The problem involves adding two fractions:

$\frac{2}{9} + \frac{7}{15}$

Steps to Solve:

1. Find the Least Common Denominator (LCD):
   The denominators are $9$ and $15$. The LCD is the smallest number divisible by both, which is $45$.

2. Convert Each Fraction to Have the Same Denominator:

   • Convert $\frac{2}{9}$:
     Multiply numerator and denominator by $5$ (since $45 \div 9 = 5$):
     $\frac{2}{9} = \frac{2 \times 5}{9 \times 5} = \frac{10}{45}$
   • Convert $\frac{7}{15}$:
     Multiply numerator and denominator by $3$ (since $45 \div 15 = 3$):
     $\frac{7}{15} = \frac{7 \times 3}{15 \times 3} = \frac{21}{45}$

3. Add the Fractions:
   Combine the numerators over the common denominator:
   $\frac{10}{45} + \frac{21}{45} = \frac{10 + 21}{45} = \frac{31}{45}$

4. Simplify if Possible:
   The fraction $\frac{31}{45}$ is already in its simplest form because $31$ and $45$ have no common factors other than $1$.

Final Answer:

$\frac{31}{45}$

Would you like a breakdown of any specific step, or do you have additional questions?

Here are 5 related questions to deepen your understanding:

1. How do you determine the least common denominator for multiple fractions?
2. What happens if one of the denominators is already a multiple of the other?
3. Can improper fractions be left unsimplified, and why?
4. How do you handle adding more than two fractions?
5. What is the process for converting a mixed number into an improper fraction before adding?

Tip: Always check if the final fraction can be simplified by finding the greatest common divisor (GCD) of the numerator and denominator.