The problem in the image asks you to simplify the expression:

$\frac{1}{2} + \frac{1}{2} \div \frac{4}{7}$

Step-by-Step Solution:

1. First, handle the division of fractions: $\frac{1}{2} \div \frac{4}{7} = \frac{1}{2} \times \frac{7}{4} = \frac{7}{8}$

2. Now, add the two fractions: $\frac{1}{2} + \frac{7}{8}$

   To add these fractions, you need a common denominator. The least common denominator of 2 and 8 is 8. So, rewrite $\frac{1}{2}$ as $\frac{4}{8}$: $\frac{4}{8} + \frac{7}{8} = \frac{11}{8}$

Final Answer:

$\frac{11}{8} \text{ or } 1 \frac{3}{8}$

Would you like a more detailed explanation of any step or have additional questions?

Here are some related questions:

1. How do you divide two fractions in general?
2. What is the process for adding fractions with different denominators?
3. Can this result be written as a decimal? What would it be?
4. What is the importance of finding a common denominator when adding fractions?
5. How can you convert improper fractions to mixed numbers?

Tip: When dividing fractions, remember that division is equivalent to multiplying by the reciprocal of the second fraction.