We are asked to find the value of:

$\frac{2}{5} + \frac{3}{7}$

Step 1: Find a common denominator

The denominators are 5 and 7, so the least common denominator (LCD) is:

$\text{LCD}(5, 7) = 35$

Step 2: Rewrite the fractions with the common denominator

Now we rewrite each fraction with 35 as the denominator:

$\frac{2}{5} = \frac{2 \times 7}{5 \times 7} = \frac{14}{35}$

$\frac{3}{7} = \frac{3 \times 5}{7 \times 5} = \frac{15}{35}$

Step 3: Add the fractions

Now that the fractions have a common denominator, we can add them:

$\frac{14}{35} + \frac{15}{35} = \frac{14 + 15}{35} = \frac{29}{35}$

Thus, the value of $\frac{2}{5} + \frac{3}{7}$ is:

$\frac{29}{35}$

The correct answer is Option D: 29/35.

Would you like more details or further clarification? Here are five related questions to deepen your understanding:

1. How do you find the least common denominator between two fractions?
2. Can you explain the steps for simplifying fractions after addition?
3. How can you apply this process to subtracting fractions?
4. How would you approach adding fractions with denominators that are not prime numbers?
5. What happens if the numerators of both fractions are negative?

Tip: When adding fractions, always make sure both fractions have the same denominator before combining the numerators.