Let's go through each problem in the image and solve them step-by-step:

1. Problem D: $\frac{2}{3} + \left(-\frac{1}{4}\right)$

• Find a common denominator: The denominators are 3 and 4, so the least common denominator is 12.
• Convert fractions:
  • $\frac{2}{3} = \frac{8}{12}$
  • $-\frac{1}{4} = -\frac{3}{12}$
• Add the fractions: $\frac{8}{12} + \left(-\frac{3}{12}\right) = \frac{5}{12}$
• Answer: $\frac{5}{12}$

2. Problem I: $-\frac{4}{5} + \frac{1}{2}$

• Find a common denominator: The denominators are 5 and 2, so the least common denominator is 10.
• Convert fractions:
  • $-\frac{4}{5} = -\frac{8}{10}$
  • $\frac{1}{2} = \frac{5}{10}$
• Add the fractions: $-\frac{8}{10} + \frac{5}{10} = -\frac{3}{10}$
• Answer: $-\frac{3}{10}$

3. Problem O: $-\frac{1}{3} + \left(-\frac{7}{8}\right)$

• Find a common denominator: The denominators are 3 and 8, so the least common denominator is 24.
• Convert fractions:
  • $-\frac{1}{3} = -\frac{8}{24}$
  • $-\frac{7}{8} = -\frac{21}{24}$
• Add the fractions: $-\frac{8}{24} + \left(-\frac{21}{24}\right) = -\frac{29}{24}$
• This is an improper fraction, which can also be written as $-1 \frac{5}{24}$.
• Answer: $-\frac{29}{24}$ or $-1 \frac{5}{24}$

4. Problem M: $-\frac{4}{5} + \frac{3}{4}$

• Find a common denominator: The denominators are 5 and 4, so the least common denominator is 20.
• Convert fractions:
  • $-\frac{4}{5} = -\frac{16}{20}$
  • $\frac{3}{4} = \frac{15}{20}$
• Add the fractions: $-\frac{16}{20} + \frac{15}{20} = -\frac{1}{20}$
• Answer: $-\frac{1}{20}$

5. Problem U: $-\frac{1}{5} + \left(-\frac{2}{3}\right)$

• Find a common denominator: The denominators are 5 and 3, so the least common denominator is 15.
• Convert fractions:
  • $-\frac{1}{5} = -\frac{3}{15}$
  • $-\frac{2}{3} = -\frac{10}{15}$
• Add the fractions: $-\frac{3}{15} + \left(-\frac{10}{15}\right) = -\frac{13}{15}$
• Answer: $-\frac{13}{15}$

6. Problem T: $\frac{5}{6} + \left(-\frac{7}{12}\right)$

• Find a common denominator: The denominators are 6 and 12, so the least common denominator is 12.
• Convert fractions:
  • $\frac{5}{6} = \frac{10}{12}$
  • $-\frac{7}{12} = -\frac{7}{12}$
• Add the fractions: $\frac{10}{12} + \left(-\frac{7}{12}\right) = \frac{3}{12} = \frac{1}{4}$
• Answer: $\frac{1}{4}$

7. Problem R: $-\frac{3}{4} + \frac{5}{6}$

• Find a common denominator: The denominators are 4 and 6, so the least common denominator is 12.
• Convert fractions:
  • $-\frac{3}{4} = -\frac{9}{12}$
  • $\frac{5}{6} = \frac{10}{12}$
• Add the fractions: $-\frac{9}{12} + \frac{10}{12} = \frac{1}{12}$
• Answer: $\frac{1}{12}$

Would you like further explanation on any of these steps?

Here are some questions to explore related concepts:

1. How do you determine the least common denominator for two fractions?
2. How can you convert improper fractions into mixed numbers?
3. Why is it necessary to find a common denominator when adding or subtracting fractions?
4. How do you handle negative signs in fraction addition and subtraction?
5. Can you simplify fractions after adding or subtracting them?

Tip: When adding or subtracting fractions, always check if you can simplify the final answer by finding the greatest common divisor of the numerator and denominator.