https://file.aiquickdraw.com/mathbot/file/1729454000096ij5v5av0.jpg

The expression in the image is the sum of two mixed numbers: \( 5 \frac{5}{7} + 3 \frac{1}{2} \).

### Steps to solve:

1. **Convert mixed numbers to improper fractions:**
   - \( 5 \frac{5}{7} = \frac{(5 \times 7) + 5}{7} = \frac{35 + 5}{7} = \frac{40}{7} \)
   - \( 3 \frac{1}{2} = \frac{(3 \times 2) + 1}{2} = \frac{6 + 1}{2} = \frac{7}{2} \)

2. **Find a common denominator:**
   - The denominators are 7 and 2. The least common denominator (LCD) is 14.
   - Convert both fractions:
     - \( \frac{40}{7} = \frac{40 \times 2}{7 \times 2} = \frac{80}{14} \)
     - \( \frac{7}{2} = \frac{7 \times 7}{2 \times 7} = \frac{49}{14} \)

3. **Add the fractions:**
   \[
   \frac{80}{14} + \frac{49}{14} = \frac{80 + 49}{14} = \frac{129}{14}
   \]

4. **Simplify or convert back to a mixed number:**
   - \( \frac{129}{14} \) can be written as a mixed number.
   - Divide \( 129 \div 14 = 9 \) remainder \( 3 \), so:
   \[
   \frac{129}{14} = 9 \frac{3}{14}
   \]

Thus, the sum is \( 9 \frac{3}{14} \).

Would you like further details on any part of the process? 

Here are 5 related questions:
1. How do you subtract mixed numbers?
2. What is the method to find the least common denominator?
3. How do you simplify improper fractions?
4. How can you multiply mixed numbers?
5. What are the steps to convert an improper fraction back to a mixed number?

**Tip:** Always check for common factors between the numerator and denominator when simplifying fractions!

Add: Write in simplest form: 5 5/7 + 3 1/2.

Learn how to add mixed numbers such as 5 5/7 and 3 1/2. This solution explains the conversion of mixed numbers to improper fractions, finding the least common denominator, and simplifying the result. Suitable for students in Grades 6-8.

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