Adding and Subtracting Unlike Denominators worksheet - Free Printable

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!