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The image you provided contains several fraction addition and subtraction exercises. Let me analyze and help clarify each section of your work.

### Problem 1:
\[
\left(\frac{1}{2} + \frac{2}{3} + \frac{3}{6}\right) + \left(\frac{3}{4} - \frac{3}{2} + \frac{3}{3}\right)
\]
- First, let's solve each set of parentheses:
  1. For \(\frac{1}{2} + \frac{2}{3} + \frac{3}{6}\), the common denominator is 6:
     \[
     \frac{1}{2} = \frac{3}{6}, \quad \frac{2}{3} = \frac{4}{6}, \quad \frac{3}{6} = \frac{3}{6}
     \]
     Adding these together:
     \[
     \frac{3}{6} + \frac{4}{6} + \frac{3}{6} = \frac{10}{6} = \frac{5}{3}
     \]

  2. For \(\frac{3}{4} - \frac{3}{2} + \frac{3}{3}\), the common denominator is 12:
     \[
     \frac{3}{4} = \frac{9}{12}, \quad \frac{3}{2} = \frac{18}{12}, \quad \frac{3}{3} = 1 = \frac{12}{12}
     \]
     Now subtract and add:
     \[
     \frac{9}{12} - \frac{18}{12} + \frac{12}{12} = \frac{9 - 18 + 12}{12} = \frac{3}{12} = \frac{1}{4}
     \]

- Now, adding the two results:
  \[
  \frac{5}{3} + \frac{1}{4} = \frac{20}{12} + \frac{3}{12} = \frac{23}{12}
  \]
  So, the result is \(\frac{23}{12}\).

### Problem 2:
\[
\frac{1}{2} + \frac{2}{4} + \frac{3}{6}
\]
- Convert all fractions to have a common denominator (6):
  \[
  \frac{1}{2} = \frac{3}{6}, \quad \frac{2}{4} = \frac{3}{6}, \quad \frac{3}{6} = \frac{3}{6}
  \]
  Now, add them together:
  \[
  \frac{3}{6} + \frac{3}{6} + \frac{3}{6} = \frac{9}{6} = \frac{3}{2}
  \]

### Problem 3:
\[
\frac{3}{4} + \frac{4}{6} - \frac{6}{12}
\]
- Convert all fractions to have a common denominator (12):
  \[
  \frac{3}{4} = \frac{9}{12}, \quad \frac{4}{6} = \frac{8}{12}, \quad \frac{6}{12} = \frac{6}{12}
  \]
  Now, perform the operations:
  \[
  \frac{9}{12} + \frac{8}{12} - \frac{6}{12} = \frac{9 + 8 - 6}{12} = \frac{11}{12}
  \]

### Problem 4:
\[
\frac{7}{3} - \frac{8}{3} + \frac{2}{9}
\]
- Convert all fractions to have a common denominator (9):
  \[
  \frac{7}{3} = \frac{21}{9}, \quad \frac{8}{3} = \frac{24}{9}, \quad \frac{2}{9} = \frac{2}{9}
  \]
  Now, perform the operations:
  \[
  \frac{21}{9} - \frac{24}{9} + \frac{2}{9} = \frac{21 - 24 + 2}{9} = \frac{-1}{9}
  \]

### Problem 5:
\[
\frac{5}{9} - \frac{3}{9} + \frac{1}{3}
\]
- Convert all fractions to have a common denominator (9):
  \[
  \frac{1}{3} = \frac{3}{9}
  \]
  Now, perform the operations:
  \[
  \frac{5}{9} - \frac{3}{9} + \frac{3}{9} = \frac{5 - 3 + 3}{9} = \frac{5}{9}
  \]

---

Would you like further details on any of the problems? Here are some related questions:

1. What are common denominators and why are they important in fraction operations?
2. How do you convert fractions to have the same denominator?
3. Why does subtraction with fractions sometimes lead to negative results?
4. What strategies can simplify complex fraction addition or subtraction?
5. Can fractions be simplified after the addition and subtraction process?

**Tip**: When dealing with fraction operations, always check if the result can be simplified by finding the greatest common divisor of the numerator and denominator!

The user submitted several fraction addition and subtraction exercises, including combining fractions with different denominators.

Learn how to solve fraction addition and subtraction problems, including finding the least common denominator and simplifying the results. These exercises are suitable for students in Grades 4-6.

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