Compare Fractions: Find the Missing Symbol Between 2/5 and 7/10

To solve this problem, we will follow these steps:

• Step 1: Convert $\frac{2}{5}$ to an equivalent fraction with a denominator of 10.
• Step 2: Compare the numerators of the two fractions with the common denominator.

Now, let's work through each step:

Step 1: Convert $\frac{2}{5}$ to an equivalent fraction with denominator 10.

To convert $\frac{2}{5}$ to have a denominator of 10, we need to determine what number, when multiplied with 5, gives us 10. It is 2. Hence, we multiply both the numerator and denominator of $\frac{2}{5}$ by 2:

$\frac{2}{5} \times \frac{2}{2} = \frac{4}{10}$

Now, $\frac{2}{5}$ is equivalent to $\frac{4}{10}$.

Step 2: Compare the fractions $\frac{4}{10}$ and $\frac{7}{10}$.

Both fractions now have the same denominator, 10. We can compare them directly by looking at their numerators:

$4 \quad \text{and} \quad 7$

Since 4 is less than 7, we have:

$\frac{4}{10} < \frac{7}{10}$

Therefore, $\frac{2}{5} < \frac{7}{10}$.

The correct mathematical sign that completes the statement is $\lt$, so:

$\frac{2}{5} < \frac{7}{10}$