Compare Fractions: Determine the Correct Symbol Between 2/5 and 6/15

Fill in the missing sign:

$\frac{2}{5}☐\frac{6}{15}$

To solve this problem, we'll take the following steps:

• Step 1: Simplify the fraction $\frac{2}{5}$.
• Step 2: Simplify the fraction $\frac{6}{15}$.
• Step 3: Compare the simplified forms.

Let's go through these steps:

Step 1: $\frac{2}{5}$ is already in its simplest form because 2 and 5 have no common divisors other than 1.

Step 2: Simplify the fraction $\frac{6}{15}$:
- The greatest common divisor (GCD) of 6 and 15 is 3.
- Divide both the numerator and the denominator by their GCD to simplify:
$\frac{6}{15} = \frac{6 \div 3}{15 \div 3} = \frac{2}{5}$

Step 3: Compare the simplified forms:
Both $\frac{2}{5}$ and $\frac{6}{15}$ simplify to $\frac{2}{5}$. Thus, they are equivalent.

Therefore, the correct mathematical sign between the fractions $\frac{2}{5}$ and $\frac{6}{15}$ is $=$.

So, the missing sign is $\mathbf{=}$.