https://file.aiquickdraw.com/mathbot/file/17260731396004rii7tgh.jpg

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.

Learn how to simplify the expression 1/2 + 1/2 ÷ 4/7. This problem demonstrates key concepts such as division and addition of fractions, with a detailed step-by-step solution. Suitable for students in Grades 6-8.

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