Adding & Subtracting Fractions (Different Denominator) Worksheet ... - Free Printable

Problem: Solve each problem involving adding and subtracting fractions. Write the answer as a mixed number fraction (if possible).

#### Step-by-Step Solution:

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1) \( \frac{2}{5} - \frac{1}{3} \)

- Find the Least Common Denominator (LCD): The denominators are 5 and 3. The LCD is 15.
- Rewrite the fractions with the LCD:
\[
\frac{2}{5} = \frac{2 \times 3}{5 \times 3} = \frac{6}{15}
\]
\[
\frac{1}{3} = \frac{1 \times 5}{3 \times 5} = \frac{5}{15}
\]
- Subtract the fractions:
\[
\frac{6}{15} - \frac{5}{15} = \frac{6 - 5}{15} = \frac{1}{15}
\]

Answer: \( \frac{1}{15} \)

---

2) \( \frac{4}{5} - \frac{1}{2} \)

- Find the LCD: The denominators are 5 and 2. The LCD is 10.
- Rewrite the fractions with the LCD:
\[
\frac{4}{5} = \frac{4 \times 2}{5 \times 2} = \frac{8}{10}
\]
\[
\frac{1}{2} = \frac{1 \times 5}{2 \times 5} = \frac{5}{10}
\]
- Subtract the fractions:
\[
\frac{8}{10} - \frac{5}{10} = \frac{8 - 5}{10} = \frac{3}{10}
\]

Answer: \( \frac{3}{10} \)

---

3) \( \frac{10}{12} - \frac{2}{3} \)

- Simplify \( \frac{10}{12} \):
\[
\frac{10}{12} = \frac{5}{6} \quad (\text{dividing numerator and denominator by 2})
\]
- Find the LCD: The denominators are 6 and 3. The LCD is 6.
- Rewrite the fractions with the LCD:
\[
\frac{5}{6} = \frac{5}{6}
\]
\[
\frac{2}{3} = \frac{2 \times 2}{3 \times 2} = \frac{4}{6}
\]
- Subtract the fractions:
\[
\frac{5}{6} - \frac{4}{6} = \frac{5 - 4}{6} = \frac{1}{6}
\]

Answer: \( \frac{1}{6} \)

---

4) \( \frac{1}{2} - \frac{1}{5} \)

- Find the LCD: The denominators are 2 and 5. The LCD is 10.
- Rewrite the fractions with the LCD:
\[
\frac{1}{2} = \frac{1 \times 5}{2 \times 5} = \frac{5}{10}
\]
\[
\frac{1}{5} = \frac{1 \times 2}{5 \times 2} = \frac{2}{10}
\]
- Subtract the fractions:
\[
\frac{5}{10} - \frac{2}{10} = \frac{5 - 2}{10} = \frac{3}{10}
\]

Answer: \( \frac{3}{10} \)

---

5) \( \frac{8}{10} - \frac{2}{4} \)

- Simplify the fractions:
\[
\frac{8}{10} = \frac{4}{5} \quad (\text{dividing numerator and denominator by 2})
\]
\[
\frac{2}{4} = \frac{1}{2} \quad (\text{dividing numerator and denominator by 2})
\]
- Find the LCD: The denominators are 5 and 2. The LCD is 10.
- Rewrite the fractions with the LCD:
\[
\frac{4}{5} = \frac{4 \times 2}{5 \times 2} = \frac{8}{10}
\]
\[
\frac{1}{2} = \frac{1 \times 5}{2 \times 5} = \frac{5}{10}
\]
- Subtract the fractions:
\[
\frac{8}{10} - \frac{5}{10} = \frac{8 - 5}{10} = \frac{3}{10}
\]

Answer: \( \frac{3}{10} \)

---

6) \( \frac{4}{6} - \frac{1}{12} \)

- Simplify \( \frac{4}{6} \):
\[
\frac{4}{6} = \frac{2}{3} \quad (\text{dividing numerator and denominator by 2})
\]
- Find the LCD: The denominators are 3 and 12. The LCD is 12.
- Rewrite the fractions with the LCD:
\[
\frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12}
\]
\[
\frac{1}{12} = \frac{1}{12}
\]
- Subtract the fractions:
\[
\frac{8}{12} - \frac{1}{12} = \frac{8 - 1}{12} = \frac{7}{12}
\]

Answer: \( \frac{7}{12} \)

---

7) \( \frac{3}{6} + \frac{3}{8} \)

- Simplify \( \frac{3}{6} \):
\[
\frac{3}{6} = \frac{1}{2} \quad (\text{dividing numerator and denominator by 3})
\]
- Find the LCD: The denominators are 2 and 8. The LCD is 8.
- Rewrite the fractions with the LCD:
\[
\frac{1}{2} = \frac{1 \times 4}{2 \times 4} = \frac{4}{8}
\]
\[
\frac{3}{8} = \frac{3}{8}
\]
- Add the fractions:
\[
\frac{4}{8} + \frac{3}{8} = \frac{4 + 3}{8} = \frac{7}{8}
\]

Answer: \( \frac{7}{8} \)

---

8) \( \frac{10}{12} + \frac{1}{2} \)

- Simplify \( \frac{10}{12} \):
\[
\frac{10}{12} = \frac{5}{6} \quad (\text{dividing numerator and denominator by 2})
\]
- Find the LCD: The denominators are 6 and 2. The LCD is 6.
- Rewrite the fractions with the LCD:
\[
\frac{5}{6} = \frac{5}{6}
\]
\[
\frac{1}{2} = \frac{1 \times 3}{2 \times 3} = \frac{3}{6}
\]
- Add the fractions:
\[
\frac{5}{6} + \frac{3}{6} = \frac{5 + 3}{6} = \frac{8}{6}
\]
- Simplify \( \frac{8}{6} \):
\[
\frac{8}{6} = \frac{4}{3} = 1 \frac{1}{3}
\]

Answer: \( 1 \frac{1}{3} \)

---

9) \( \frac{4}{5} + \frac{5}{12} \)

- Find the LCD: The denominators are 5 and 12. The LCD is 60.
- Rewrite the fractions with the LCD:
\[
\frac{4}{5} = \frac{4 \times 12}{5 \times 12} = \frac{48}{60}
\]
\[
\frac{5}{12} = \frac{5 \times 5}{12 \times 5} = \frac{25}{60}
\]
- Add the fractions:
\[
\frac{48}{60} + \frac{25}{60} = \frac{48 + 25}{60} = \frac{73}{60}
\]
- Convert to a mixed number:
\[
\frac{73}{60} = 1 \frac{13}{60}
\]

Answer: \( 1 \frac{13}{60} \)

---

10) \( \frac{5}{6} + \frac{6}{12} \)

- Simplify \( \frac{6}{12} \):
\[
\frac{6}{12} = \frac{1}{2} \quad (\text{dividing numerator and denominator by 6})
\]
- Find the LCD: The denominators are 6 and 2. The LCD is 6.
- Rewrite the fractions with the LCD:
\[
\frac{5}{6} = \frac{5}{6}
\]
\[
\frac{1}{2} = \frac{1 \times 3}{2 \times 3} = \frac{3}{6}
\]
- Add the fractions:
\[
\frac{5}{6} + \frac{3}{6} = \frac{5 + 3}{6} = \frac{8}{6}
\]
- Simplify \( \frac{8}{6} \):
\[
\frac{8}{6} = \frac{4}{3} = 1 \frac{1}{3}
\]

Answer: \( 1 \frac{1}{3} \)

---

11) \( \frac{1}{3} + \frac{2}{6} \)

- Simplify \( \frac{2}{6} \):
\[
\frac{2}{6} = \frac{1}{3} \quad (\text{dividing numerator and denominator by 2})
\]
- Find the LCD: The denominators are 3 and 3. The LCD is 3.
- Rewrite the fractions with the LCD:
\[
\frac{1}{3} = \frac{1}{3}
\]
\[
\frac{1}{3} = \frac{1}{3}
\]
- Add the fractions:
\[
\frac{1}{3} + \frac{1}{3} = \frac{1 + 1}{3} = \frac{2}{3}
\]

Answer: \( \frac{2}{3} \)

---

12) \( \frac{7}{8} + \frac{8}{10} \)

- Simplify \( \frac{8}{10} \):
\[
\frac{8}{10} = \frac{4}{5} \quad (\text{dividing numerator and denominator by 2})
\]
- Find the LCD: The denominators are 8 and 5. The LCD is 40.
- Rewrite the fractions with the LCD:
\[
\frac{7}{8} = \frac{7 \times 5}{8 \times 5} = \frac{35}{40}
\]
\[
\frac{4}{5} = \frac{4 \times 8}{5 \times 8} = \frac{32}{40}
\]
- Add the fractions:
\[
\frac{35}{40} + \frac{32}{40} = \frac{35 + 32}{40} = \frac{67}{40}
\]
- Convert to a mixed number:
\[
\frac{67}{40} = 1 \frac{27}{40}
\]

Answer: \( 1 \frac{27}{40} \)

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Final Answers:

1. \( \frac{1}{15} \)
2. \( \frac{3}{10} \)
3. \( \frac{1}{6} \)
4. \( \frac{3}{10} \)
5. \( \frac{3}{10} \)
6. \( \frac{7}{12} \)
7. \( \frac{7}{8} \)
8. \( 1 \frac{1}{3} \)
9. \( 1 \frac{13}{60} \)
10. \( 1 \frac{1}{3} \)
11. \( \frac{2}{3} \)
12. \( 1 \frac{27}{40} \)

\boxed{\text{See above for detailed steps and answers.}}