Compare Fractions: Determine the Symbol Between 2/9 and 3/14

Fill in the missing sign:

$\frac{2}{9}☐\frac{3}{14}$

To solve this problem, we'll compare the fractions $\frac{2}{9}$ and $\frac{3}{14}$ by finding a common denominator:

• Step 1: Find the common denominator. The denominators are $9$ and $14$. The least common multiple of $9$ and $14$ is $126$.
• Step 2: Convert each fraction to an equivalent fraction with a denominator of $126$.
  For $\frac{2}{9}$: $\frac{2}{9} = \frac{2 \times 14}{9 \times 14} = \frac{28}{126}$.
  For $\frac{3}{14}$: $\frac{3}{14} = \frac{3 \times 9}{14 \times 9} = \frac{27}{126}$.
• Step 3: Compare the numerators of the equivalent fractions. $28 > 27$, so $\frac{28}{126} > \frac{27}{126}$.

Therefore, the fraction $\frac{2}{9}$ is greater than $\frac{3}{14}$, and the correct inequality sign is $>$.

Hence, the answer is $\frac{2}{9} > \frac{3}{14}$.