Math worksheet for adding and subtracting mixed fractions with 12 practice problems.

To solve the problems involving adding and subtracting mixed fractions, we need to follow these steps:

1. Convert mixed fractions to improper fractions.
2. Find a common denominator if necessary.
3. Perform the addition or subtraction.
4. Simplify the result to its lowest terms.
5. Convert back to a mixed fraction if needed.

Let's solve each problem step by step.

---

Problem 1: \( 2\frac{1}{5} + 1\frac{3}{4} \)

#### Step 1: Convert to improper fractions
- \( 2\frac{1}{5} = \frac{2 \times 5 + 1}{5} = \frac{11}{5} \)
- \( 1\frac{3}{4} = \frac{1 \times 4 + 3}{4} = \frac{7}{4} \)

#### Step 2: Find a common denominator
The denominators are 5 and 4. The least common denominator (LCD) is 20.

- Convert \( \frac{11}{5} \) to a fraction with denominator 20:
\[
\frac{11}{5} = \frac{11 \times 4}{5 \times 4} = \frac{44}{20}
\]
- Convert \( \frac{7}{4} \) to a fraction with denominator 20:
\[
\frac{7}{4} = \frac{7 \times 5}{4 \times 5} = \frac{35}{20}
\]

#### Step 3: Add the fractions
\[
\frac{44}{20} + \frac{35}{20} = \frac{44 + 35}{20} = \frac{79}{20}
\]

#### Step 4: Convert back to a mixed fraction
\[
\frac{79}{20} = 3 \frac{19}{20}
\]

#### Final Answer:
\[
\boxed{3\frac{19}{20}}
\]

---

Problem 2: \( 3\frac{1}{2} - 2\frac{2}{3} \)

#### Step 1: Convert to improper fractions
- \( 3\frac{1}{2} = \frac{3 \times 2 + 1}{2} = \frac{7}{2} \)
- \( 2\frac{2}{3} = \frac{2 \times 3 + 2}{3} = \frac{8}{3} \)

#### Step 2: Find a common denominator
The denominators are 2 and 3. The least common denominator (LCD) is 6.

- Convert \( \frac{7}{2} \) to a fraction with denominator 6:
\[
\frac{7}{2} = \frac{7 \times 3}{2 \times 3} = \frac{21}{6}
\]
- Convert \( \frac{8}{3} \) to a fraction with denominator 6:
\[
\frac{8}{3} = \frac{8 \times 2}{3 \times 2} = \frac{16}{6}
\]

#### Step 3: Subtract the fractions
\[
\frac{21}{6} - \frac{16}{6} = \frac{21 - 16}{6} = \frac{5}{6}
\]

#### Final Answer:
\[
\boxed{\frac{5}{6}}
\]

---

Problem 3: \( 3\frac{1}{2} - 3\frac{1}{2} \)

#### Step 1: Convert to improper fractions
- \( 3\frac{1}{2} = \frac{3 \times 2 + 1}{2} = \frac{7}{2} \)

#### Step 2: Subtract the fractions
\[
\frac{7}{2} - \frac{7}{2} = \frac{7 - 7}{2} = \frac{0}{2} = 0
\]

#### Final Answer:
\[
\boxed{0}
\]

---

Problem 4: \( 5\frac{3}{4} - 5\frac{1}{4} \)

#### Step 1: Convert to improper fractions
- \( 5\frac{3}{4} = \frac{5 \times 4 + 3}{4} = \frac{23}{4} \)
- \( 5\frac{1}{4} = \frac{5 \times 4 + 1}{4} = \frac{21}{4} \)

#### Step 2: Subtract the fractions
\[
\frac{23}{4} - \frac{21}{4} = \frac{23 - 21}{4} = \frac{2}{4} = \frac{1}{2}
\]

#### Final Answer:
\[
\boxed{\frac{1}{2}}
\]

---

Problem 5: \( 1\frac{1}{2} + 2\frac{3}{5} \)

#### Step 1: Convert to improper fractions
- \( 1\frac{1}{2} = \frac{1 \times 2 + 1}{2} = \frac{3}{2} \)
- \( 2\frac{3}{5} = \frac{2 \times 5 + 3}{5} = \frac{13}{5} \)

#### Step 2: Find a common denominator
The denominators are 2 and 5. The least common denominator (LCD) is 10.

- Convert \( \frac{3}{2} \) to a fraction with denominator 10:
\[
\frac{3}{2} = \frac{3 \times 5}{2 \times 5} = \frac{15}{10}
\]
- Convert \( \frac{13}{5} \) to a fraction with denominator 10:
\[
\frac{13}{5} = \frac{13 \times 2}{5 \times 2} = \frac{26}{10}
\]

#### Step 3: Add the fractions
\[
\frac{15}{10} + \frac{26}{10} = \frac{15 + 26}{10} = \frac{41}{10}
\]

#### Step 4: Convert back to a mixed fraction
\[
\frac{41}{10} = 4 \frac{1}{10}
\]

#### Final Answer:
\[
\boxed{4\frac{1}{10}}
\]

---

Problem 6: \( 3\frac{1}{2} - 2\frac{5}{9} \)

#### Step 1: Convert to improper fractions
- \( 3\frac{1}{2} = \frac{3 \times 2 + 1}{2} = \frac{7}{2} \)
- \( 2\frac{5}{9} = \frac{2 \times 9 + 5}{9} = \frac{23}{9} \)

#### Step 2: Find a common denominator
The denominators are 2 and 9. The least common denominator (LCD) is 18.

- Convert \( \frac{7}{2} \) to a fraction with denominator 18:
\[
\frac{7}{2} = \frac{7 \times 9}{2 \times 9} = \frac{63}{18}
\]
- Convert \( \frac{23}{9} \) to a fraction with denominator 18:
\[
\frac{23}{9} = \frac{23 \times 2}{9 \times 2} = \frac{46}{18}
\]

#### Step 3: Subtract the fractions
\[
\frac{63}{18} - \frac{46}{18} = \frac{63 - 46}{18} = \frac{17}{18}
\]

#### Final Answer:
\[
\boxed{\frac{17}{18}}
\]

---

Problem 7: \( 2\frac{3}{4} + 1\frac{1}{5} \)

#### Step 1: Convert to improper fractions
- \( 2\frac{3}{4} = \frac{2 \times 4 + 3}{4} = \frac{11}{4} \)
- \( 1\frac{1}{5} = \frac{1 \times 5 + 1}{5} = \frac{6}{5} \)

#### Step 2: Find a common denominator
The denominators are 4 and 5. The least common denominator (LCD) is 20.

- Convert \( \frac{11}{4} \) to a fraction with denominator 20:
\[
\frac{11}{4} = \frac{11 \times 5}{4 \times 5} = \frac{55}{20}
\]
- Convert \( \frac{6}{5} \) to a fraction with denominator 20:
\[
\frac{6}{5} = \frac{6 \times 4}{5 \times 4} = \frac{24}{20}
\]

#### Step 3: Add the fractions
\[
\frac{55}{20} + \frac{24}{20} = \frac{55 + 24}{20} = \frac{79}{20}
\]

#### Step 4: Convert back to a mixed fraction
\[
\frac{79}{20} = 3 \frac{19}{20}
\]

#### Final Answer:
\[
\boxed{3\frac{19}{20}}
\]

---

Problem 8: \( 3\frac{1}{4} - 2\frac{3}{8} \)

#### Step 1: Convert to improper fractions
- \( 3\frac{1}{4} = \frac{3 \times 4 + 1}{4} = \frac{13}{4} \)
- \( 2\frac{3}{8} = \frac{2 \times 8 + 3}{8} = \frac{19}{8} \)

#### Step 2: Find a common denominator
The denominators are 4 and 8. The least common denominator (LCD) is 8.

- Convert \( \frac{13}{4} \) to a fraction with denominator 8:
\[
\frac{13}{4} = \frac{13 \times 2}{4 \times 2} = \frac{26}{8}
\]
- \( \frac{19}{8} \) already has denominator 8.

#### Step 3: Subtract the fractions
\[
\frac{26}{8} - \frac{19}{8} = \frac{26 - 19}{8} = \frac{7}{8}
\]

#### Final Answer:
\[
\boxed{\frac{7}{8}}
\]

---

Problem 9: \( 3\frac{1}{2} - 1\frac{1}{2} \)

#### Step 1: Convert to improper fractions
- \( 3\frac{1}{2} = \frac{3 \times 2 + 1}{2} = \frac{7}{2} \)
- \( 1\frac{1}{2} = \frac{1 \times 2 + 1}{2} = \frac{3}{2} \)

#### Step 2: Subtract the fractions
\[
\frac{7}{2} - \frac{3}{2} = \frac{7 - 3}{2} = \frac{4}{2} = 2
\]

#### Final Answer:
\[
\boxed{2}
\]

---

Problem 10: \( 5\frac{1}{2} + 5\frac{1}{4} \)

#### Step 1: Convert to improper fractions
- \( 5\frac{1}{2} = \frac{5 \times 2 + 1}{2} = \frac{11}{2} \)
- \( 5\frac{1}{4} = \frac{5 \times 4 + 1}{4} = \frac{21}{4} \)

#### Step 2: Find a common denominator
The denominators are 2 and 4. The least common denominator (LCD) is 4.

- Convert \( \frac{11}{2} \) to a fraction with denominator 4:
\[
\frac{11}{2} = \frac{11 \times 2}{2 \times 2} = \frac{22}{4}
\]
- \( \frac{21}{4} \) already has denominator 4.

#### Step 3: Add the fractions
\[
\frac{22}{4} + \frac{21}{4} = \frac{22 + 21}{4} = \frac{43}{4}
\]

#### Step 4: Convert back to a mixed fraction
\[
\frac{43}{4} = 10 \frac{3}{4}
\]

#### Final Answer:
\[
\boxed{10\frac{3}{4}}
\]

---

Problem 11: \( 1\frac{10}{11} - 1\frac{1}{3} \)

#### Step 1: Convert to improper fractions
- \( 1\frac{10}{11} = \frac{1 \times 11 + 10}{11} = \frac{21}{11} \)
- \( 1\frac{1}{3} = \frac{1 \times 3 + 1}{3} = \frac{4}{3} \)

#### Step 2: Find a common denominator
The denominators are 11 and 3. The least common denominator (LCD) is 33.

- Convert \( \frac{21}{11} \) to a fraction with denominator 33:
\[
\frac{21}{11} = \frac{21 \times 3}{11 \times 3} = \frac{63}{33}
\]
- Convert \( \frac{4}{3} \) to a fraction with denominator 33:
\[
\frac{4}{3} = \frac{4 \times 11}{3 \times 11} = \frac{44}{33}
\]

#### Step 3: Subtract the fractions
\[
\frac{63}{33} - \frac{44}{33} = \frac{63 - 44}{33} = \frac{19}{33}
\]

#### Final Answer:
\[
\boxed{\frac{19}{33}}
\]

---

Problem 12: \( 1\frac{5}{12} + 3\frac{1}{3} \)

#### Step 1: Convert to improper fractions
- \( 1\frac{5}{12} = \frac{1 \times 12 + 5}{12} = \frac{17}{12} \)
- \( 3\frac{1}{3} = \frac{3 \times 3 + 1}{3} = \frac{10}{3} \)

#### Step 2: Find a common denominator
The denominators are 12 and 3. The least common denominator (LCD) is 12.

- \( \frac{17}{12} \) already has denominator 12.
- Convert \( \frac{10}{3} \) to a fraction with denominator 12:
\[
\frac{10}{3} = \frac{10 \times 4}{3 \times 4} = \frac{40}{12}
\]

#### Step 3: Add the fractions
\[
\frac{17}{12} + \frac{40}{12} = \frac{17 + 40}{12} = \frac{57}{12}
\]

#### Step 4: Simplify the fraction
\[
\frac{57}{12} = \frac{19}{4}
\]

#### Step 5: Convert back to a mixed fraction
\[
\frac{19}{4} = 4 \frac{3}{4}
\]

#### Final Answer:
\[
\boxed{4\frac{3}{4}}
\]

---

Final Answers:

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