Practice sheet for adding and subtracting fractions with unlike denominators.

Let's solve each of these fraction problems step by step. The key idea when adding or subtracting fractions with unlike denominators is to:

1. Find the Least Common Denominator (LCD).
2. Convert each fraction to an equivalent fraction with the LCD.
3. Add or subtract the numerators.
4. Simplify the result if needed.

---

Problem 1:

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

- LCD of 3 and 2 is 6
- Convert:
$$
\frac{2}{3} = \frac{4}{6},\quad \frac{1}{2} = \frac{3}{6}
$$
- Add:
$$
\frac{4}{6} + \frac{3}{6} = \frac{7}{6}
$$
- Answer: $\boxed{\frac{7}{6}}$ or $1\frac{1}{6}$

---

Problem 2:

$$
\frac{2}{5} + \frac{1}{10}
$$

- LCD of 5 and 10 is 10
- Convert:
$$
\frac{2}{5} = \frac{4}{10},\quad \frac{1}{10} = \frac{1}{10}
$$
- Add:
$$
\frac{4}{10} + \frac{1}{10} = \frac{5}{10} = \frac{1}{2}
$$
- Answer: $\boxed{\frac{1}{2}}$

---

Problem 3:

$$
\frac{1}{5} + \frac{2}{4}
$$

- Simplify $\frac{2}{4} = \frac{1}{2}$
- Now: $\frac{1}{5} + \frac{1}{2}$
- LCD of 5 and 2 is 10
- Convert:
$$
\frac{1}{5} = \frac{2}{10},\quad \frac{1}{2} = \frac{5}{10}
$$
- Add:
$$
\frac{2}{10} + \frac{5}{10} = \frac{7}{10}
$$
- Answer: $\boxed{\frac{7}{10}}$

---

Problem 4:

$$
\frac{3}{5} + \frac{3}{8}
$$

- LCD of 5 and 8 is 40
- Convert:
$$
\frac{3}{5} = \frac{24}{40},\quad \frac{3}{8} = \frac{15}{40}
$$
- Add:
$$
\frac{24}{40} + \frac{15}{40} = \frac{39}{40}
$$
- Answer: $\boxed{\frac{39}{40}}$

---

Problem 5:

$$
\frac{2}{7} + \frac{1}{4}
$$

- LCD of 7 and 4 is 28
- Convert:
$$
\frac{2}{7} = \frac{8}{28},\quad \frac{1}{4} = \frac{7}{28}
$$
- Add:
$$
\frac{8}{28} + \frac{7}{28} = \frac{15}{28}
$$
- Answer: $\boxed{\frac{15}{28}}$

---

Problem 6:

$$
\frac{3}{5} - \frac{3}{10}
$$

- LCD of 5 and 10 is 10
- Convert:
$$
\frac{3}{5} = \frac{6}{10},\quad \frac{3}{10} = \frac{3}{10}
$$
- Subtract:
$$
\frac{6}{10} - \frac{3}{10} = \frac{3}{10}
$$
- Answer: $\boxed{\frac{3}{10}}$

---

Problem 7:

$$
\frac{4}{6} - \frac{1}{12}
$$

- Simplify $\frac{4}{6} = \frac{2}{3}$
- Now: $\frac{2}{3} - \frac{1}{12}$
- LCD of 3 and 12 is 12
- Convert:
$$
\frac{2}{3} = \frac{8}{12},\quad \frac{1}{12} = \frac{1}{12}
$$
- Subtract:
$$
\frac{8}{12} - \frac{1}{12} = \frac{7}{12}
$$
- Answer: $\boxed{\frac{7}{12}}$

---

Problem 8:

$$
\frac{4}{6} - \frac{1}{2}
$$

- Simplify $\frac{4}{6} = \frac{2}{3}$
- Now: $\frac{2}{3} - \frac{1}{2}$
- LCD of 3 and 2 is 6
- Convert:
$$
\frac{2}{3} = \frac{4}{6},\quad \frac{1}{2} = \frac{3}{6}
$$
- Subtract:
$$
\frac{4}{6} - \frac{3}{6} = \frac{1}{6}
$$
- Answer: $\boxed{\frac{1}{6}}$

---

Problem 9:

$$
\frac{3}{4} - \frac{1}{3}
$$

- LCD of 4 and 3 is 12
- Convert:
$$
\frac{3}{4} = \frac{9}{12},\quad \frac{1}{3} = \frac{4}{12}
$$
- Subtract:
$$
\frac{9}{12} - \frac{4}{12} = \frac{5}{12}
$$
- Answer: $\boxed{\frac{5}{12}}$

---

Problem 10:

$$
\frac{7}{8} - \frac{3}{4}
$$

- LCD of 8 and 4 is 8
- Convert:
$$
\frac{3}{4} = \frac{6}{8}
$$
- Subtract:
$$
\frac{7}{8} - \frac{6}{8} = \frac{1}{8}
$$
- Answer: $\boxed{\frac{1}{8}}$

---

✔ Final Answers:

| Problem | Answer |
|--------|----------------|
| 1 | $\frac{7}{6}$ |
| 2 | $\frac{1}{2}$ |
| 3 | $\frac{7}{10}$|
| 4 | $\frac{39}{40}$|
| 5 | $\frac{15}{28}$|
| 6 | $\frac{3}{10}$|
| 7 | $\frac{7}{12}$|
| 8 | $\frac{1}{6}$ |
| 9 | $\frac{5}{12}$|
| 10 | $\frac{1}{8}$ |

Let me know if you'd like this in a printable format!