35}=0.971$$ Clearly, $0.9375<0.95<0.96<0.971$. So, $\frac{15}{16}<\frac{19}{20}<\frac{24}{25}<\frac{34}{35}$.
Explanation as extracted from the printed page; notation may be imperfect.