Math worksheet for practicing addition and subtraction of mixed fractions with 12 problems.

Sure! Let’s solve each of the 12 problems step by step. The goal is to add or subtract mixed fractions and express each answer in lowest terms (simplified form).

---

🔢 General Strategy:

1. Convert mixed numbers to improper fractions (optional, but helpful for some).
2. Find a common denominator.
3. Add or subtract numerators.
4. Simplify the result (convert back to mixed number if needed).
5. Reduce the fraction part to lowest terms.

---

## ✔ Problem-by-Problem Solutions:

---

1. $2\frac{1}{5} + 1\frac{3}{4}$

- Convert to improper fractions:
- $2\frac{1}{5} = \frac{11}{5}$
- $1\frac{3}{4} = \frac{7}{4}$

- Common denominator: LCM of 5 and 4 = 20

- Convert:
- $\frac{11}{5} = \frac{44}{20}$
- $\frac{7}{4} = \frac{35}{20}$

- Add: $\frac{44 + 35}{20} = \frac{79}{20}$

- Convert to mixed number: $3\frac{19}{20}$ → Already in lowest terms.

✔ Answer: $3\frac{19}{20}$

---

2. $3\frac{1}{2} - 2\frac{2}{3}$

- Convert:
- $3\frac{1}{2} = \frac{7}{2}$
- $2\frac{2}{3} = \frac{8}{3}$

- Common denominator: LCM of 2 and 3 = 6

- Convert:
- $\frac{7}{2} = \frac{21}{6}$
- $\frac{8}{3} = \frac{16}{6}$

- Subtract: $\frac{21 - 16}{6} = \frac{5}{6}$

✔ Answer: $\frac{5}{6}$

---

3. $3\frac{1}{2} - 3\frac{1}{2}$

- Same number minus itself → 0

✔ Answer: $0$

---

4. $5\frac{3}{4} - 5\frac{1}{4}$

- Subtract whole parts: $5 - 5 = 0$
- Subtract fractions: $\frac{3}{4} - \frac{1}{4} = \frac{2}{4} = \frac{1}{2}$

✔ Answer: $\frac{1}{2}$

---

5. $1\frac{1}{2} + 2\frac{3}{5}$

- Convert:
- $1\frac{1}{2} = \frac{3}{2}$
- $2\frac{3}{5} = \frac{13}{5}$

- Common denominator: LCM of 2 and 5 = 10

- Convert:
- $\frac{3}{2} = \frac{15}{10}$
- $\frac{13}{5} = \frac{26}{10}$

- Add: $\frac{15 + 26}{10} = \frac{41}{10} = 4\frac{1}{10}$

✔ Answer: $4\frac{1}{10}$

---

6. $3\frac{1}{2} - 2\frac{5}{9}$

- Convert:
- $3\frac{1}{2} = \frac{7}{2}$
- $2\frac{5}{9} = \frac{23}{9}$

- Common denominator: LCM of 2 and 9 = 18

- Convert:
- $\frac{7}{2} = \frac{63}{18}$
- $\frac{23}{9} = \frac{46}{18}$

- Subtract: $\frac{63 - 46}{18} = \frac{17}{18}$

✔ Answer: $\frac{17}{18}$

---

7. $2\frac{3}{4} + 1\frac{1}{5}$

- Convert:
- $2\frac{3}{4} = \frac{11}{4}$
- $1\frac{1}{5} = \frac{6}{5}$

- Common denominator: LCM of 4 and 5 = 20

- Convert:
- $\frac{11}{4} = \frac{55}{20}$
- $\frac{6}{5} = \frac{24}{20}$

- Add: $\frac{55 + 24}{20} = \frac{79}{20} = 3\frac{19}{20}$

✔ Answer: $3\frac{19}{20}$

---

8. $3\frac{1}{4} - 2\frac{3}{8}$

- Convert:
- $3\frac{1}{4} = \frac{13}{4}$
- $2\frac{3}{8} = \frac{19}{8}$

- Common denominator: LCM of 4 and 8 = 8

- Convert:
- $\frac{13}{4} = \frac{26}{8}$
- $\frac{19}{8} = \frac{19}{8}$

- Subtract: $\frac{26 - 19}{8} = \frac{7}{8}$

✔ Answer: $\frac{7}{8}$

---

9. $3\frac{1}{2} - 1\frac{1}{2}$

- Whole parts: $3 - 1 = 2$
- Fractions: $\frac{1}{2} - \frac{1}{2} = 0$

✔ Answer: $2$

---

10. $5\frac{1}{2} + 5\frac{1}{4}$

- Convert:
- $5\frac{1}{2} = \frac{11}{2}$
- $5\frac{1}{4} = \frac{21}{4}$

- Common denominator: LCM of 2 and 4 = 4

- Convert:
- $\frac{11}{2} = \frac{22}{4}$
- $\frac{21}{4} = \frac{21}{4}$

- Add: $\frac{22 + 21}{4} = \frac{43}{4} = 10\frac{3}{4}$

✔ Answer: $10\frac{3}{4}$

---

11. $1\frac{10}{11} - 1\frac{1}{3}$

- Convert:
- $1\frac{10}{11} = \frac{21}{11}$
- $1\frac{1}{3} = \frac{4}{3}$

- Common denominator: LCM of 11 and 3 = 33

- Convert:
- $\frac{21}{11} = \frac{63}{33}$
- $\frac{4}{3} = \frac{44}{33}$

- Subtract: $\frac{63 - 44}{33} = \frac{19}{33}$

✔ Answer: $\frac{19}{33}$

---

12. $1\frac{5}{12} + 3\frac{1}{3}$

- Convert:
- $1\frac{5}{12} = \frac{17}{12}$
- $3\frac{1}{3} = \frac{10}{3}$

- Common denominator: LCM of 12 and 3 = 12

- Convert:
- $\frac{17}{12} = \frac{17}{12}$
- $\frac{10}{3} = \frac{40}{12}$

- Add: $\frac{17 + 40}{12} = \frac{57}{12}$

- Simplify: Divide numerator and denominator by 3 → $\frac{19}{4} = 4\frac{3}{4}$

✔ Answer: $4\frac{3}{4}$

---

## 📋 Final Answers Summary:

1. $3\frac{19}{20}$
2. $\frac{5}{6}$
3. $0$
4. $\frac{1}{2}$
5. $4\frac{1}{10}$
6. $\frac{17}{18}$
7. $3\frac{19}{20}$
8. $\frac{7}{8}$
9. $2$
10. $10\frac{3}{4}$
11. $\frac{19}{33}$
12. $4\frac{3}{4}$

---

Let me know if you’d like to see any step explained further! 😊