https://r2.erweima.ai/mathbot/image/172617451309921ekkr70.jpg

I see the image contains several fraction addition and subtraction problems. Let me help by solving each of them step by step.

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### First Row:
1. **\( \frac{4}{3} + \frac{11}{3} \)**  
   - Since the denominators are the same, you can add the numerators directly:  
   \( \frac{4 + 11}{3} = \frac{15}{3} = 5 \)

2. **\( \frac{1}{6} + \frac{2}{6} + \frac{3}{6} \)**  
   - Same denominator, so add the numerators:  
   \( \frac{1 + 2 + 3}{6} = \frac{6}{6} = 1 \)

3. **\( \frac{7}{9} + \frac{2}{15} \)**  
   - Find the least common denominator (LCD), which is 45:  
     \( \frac{7}{9} = \frac{35}{45}, \frac{2}{15} = \frac{6}{45} \)  
   - Add the fractions:  
     \( \frac{35 + 6}{45} = \frac{41}{45} \)

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### Second Row:
1. **\( \frac{3}{2} - \frac{9}{2} \)**  
   - Same denominator, so subtract the numerators:  
     \( \frac{3 - 9}{2} = \frac{-6}{2} = -3 \)

2. **\( \frac{40}{5} + \frac{10}{5} - \frac{5}{5} \)**  
   - Add and subtract the numerators directly:  
     \( \frac{40 + 10 - 5}{5} = \frac{45}{5} = 9 \)

3. **\( \frac{5}{6} - \frac{3}{8} \)**  
   - LCD is 24:  
     \( \frac{5}{6} = \frac{20}{24}, \frac{3}{8} = \frac{9}{24} \)  
   - Subtract the fractions:  
     \( \frac{20 - 9}{24} = \frac{11}{24} \)

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### Third Row:
1. **\( \frac{11}{7} + \frac{23}{7} \)**  
   - Same denominator, so add the numerators:  
     \( \frac{11 + 23}{7} = \frac{34}{7} \)

2. **\( \frac{66}{4} - \frac{33}{4} - \frac{1}{4} \)**  
   - Subtract the numerators directly:  
     \( \frac{66 - 33 - 1}{4} = \frac{32}{4} = 8 \)

3. **\( \frac{3}{4} + \frac{3}{10} \)**  
   - LCD is 20:  
     \( \frac{3}{4} = \frac{15}{20}, \frac{3}{10} = \frac{6}{20} \)  
   - Add the fractions:  
     \( \frac{15 + 6}{20} = \frac{21}{20} \)

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### Fourth Row:
1. **\( \frac{1}{5} - \frac{2}{5} \)**  
   - Same denominator, subtract the numerators:  
     \( \frac{1 - 2}{5} = \frac{-1}{5} \)

2. **\( \frac{3}{9} - \frac{3}{9} + \frac{3}{9} \)**  
   - Perform the operations:  
     \( \frac{3 - 3 + 3}{9} = \frac{3}{9} = \frac{1}{3} \)

3. **\( \frac{3}{5} - \frac{1}{3} \)**  
   - LCD is 15:  
     \( \frac{3}{5} = \frac{9}{15}, \frac{1}{3} = \frac{5}{15} \)  
   - Subtract the fractions:  
     \( \frac{9 - 5}{15} = \frac{4}{15} \)

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### Fifth Row:
1. **\( \frac{15}{14} + \frac{13}{14} \)**  
   - Same denominator, add the numerators:  
     \( \frac{15 + 13}{14} = \frac{28}{14} = 2 \)

2. **\( \frac{3}{10} - \frac{2}{10} + \frac{4}{10} \)**  
   - Perform the operations:  
     \( \frac{3 - 2 + 4}{10} = \frac{5}{10} = \frac{1}{2} \)

3. **\( \frac{6}{7} + \frac{8}{3} \)**  
   - LCD is 21:  
     \( \frac{6}{7} = \frac{18}{21}, \frac{8}{3} = \frac{56}{21} \)  
   - Add the fractions:  
     \( \frac{18 + 56}{21} = \frac{74}{21} \)

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### Sixth Row:
1. **\( \frac{13}{2} - \frac{31}{2} \)**  
   - Same denominator, subtract the numerators:  
     \( \frac{13 - 31}{2} = \frac{-18}{2} = -9 \)

2. **\( \frac{34}{31} + \frac{-3}{31} \)**  
   - Same denominator, add the numerators:  
     \( \frac{34 + (-3)}{31} = \frac{31}{31} = 1 \)

3. **\( \frac{31}{21} - \frac{3}{14} \)**  
   - LCD is 42:  
     \( \frac{31}{21} = \frac{62}{42}, \frac{3}{14} = \frac{9}{42} \)  
   - Subtract the fractions:  
     \( \frac{62 - 9}{42} = \frac{53}{42} \)

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Would you like more detailed steps for any of these problems or explanations on how to find the LCD? Here are some relative questions for deeper exploration:

1. How do you find the least common denominator (LCD) between two fractions?
2. Why is it important to have the same denominator before adding or subtracting fractions?
3. How can you simplify fractions after performing operations on them?
4. How does improper fraction conversion work when you have a larger numerator?
5. What is the relationship between mixed numbers and improper fractions?

### Tip:
Always simplify fractions after performing any arithmetic operations. This will make your final answer clearer and easier to interpret!

Solve the set of fraction addition and subtraction problems provided in the image.

This page provides a detailed step-by-step solution to several fraction addition and subtraction problems, covering concepts like finding the least common denominator (LCD), simplifying fractions, and performing operations with fractions. Suitable for students in Grades 6-8.

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