Printable worksheet for practicing adding and subtracting mixed fractions with 12 problems.

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

1. Convert mixed fractions to improper fractions (if necessary).
2. Find a common denominator for the fractions.
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.

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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.

#### Step 3: Rewrite fractions with the common denominator
- \( \frac{11}{5} = \frac{11 \times 4}{5 \times 4} = \frac{44}{20} \)
- \( \frac{7}{4} = \frac{7 \times 5}{4 \times 5} = \frac{35}{20} \)

#### Step 4: Add the fractions
\[ \frac{44}{20} + \frac{35}{20} = \frac{44 + 35}{20} = \frac{79}{20} \]

#### Step 5: Convert back to a mixed fraction
\[ \frac{79}{20} = 3 \frac{19}{20} \]

Answer: \( 3 \frac{19}{20} \)

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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 LCD is 6.

#### Step 3: Rewrite fractions with the common denominator
- \( \frac{7}{2} = \frac{7 \times 3}{2 \times 3} = \frac{21}{6} \)
- \( \frac{8}{3} = \frac{8 \times 2}{3 \times 2} = \frac{16}{6} \)

#### Step 4: Subtract the fractions
\[ \frac{21}{6} - \frac{16}{6} = \frac{21 - 16}{6} = \frac{5}{6} \]

Answer: \( \frac{5}{6} \)

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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
\[ \frac{7}{2} - \frac{7}{2} = \frac{7 - 7}{2} = \frac{0}{2} = 0 \]

Answer: \( 0 \)

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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
\[ \frac{23}{4} - \frac{21}{4} = \frac{23 - 21}{4} = \frac{2}{4} = \frac{1}{2} \]

Answer: \( \frac{1}{2} \)

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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 LCD is 10.

#### Step 3: Rewrite fractions with the common denominator
- \( \frac{3}{2} = \frac{3 \times 5}{2 \times 5} = \frac{15}{10} \)
- \( \frac{13}{5} = \frac{13 \times 2}{5 \times 2} = \frac{26}{10} \)

#### Step 4: Add the fractions
\[ \frac{15}{10} + \frac{26}{10} = \frac{15 + 26}{10} = \frac{41}{10} \]

#### Step 5: Convert back to a mixed fraction
\[ \frac{41}{10} = 4 \frac{1}{10} \]

Answer: \( 4 \frac{1}{10} \)

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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 LCD is 18.

#### Step 3: Rewrite fractions with the common denominator
- \( \frac{7}{2} = \frac{7 \times 9}{2 \times 9} = \frac{63}{18} \)
- \( \frac{23}{9} = \frac{23 \times 2}{9 \times 2} = \frac{46}{18} \)

#### Step 4: Subtract the fractions
\[ \frac{63}{18} - \frac{46}{18} = \frac{63 - 46}{18} = \frac{17}{18} \]

Answer: \( \frac{17}{18} \)

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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 LCD is 20.

#### Step 3: Rewrite fractions with the common denominator
- \( \frac{11}{4} = \frac{11 \times 5}{4 \times 5} = \frac{55}{20} \)
- \( \frac{6}{5} = \frac{6 \times 4}{5 \times 4} = \frac{24}{20} \)

#### Step 4: Add the fractions
\[ \frac{55}{20} + \frac{24}{20} = \frac{55 + 24}{20} = \frac{79}{20} \]

#### Step 5: Convert back to a mixed fraction
\[ \frac{79}{20} = 3 \frac{19}{20} \]

Answer: \( 3 \frac{19}{20} \)

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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 LCD is 8.

#### Step 3: Rewrite fractions with the common denominator
- \( \frac{13}{4} = \frac{13 \times 2}{4 \times 2} = \frac{26}{8} \)
- \( \frac{19}{8} = \frac{19}{8} \)

#### Step 4: Subtract the fractions
\[ \frac{26}{8} - \frac{19}{8} = \frac{26 - 19}{8} = \frac{7}{8} \]

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

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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
\[ \frac{7}{2} - \frac{3}{2} = \frac{7 - 3}{2} = \frac{4}{2} = 2 \]

Answer: \( 2 \)

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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 LCD is 4.

#### Step 3: Rewrite fractions with the common denominator
- \( \frac{11}{2} = \frac{11 \times 2}{2 \times 2} = \frac{22}{4} \)
- \( \frac{21}{4} = \frac{21}{4} \)

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

#### Step 5: Convert back to a mixed fraction
\[ \frac{43}{4} = 10 \frac{3}{4} \]

Answer: \( 10 \frac{3}{4} \)

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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 LCD is 33.

#### Step 3: Rewrite fractions with the common denominator
- \( \frac{21}{11} = \frac{21 \times 3}{11 \times 3} = \frac{63}{33} \)
- \( \frac{4}{3} = \frac{4 \times 11}{3 \times 11} = \frac{44}{33} \)

#### Step 4: Subtract the fractions
\[ \frac{63}{33} - \frac{44}{33} = \frac{63 - 44}{33} = \frac{19}{33} \]

Answer: \( \frac{19}{33} \)

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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 LCD is 12.

#### Step 3: Rewrite fractions with the common denominator
- \( \frac{17}{12} = \frac{17}{12} \)
- \( \frac{10}{3} = \frac{10 \times 4}{3 \times 4} = \frac{40}{12} \)

#### Step 4: Add the fractions
\[ \frac{17}{12} + \frac{40}{12} = \frac{17 + 40}{12} = \frac{57}{12} \]

#### Step 5: Simplify the fraction
\[ \frac{57}{12} = \frac{19}{4} \]

#### Step 6: Convert back to a mixed fraction
\[ \frac{19}{4} = 4 \frac{3}{4} \]

Answer: \( 4 \frac{3}{4} \)

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Final Answers

\[
\boxed{
\begin{array}{lll}
1. & 3 \frac{19}{20} & \\
2. & \frac{5}{6} & \\
3. & 0 & \\
4. & \frac{1}{2} & \\
5. & 4 \frac{1}{10} & \\
6. & \frac{17}{18} & \\
7. & 3 \frac{19}{20} & \\
8. & \frac{7}{8} & \\
9. & 2 & \\
10. & 10 \frac{3}{4} & \\
11. & \frac{19}{33} & \\
12. & 4 \frac{3}{4} &
\end{array}
}
\]