Math worksheet for adding fractions with unlike denominators.

To solve the problem of adding fractions with unlike denominators, we need to follow these steps:

1. Find a Common Denominator: The least common denominator (LCD) is the smallest number that is a multiple of both denominators.
2. Adjust the Fractions: Rewrite each fraction with the common denominator by multiplying both the numerator and the denominator by the necessary factor.
3. Add the Numerators: Add the numerators of the adjusted fractions while keeping the common denominator.
4. Simplify the Result: Reduce the resulting fraction to its simplest form if possible.

Let's solve each problem step by step.

---

Problem 1: $\frac{1}{4} + \frac{1}{2}$

- Step 1: Find the LCD of 4 and 2. The LCD is 4.
- Step 2: Adjust the fractions:
$$
\frac{1}{4} = \frac{1}{4}, \quad \frac{1}{2} = \frac{1 \times 2}{2 \times 2} = \frac{2}{4}
$$
- Step 3: Add the numerators:
$$
\frac{1}{4} + \frac{2}{4} = \frac{1 + 2}{4} = \frac{3}{4}
$$
- Step 4: Simplify (if needed). $\frac{3}{4}$ is already in simplest form.
- Answer: $\boxed{\frac{3}{4}}$

---

Problem 2: $\frac{3}{4} + \frac{3}{8}$

- Step 1: Find the LCD of 4 and 8. The LCD is 8.
- Step 2: Adjust the fractions:
$$
\frac{3}{4} = \frac{3 \times 2}{4 \times 2} = \frac{6}{8}, \quad \frac{3}{8} = \frac{3}{8}
$$
- Step 3: Add the numerators:
$$
\frac{6}{8} + \frac{3}{8} = \frac{6 + 3}{8} = \frac{9}{8}
$$
- Step 4: Simplify (if needed). $\frac{9}{8}$ is already in simplest form.
- Answer: $\boxed{\frac{9}{8}}$

---

Problem 3: $\frac{2}{4} + \frac{5}{6}$

- Step 1: Find the LCD of 4 and 6. The LCD is 12.
- Step 2: Adjust the fractions:
$$
\frac{2}{4} = \frac{2 \times 3}{4 \times 3} = \frac{6}{12}, \quad \frac{5}{6} = \frac{5 \times 2}{6 \times 2} = \frac{10}{12}
$$
- Step 3: Add the numerators:
$$
\frac{6}{12} + \frac{10}{12} = \frac{6 + 10}{12} = \frac{16}{12}
$$
- Step 4: Simplify:
$$
\frac{16}{12} = \frac{4}{3}
$$
- Answer: $\boxed{\frac{4}{3}}$

---

Problem 4: $\frac{3}{6} + \frac{1}{3}$

- Step 1: Find the LCD of 6 and 3. The LCD is 6.
- Step 2: Adjust the fractions:
$$
\frac{3}{6} = \frac{3}{6}, \quad \frac{1}{3} = \frac{1 \times 2}{3 \times 2} = \frac{2}{6}
$$
- Step 3: Add the numerators:
$$
\frac{3}{6} + \frac{2}{6} = \frac{3 + 2}{6} = \frac{5}{6}
$$
- Step 4: Simplify (if needed). $\frac{5}{6}$ is already in simplest form.
- Answer: $\boxed{\frac{5}{6}}$

---

Problem 5: $\frac{8}{3} + \frac{4}{5}$

- Step 1: Find the LCD of 3 and 5. The LCD is 15.
- Step 2: Adjust the fractions:
$$
\frac{8}{3} = \frac{8 \times 5}{3 \times 5} = \frac{40}{15}, \quad \frac{4}{5} = \frac{4 \times 3}{5 \times 3} = \frac{12}{15}
$$
- Step 3: Add the numerators:
$$
\frac{40}{15} + \frac{12}{15} = \frac{40 + 12}{15} = \frac{52}{15}
$$
- Step 4: Simplify (if needed). $\frac{52}{15}$ is already in simplest form.
- Answer: $\boxed{\frac{52}{15}}$

---

Problem 6: $\frac{2}{5} + \frac{5}{10}$

- Step 1: Find the LCD of 5 and 10. The LCD is 10.
- Step 2: Adjust the fractions:
$$
\frac{2}{5} = \frac{2 \times 2}{5 \times 2} = \frac{4}{10}, \quad \frac{5}{10} = \frac{5}{10}
$$
- Step 3: Add the numerators:
$$
\frac{4}{10} + \frac{5}{10} = \frac{4 + 5}{10} = \frac{9}{10}
$$
- Step 4: Simplify (if needed). $\frac{9}{10}$ is already in simplest form.
- Answer: $\boxed{\frac{9}{10}}$

---

Problem 7: $\frac{2}{3} + \frac{1}{2}$

- Step 1: Find the LCD of 3 and 2. The LCD is 6.
- Step 2: Adjust the fractions:
$$
\frac{2}{3} = \frac{2 \times 2}{3 \times 2} = \frac{4}{6}, \quad \frac{1}{2} = \frac{1 \times 3}{2 \times 3} = \frac{3}{6}
$$
- Step 3: Add the numerators:
$$
\frac{4}{6} + \frac{3}{6} = \frac{4 + 3}{6} = \frac{7}{6}
$$
- Step 4: Simplify (if needed). $\frac{7}{6}$ is already in simplest form.
- Answer: $\boxed{\frac{7}{6}}$

---

Problem 8: $\frac{4}{6} + \frac{5}{8}$

- Step 1: Find the LCD of 6 and 8. The LCD is 24.
- Step 2: Adjust the fractions:
$$
\frac{4}{6} = \frac{4 \times 4}{6 \times 4} = \frac{16}{24}, \quad \frac{5}{8} = \frac{5 \times 3}{8 \times 3} = \frac{15}{24}
$$
- Step 3: Add the numerators:
$$
\frac{16}{24} + \frac{15}{24} = \frac{16 + 15}{24} = \frac{31}{24}
$$
- Step 4: Simplify (if needed). $\frac{31}{24}$ is already in simplest form.
- Answer: $\boxed{\frac{31}{24}}$

---

Problem 9: $\frac{3}{9} + \frac{1}{3}$

- Step 1: Find the LCD of 9 and 3. The LCD is 9.
- Step 2: Adjust the fractions:
$$
\frac{3}{9} = \frac{3}{9}, \quad \frac{1}{3} = \frac{1 \times 3}{3 \times 3} = \frac{3}{9}
$$
- Step 3: Add the numerators:
$$
\frac{3}{9} + \frac{3}{9} = \frac{3 + 3}{9} = \frac{6}{9}
$$
- Step 4: Simplify:
$$
\frac{6}{9} = \frac{2}{3}
$$
- Answer: $\boxed{\frac{2}{3}}$

---

Problem 10: $\frac{6}{4} + \frac{5}{12}$

- Step 1: Find the LCD of 4 and 12. The LCD is 12.
- Step 2: Adjust the fractions:
$$
\frac{6}{4} = \frac{6 \times 3}{4 \times 3} = \frac{18}{12}, \quad \frac{5}{12} = \frac{5}{12}
$$
- Step 3: Add the numerators:
$$
\frac{18}{12} + \frac{5}{12} = \frac{18 + 5}{12} = \frac{23}{12}
$$
- Step 4: Simplify (if needed). $\frac{23}{12}$ is already in simplest form.
- Answer: $\boxed{\frac{23}{12}}$

---

Problem 11: $\frac{4}{6} + \frac{2}{9}$

- Step 1: Find the LCD of 6 and 9. The LCD is 18.
- Step 2: Adjust the fractions:
$$
\frac{4}{6} = \frac{4 \times 3}{6 \times 3} = \frac{12}{18}, \quad \frac{2}{9} = \frac{2 \times 2}{9 \times 2} = \frac{4}{18}
$$
- Step 3: Add the numerators:
$$
\frac{12}{18} + \frac{4}{18} = \frac{12 + 4}{18} = \frac{16}{18}
$$
- Step 4: Simplify:
$$
\frac{16}{18} = \frac{8}{9}
$$
- Answer: $\boxed{\frac{8}{9}}$

---

Problem 12: $\frac{9}{2} + \frac{2}{8}$

- Step 1: Find the LCD of 2 and 8. The LCD is 8.
- Step 2: Adjust the fractions:
$$
\frac{9}{2} = \frac{9 \times 4}{2 \times 4} = \frac{36}{8}, \quad \frac{2}{8} = \frac{2}{8}
$$
- Step 3: Add the numerators:
$$
\frac{36}{8} + \frac{2}{8} = \frac{36 + 2}{8} = \frac{38}{8}
$$
- Step 4: Simplify:
$$
\frac{38}{8} = \frac{19}{4}
$$
- Answer: $\boxed{\frac{19}{4}}$

---

Final Answers:

1. $\boxed{\frac{3}{4}}$
2. $\boxed{\frac{9}{8}}$
3. $\boxed{\frac{4}{3}}$
4. $\boxed{\frac{5}{6}}$
5. $\boxed{\frac{52}{15}}$
6. $\boxed{\frac{9}{10}}$
7. $\boxed{\frac{7}{6}}$
8. $\boxed{\frac{31}{24}}$
9. $\boxed{\frac{2}{3}}$
10. $\boxed{\frac{23}{12}}$
11. $\boxed{\frac{8}{9}}$
12. $\boxed{\frac{19}{4}}$