Let's solve each of the problems step by step.

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4) $\frac{7}{10} + \frac{2}{3}$: To add these fractions, we need a common denominator:

• The least common denominator (LCD) of 10 and 3 is 30.
• Rewrite the fractions:
  $\frac{7}{10} = \frac{21}{30}$,
  $\frac{2}{3} = \frac{20}{30}$.
• Add the fractions:
  $\frac{21}{30} + \frac{20}{30} = \frac{41}{30}$.
• Simplify:
  $\frac{41}{30}$ is an improper fraction.

Answer: $\frac{41}{30}$ or $1 \frac{11}{30}$.

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5) $\frac{1}{2} + \frac{3}{10}$:

• The LCD of 2 and 10 is 10.
• Rewrite the fractions:
  $\frac{1}{2} = \frac{5}{10}$,
  $\frac{3}{10}$ stays the same.
• Add the fractions:
  $\frac{5}{10} + \frac{3}{10} = \frac{8}{10}$.
• Simplify:
  $\frac{8}{10} = \frac{4}{5}$.

Answer: $\frac{4}{5}$.

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6) $\frac{3}{5} + \frac{3}{4}$:

• The LCD of 5 and 4 is 20.
• Rewrite the fractions:
  $\frac{3}{5} = \frac{12}{20}$,
  $\frac{3}{4} = \frac{15}{20}$.
• Add the fractions:
  $\frac{12}{20} + \frac{15}{20} = \frac{27}{20}$.
• Simplify:
  $\frac{27}{20}$ is an improper fraction.

Answer: $\frac{27}{20}$ or $1 \frac{7}{20}$.

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7) $\frac{2}{10} + \frac{3}{5}$:

• The LCD of 10 and 5 is 10.
• Rewrite the fractions:
  $\frac{2}{10}$ stays the same,
  $\frac{3}{5} = \frac{6}{10}$.
• Add the fractions:
  $\frac{2}{10} + \frac{6}{10} = \frac{8}{10}$.
• Simplify:
  $\frac{8}{10} = \frac{4}{5}$.

Answer: $\frac{4}{5}$.

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8) $\frac{2}{4} + \frac{1}{2}$:

• Simplify $\frac{2}{4} = \frac{1}{2}$.
• Add the fractions:
  $\frac{1}{2} + \frac{1}{2} = \frac{2}{2} = 1$.

Answer: $1$.

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9) $\frac{2}{10} + \frac{1}{3}$:

• The LCD of 10 and 3 is 30.
• Rewrite the fractions:
  $\frac{2}{10} = \frac{6}{30}$,
  $\frac{1}{3} = \frac{10}{30}$.
• Add the fractions:
  $\frac{6}{30} + \frac{10}{30} = \frac{16}{30}$.
• Simplify:
  $\frac{16}{30} = \frac{8}{15}$.

Answer: $\frac{8}{15}$.

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Would you like more detailed steps for any problem?

Related Questions:

1. How do you find the least common denominator?
2. How do you simplify improper fractions to mixed numbers?
3. What are some techniques for adding fractions with large denominators?
4. How can you convert fractions to decimals?
5. What are examples of adding three or more fractions?

Tip: Always simplify fractions to their lowest terms for a clean and clear final answer!