Comparing Fractions

Since both fractions have the same denominator, comparing the numerators tells us that $\frac{5}{7}$ is greater than $\frac{3}{7}$.

Since both fractions have the same numerator, the fraction with the smaller denominator represents a larger value, so $\frac{4}{9}$ is greater.

Bring both fractions to a common denominator of 30: $\frac{11}{15}=\frac{22}{30}$ and $\frac{7}{10}=\frac{21}{30}$. Since $22>21$, $\frac{11}{15}$ is greater.

Using a common denominator of 30: $\frac{7}{10}=\frac{21}{30}$ and $\frac{2}{3}=\frac{20}{30}$. Since $21>20$, $\frac{7}{10}$ is greater.

Using a common denominator of 24: $\frac{7}{12}=\frac{14}{24}$ and $\frac{5}{8}=\frac{15}{24}$. Since $15>14$, $\frac{5}{8}$ is greater.

Bring both fractions to a common denominator of 52: $\frac{9}{13}=\frac{36}{52}$ and $\frac{3}{4}=\frac{39}{52}$. Since $36<39$, $\frac{9}{13}$ is smaller.