Let's analyze and solve the given expression from the image:

The expression is: $2 \frac{3}{11} + \frac{4}{9} \div 1 \frac{7}{15}$

To solve this, we can break it down into a series of steps:

Step 1: Convert Mixed Numbers to Improper Fractions

1. $2 \frac{3}{11}$ becomes $\frac{25}{11}$ (since $2 \times 11 + 3 = 25$).
2. $1 \frac{7}{15}$ becomes $\frac{22}{15}$ (since $1 \times 15 + 7 = 22$).

The expression now looks like: $\frac{25}{11} + \frac{4}{9} \div \frac{22}{15}$

Step 2: Handle the Division

Division by a fraction is equivalent to multiplying by its reciprocal. So, we rewrite the division as multiplication: $\frac{25}{11} + \frac{4}{9} \times \frac{15}{22}$

Step 3: Perform the Multiplication

Now, multiply $\frac{4}{9}$ by $\frac{15}{22}$: $\frac{4 \times 15}{9 \times 22} = \frac{60}{198}$

To simplify $\frac{60}{198}$, we find the greatest common divisor of 60 and 198, which is 6. So, $\frac{60}{198} = \frac{10}{33}$

Now the expression is: $\frac{25}{11} + \frac{10}{33}$

Step 4: Add the Fractions

To add $\frac{25}{11}$ and $\frac{10}{33}$, we need a common denominator. The least common multiple of 11 and 33 is 33.

1. Convert $\frac{25}{11}$ to a fraction with denominator 33: $\frac{25}{11} = \frac{75}{33}$

2. Now add: $\frac{75}{33} + \frac{10}{33} = \frac{85}{33}$

Step 5: Simplify the Result

The fraction $\frac{85}{33}$ is already in its simplest form, but it can be expressed as a mixed number: $\frac{85}{33} = 2 \frac{19}{33}$

Final Answer

The result of the expression is: $2 \frac{19}{33}$

Would you like more details on any of the steps, or do you have further questions?

---

Here are five related questions for further exploration:

1. How do you convert mixed numbers to improper fractions?
2. What is the process of dividing fractions, and why do we use reciprocals?
3. How can you determine the least common multiple when adding fractions?
4. Why is it necessary to simplify fractions, and how do you find the greatest common divisor?
5. How can improper fractions be converted back into mixed numbers?

Tip: Always remember to simplify fractions at each step to make calculations easier and reduce potential errors.