Let's solve the problems step by step. The image contains six fraction problems. I'll provide solutions for each.

Problem (10):

$\frac{1}{9} - \frac{2}{3}$

1. Find a common denominator between $9$ and $3$. The least common denominator (LCD) is $9$.
   Rewrite $\frac{2}{3}$ as $\frac{6}{9}$:
   $\frac{1}{9} - \frac{2}{3} = \frac{1}{9} - \frac{6}{9}$

2. Subtract the fractions:
   $\frac{1}{9} - \frac{6}{9} = \frac{-5}{9}$

Answer: $-\frac{5}{9}$

Problem (11):

$\frac{1}{9} - \frac{2}{3}$

This is the same as Problem (10). The solution is:
Answer: $-\frac{5}{9}$

Problem (12):

$\frac{2}{3} - \frac{1}{9}$

1. Find the LCD between $9$ and $3$. The LCD is $9$.
   Rewrite $\frac{2}{3}$ as $\frac{6}{9}$:
   $\frac{2}{3} - \frac{1}{9} = \frac{6}{9} - \frac{1}{9}$

2. Subtract the fractions:
   $\frac{6}{9} - \frac{1}{9} = \frac{5}{9}$

Answer: $\frac{5}{9}$

Problem (13):

$-\frac{2}{3} + \frac{1}{9}$

1. Find the LCD between $3$ and $9$. The LCD is $9$.
   Rewrite $-\frac{2}{3}$ as $-\frac{6}{9}$:
   $-\frac{2}{3} + \frac{1}{9} = -\frac{6}{9} + \frac{1}{9}$

2. Add the fractions:
   $-\frac{6}{9} + \frac{1}{9} = -\frac{5}{9}$

Answer: $-\frac{5}{9}$

Problem (14):

$-\frac{1}{9} + \frac{2}{3}$

1. Find the LCD between $9$ and $3$. The LCD is $9$.
   Rewrite $\frac{2}{3}$ as $\frac{6}{9}$:
   $-\frac{1}{9} + \frac{2}{3} = -\frac{1}{9} + \frac{6}{9}$

2. Add the fractions:
   $-\frac{1}{9} + \frac{6}{9} = \frac{5}{9}$

Answer: $\frac{5}{9}$

Problem (15):

$-\frac{2}{9} + \frac{2}{3}$

1. Find the LCD between $9$ and $3$. The LCD is $9$.
   Rewrite $\frac{2}{3}$ as $\frac{6}{9}$:
   $-\frac{2}{9} + \frac{2}{3} = -\frac{2}{9} + \frac{6}{9}$

2. Add the fractions:
   $-\frac{2}{9} + \frac{6}{9} = \frac{4}{9}$

Answer: $\frac{4}{9}$

Problem (16):

$-\frac{2}{3} + \frac{2}{9}$

1. Find the LCD between $3$ and $9$. The LCD is $9$.
   Rewrite $-\frac{2}{3}$ as $-\frac{6}{9}$:
   $-\frac{2}{3} + \frac{2}{9} = -\frac{6}{9} + \frac{2}{9}$

2. Add the fractions:
   $-\frac{6}{9} + \frac{2}{9} = -\frac{4}{9}$

Answer: $-\frac{4}{9}$

Summary of Answers:

10. $-\frac{5}{9}$
11. $-\frac{5}{9}$
12. $\frac{5}{9}$
13. $-\frac{5}{9}$
14. $\frac{5}{9}$
15. $\frac{4}{9}$
16. $-\frac{4}{9}$

Would you like detailed explanations or additional help on any step?

Expansion Questions:

1. How can you simplify operations with negative fractions?
2. What is the process of finding the least common denominator?
3. How do you convert improper fractions into mixed numbers?
4. Can these calculations be verified visually using a number line?
5. What are some common mistakes to avoid in fraction subtraction?

Tip:

Always reduce your final fraction to its simplest form to ensure accuracy and clarity!