Twelve fraction addition problems requiring students to find common denominators and simplify their answers.

Problem Overview:

The task is to add fractions and reduce the resulting sums to their lowest terms. Each fraction addition problem needs to be solved step by step, ensuring that the final answer is in its simplest form.

Solution:

#### 1. \( \frac{2}{3} + \frac{2}{3} \)
- Step 1: Add the numerators since the denominators are the same.
\[
\frac{2}{3} + \frac{2}{3} = \frac{2 + 2}{3} = \frac{4}{3}
\]
- Step 2: The fraction \( \frac{4}{3} \) is already in its lowest terms.
- Final Answer: \( \frac{4}{3} \)

#### 2. \( \frac{3}{5} + \frac{7}{8} \)
- Step 1: Find the least common denominator (LCD) of 5 and 8. The LCD is 40.
- Step 2: Rewrite each fraction with the LCD as the denominator.
\[
\frac{3}{5} = \frac{3 \times 8}{5 \times 8} = \frac{24}{40}
\]
\[
\frac{7}{8} = \frac{7 \times 5}{8 \times 5} = \frac{35}{40}
\]
- Step 3: Add the fractions.
\[
\frac{24}{40} + \frac{35}{40} = \frac{24 + 35}{40} = \frac{59}{40}
\]
- Step 4: The fraction \( \frac{59}{40} \) is already in its lowest terms.
- Final Answer: \( \frac{59}{40} \)

#### 3. \( \frac{2}{4} + \frac{1}{3} \)
- Step 1: Simplify \( \frac{2}{4} \) to \( \frac{1}{2} \).
- Step 2: Find the LCD of 2 and 3. The LCD is 6.
- Step 3: Rewrite each fraction with the LCD as the denominator.
\[
\frac{1}{2} = \frac{1 \times 3}{2 \times 3} = \frac{3}{6}
\]
\[
\frac{1}{3} = \frac{1 \times 2}{3 \times 2} = \frac{2}{6}
\]
- Step 4: Add the fractions.
\[
\frac{3}{6} + \frac{2}{6} = \frac{3 + 2}{6} = \frac{5}{6}
\]
- Step 5: The fraction \( \frac{5}{6} \) is already in its lowest terms.
- Final Answer: \( \frac{5}{6} \)

#### 4. \( \frac{1}{5} + \frac{3}{6} \)
- Step 1: Simplify \( \frac{3}{6} \) to \( \frac{1}{2} \).
- Step 2: Find the LCD of 5 and 2. The LCD is 10.
- Step 3: Rewrite each fraction with the LCD as the denominator.
\[
\frac{1}{5} = \frac{1 \times 2}{5 \times 2} = \frac{2}{10}
\]
\[
\frac{1}{2} = \frac{1 \times 5}{2 \times 5} = \frac{5}{10}
\]
- Step 4: Add the fractions.
\[
\frac{2}{10} + \frac{5}{10} = \frac{2 + 5}{10} = \frac{7}{10}
\]
- Step 5: The fraction \( \frac{7}{10} \) is already in its lowest terms.
- Final Answer: \( \frac{7}{10} \)

#### 5. \( \frac{3}{5} + \frac{6}{8} \)
- Step 1: Simplify \( \frac{6}{8} \) to \( \frac{3}{4} \).
- Step 2: Find the LCD of 5 and 4. The LCD is 20.
- Step 3: Rewrite each fraction with the LCD as the denominator.
\[
\frac{3}{5} = \frac{3 \times 4}{5 \times 4} = \frac{12}{20}
\]
\[
\frac{3}{4} = \frac{3 \times 5}{4 \times 5} = \frac{15}{20}
\]
- Step 4: Add the fractions.
\[
\frac{12}{20} + \frac{15}{20} = \frac{12 + 15}{20} = \frac{27}{20}
\]
- Step 5: The fraction \( \frac{27}{20} \) is already in its lowest terms.
- Final Answer: \( \frac{27}{20} \)

#### 6. \( \frac{3}{4} + \frac{2}{5} \)
- Step 1: Find the LCD of 4 and 5. The LCD is 20.
- Step 2: Rewrite each fraction with the LCD as the denominator.
\[
\frac{3}{4} = \frac{3 \times 5}{4 \times 5} = \frac{15}{20}
\]
\[
\frac{2}{5} = \frac{2 \times 4}{5 \times 4} = \frac{8}{20}
\]
- Step 3: Add the fractions.
\[
\frac{15}{20} + \frac{8}{20} = \frac{15 + 8}{20} = \frac{23}{20}
\]
- Step 4: The fraction \( \frac{23}{20} \) is already in its lowest terms.
- Final Answer: \( \frac{23}{20} \)

#### 7. \( \frac{4}{6} + \frac{1}{8} \)
- Step 1: Simplify \( \frac{4}{6} \) to \( \frac{2}{3} \).
- Step 2: Find the LCD of 3 and 8. The LCD is 24.
- Step 3: Rewrite each fraction with the LCD as the denominator.
\[
\frac{2}{3} = \frac{2 \times 8}{3 \times 8} = \frac{16}{24}
\]
\[
\frac{1}{8} = \frac{1 \times 3}{8 \times 3} = \frac{3}{24}
\]
- Step 4: Add the fractions.
\[
\frac{16}{24} + \frac{3}{24} = \frac{16 + 3}{24} = \frac{19}{24}
\]
- Step 5: The fraction \( \frac{19}{24} \) is already in its lowest terms.
- Final Answer: \( \frac{19}{24} \)

#### 8. \( \frac{2}{5} + \frac{5}{6} \)
- Step 1: Find the LCD of 5 and 6. The LCD is 30.
- Step 2: Rewrite each fraction with the LCD as the denominator.
\[
\frac{2}{5} = \frac{2 \times 6}{5 \times 6} = \frac{12}{30}
\]
\[
\frac{5}{6} = \frac{5 \times 5}{6 \times 5} = \frac{25}{30}
\]
- Step 3: Add the fractions.
\[
\frac{12}{30} + \frac{25}{30} = \frac{12 + 25}{30} = \frac{37}{30}
\]
- Step 4: The fraction \( \frac{37}{30} \) is already in its lowest terms.
- Final Answer: \( \frac{37}{30} \)

#### 9. \( \frac{3}{6} + \frac{2}{3} \)
- Step 1: Simplify \( \frac{3}{6} \) to \( \frac{1}{2} \).
- Step 2: Find the LCD of 2 and 3. The LCD is 6.
- Step 3: Rewrite each fraction with the LCD as the denominator.
\[
\frac{1}{2} = \frac{1 \times 3}{2 \times 3} = \frac{3}{6}
\]
\[
\frac{2}{3} = \frac{2 \times 2}{3 \times 2} = \frac{4}{6}
\]
- Step 4: Add the fractions.
\[
\frac{3}{6} + \frac{4}{6} = \frac{3 + 4}{6} = \frac{7}{6}
\]
- Step 5: The fraction \( \frac{7}{6} \) is already in its lowest terms.
- Final Answer: \( \frac{7}{6} \)

#### 10. \( \frac{5}{6} + \frac{3}{4} \)
- Step 1: Find the LCD of 6 and 4. The LCD is 12.
- Step 2: Rewrite each fraction with the LCD as the denominator.
\[
\frac{5}{6} = \frac{5 \times 2}{6 \times 2} = \frac{10}{12}
\]
\[
\frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12}
\]
- Step 3: Add the fractions.
\[
\frac{10}{12} + \frac{9}{12} = \frac{10 + 9}{12} = \frac{19}{12}
\]
- Step 4: The fraction \( \frac{19}{12} \) is already in its lowest terms.
- Final Answer: \( \frac{19}{12} \)

#### 11. \( \frac{4}{5} + \frac{2}{6} \)
- Step 1: Simplify \( \frac{2}{6} \) to \( \frac{1}{3} \).
- Step 2: Find the LCD of 5 and 3. The LCD is 15.
- Step 3: Rewrite each fraction with the LCD as the denominator.
\[
\frac{4}{5} = \frac{4 \times 3}{5 \times 3} = \frac{12}{15}
\]
\[
\frac{1}{3} = \frac{1 \times 5}{3 \times 5} = \frac{5}{15}
\]
- Step 4: Add the fractions.
\[
\frac{12}{15} + \frac{5}{15} = \frac{12 + 5}{15} = \frac{17}{15}
\]
- Step 5: The fraction \( \frac{17}{15} \) is already in its lowest terms.
- Final Answer: \( \frac{17}{15} \)

#### 12. \( \frac{1}{3} + \frac{2}{8} \)
- Step 1: Simplify \( \frac{2}{8} \) to \( \frac{1}{4} \).
- Step 2: Find the LCD of 3 and 4. The LCD is 12.
- Step 3: Rewrite each fraction with the LCD as the denominator.
\[
\frac{1}{3} = \frac{1 \times 4}{3 \times 4} = \frac{4}{12}
\]
\[
\frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12}
\]
- Step 4: Add the fractions.
\[
\frac{4}{12} + \frac{3}{12} = \frac{4 + 3}{12} = \frac{7}{12}
\]
- Step 5: The fraction \( \frac{7}{12} \) is already in its lowest terms.
- Final Answer: \( \frac{7}{12} \)

Final Answers:

\[
\boxed{
\begin{array}{ll}
1. & \frac{4}{3} \\
2. & \frac{59}{40} \\
3. & \frac{5}{6} \\
4. & \frac{7}{10} \\
5. & \frac{27}{20} \\
6. & \frac{23}{20} \\
7. & \frac{19}{24} \\
8. & \frac{37}{30} \\
9. & \frac{7}{6} \\
10. & \frac{19}{12} \\
11. & \frac{17}{15} \\
12. & \frac{7}{12} \\
\end{array}
}
\]