Compare Fractions: Find the Symbol Between 3/7 and 1/6

To solve this problem, we'll follow these steps:

• Step 1: Determine a common denominator for the fractions.
• Step 2: Convert each fraction to have the common denominator.
• Step 3: Compare the numerators to find the correct inequality.

Now, let's work through each step:
Step 1: Determine a common denominator for $\frac{3}{7}$ and $\frac{1}{6}$. The common denominator is the product of the denominators $7 \times 6 = 42$.
Step 2: Convert each fraction to have this common denominator:
- Convert $\frac{3}{7}$: Multiply the numerator and denominator by 6: $\frac{3 \times 6}{7 \times 6} = \frac{18}{42}$.
- Convert $\frac{1}{6}$: Multiply the numerator and denominator by 7: $\frac{1 \times 7}{6 \times 7} = \frac{7}{42}$.
Step 3: Compare the numerators: $18$ and $7$.
Since $18 > 7$, we have $\frac{18}{42} > \frac{7}{42}$. Thus, $\frac{3}{7} > \frac{1}{6}$.

Therefore, the correct inequality sign is $>$.