To add the fractions $\frac{2}{5} + \frac{2}{7}$, we need to find a common denominator.

Step 1: Find the Least Common Denominator (LCD)

The denominators are 5 and 7. Since they are coprime (they have no common factors other than 1), their LCD is simply the product of 5 and 7:

$\text{LCD} = 5 \times 7 = 35$

Step 2: Rewrite each fraction with the LCD

Now, we need to express each fraction with a denominator of 35.

For $\frac{2}{5}$, multiply both the numerator and the denominator by 7: $\frac{2}{5} = \frac{2 \times 7}{5 \times 7} = \frac{14}{35}$

For $\frac{2}{7}$, multiply both the numerator and the denominator by 5: $\frac{2}{7} = \frac{2 \times 5}{7 \times 5} = \frac{10}{35}$

Step 3: Add the fractions

Now, add the fractions:

$\frac{14}{35} + \frac{10}{35} = \frac{14 + 10}{35} = \frac{24}{35}$

Final Answer:

$\frac{2}{5} + \frac{2}{7} = \frac{24}{35}$

Would you like more details on how to add fractions or any related questions?

Expanding Questions:

1. How do you find the Least Common Denominator of two fractions?
2. What if the denominators are not coprime? How do you handle that?
3. How do you subtract fractions with different denominators?
4. Can you simplify fractions like $\frac{24}{35}$?
5. How do you convert fractions to decimals?

Tip: Always simplify fractions if possible after performing operations!