Compare Fractions: Finding the Correct Symbol Between 3/4 and 2/6

To solve this problem, we will follow these steps:

• Step 1: Identify the fractions we need to compare, which are $\frac{3}{4}$ and $\frac{2}{6}$.
• Step 2: Simplify $\frac{2}{6}$ to its simplest form.
• Step 3: Find a common denominator for the two fractions.
• Step 4: Convert each fraction to have the common denominator.
• Step 5: Compare the resulting numerators to determine the relationship.

Now, let's work through each step:

Step 1: The fractions we have are $\frac{3}{4}$ and $\frac{2}{6}$.

Step 2: Simplify $\frac{2}{6}$. The greatest common factor of 2 and 6 is 2, so $\frac{2}{6} = \frac{1}{3}$.

Step 3: Find a common denominator for $\frac{3}{4}$ and $\frac{1}{3}$. The least common multiple of 4 and 3 is 12.

Step 4: Convert each fraction to have the common denominator:

$\frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12}$

$\frac{1}{3} = \frac{1 \times 4}{3 \times 4} = \frac{4}{12}$

Step 5: Compare the numerators of the converted fractions:

Now, compare $\frac{9}{12}$ and $\frac{4}{12}$.

Since $9 > 4$, it follows that $\frac{9}{12} > \frac{4}{12}$.

Therefore, $\frac{3}{4} > \frac{1}{3}$, and hence $\frac{3}{4} > \frac{2}{6}$.

The correct comparison sign is $>$.