This printable worksheet provides ten practice problems for students to solve equations involving the addition of mixed numbers.

To solve the problems involving the addition of mixed numbers, we need to follow these steps:

1. Convert mixed numbers to improper fractions.
2. Find a common denominator for the fractions.
3. Add the fractions.
4. Simplify the result, converting back to a mixed number if necessary.

Let's solve each problem step by step.

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Problem 1: \( 4 \frac{1}{8} + 2 \frac{4}{5} \)

#### Step 1: Convert mixed numbers to improper fractions
- \( 4 \frac{1}{8} = \frac{4 \times 8 + 1}{8} = \frac{33}{8} \)
- \( 2 \frac{4}{5} = \frac{2 \times 5 + 4}{5} = \frac{14}{5} \)

#### Step 2: Find a common denominator
The denominators are 8 and 5. The least common denominator (LCD) is 40.

#### Step 3: Rewrite fractions with the common denominator
- \( \frac{33}{8} = \frac{33 \times 5}{8 \times 5} = \frac{165}{40} \)
- \( \frac{14}{5} = \frac{14 \times 8}{5 \times 8} = \frac{112}{40} \)

#### Step 4: Add the fractions
\[ \frac{165}{40} + \frac{112}{40} = \frac{165 + 112}{40} = \frac{277}{40} \]

#### Step 5: Convert back to a mixed number
\[ \frac{277}{40} = 6 \frac{37}{40} \]

Answer: \( 6 \frac{37}{40} \)

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Problem 2: \( 3 \frac{1}{6} + 7 \frac{1}{4} \)

#### Step 1: Convert mixed numbers to improper fractions
- \( 3 \frac{1}{6} = \frac{3 \times 6 + 1}{6} = \frac{19}{6} \)
- \( 7 \frac{1}{4} = \frac{7 \times 4 + 1}{4} = \frac{29}{4} \)

#### Step 2: Find a common denominator
The denominators are 6 and 4. The LCD is 12.

#### Step 3: Rewrite fractions with the common denominator
- \( \frac{19}{6} = \frac{19 \times 2}{6 \times 2} = \frac{38}{12} \)
- \( \frac{29}{4} = \frac{29 \times 3}{4 \times 3} = \frac{87}{12} \)

#### Step 4: Add the fractions
\[ \frac{38}{12} + \frac{87}{12} = \frac{38 + 87}{12} = \frac{125}{12} \]

#### Step 5: Convert back to a mixed number
\[ \frac{125}{12} = 10 \frac{5}{12} \]

Answer: \( 10 \frac{5}{12} \)

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Problem 3: \( 5 \frac{7}{9} + 8 \frac{1}{3} \)

#### Step 1: Convert mixed numbers to improper fractions
- \( 5 \frac{7}{9} = \frac{5 \times 9 + 7}{9} = \frac{52}{9} \)
- \( 8 \frac{1}{3} = \frac{8 \times 3 + 1}{3} = \frac{25}{3} \)

#### Step 2: Find a common denominator
The denominators are 9 and 3. The LCD is 9.

#### Step 3: Rewrite fractions with the common denominator
- \( \frac{52}{9} \) remains \( \frac{52}{9} \)
- \( \frac{25}{3} = \frac{25 \times 3}{3 \times 3} = \frac{75}{9} \)

#### Step 4: Add the fractions
\[ \frac{52}{9} + \frac{75}{9} = \frac{52 + 75}{9} = \frac{127}{9} \]

#### Step 5: Convert back to a mixed number
\[ \frac{127}{9} = 14 \frac{1}{9} \]

Answer: \( 14 \frac{1}{9} \)

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Problem 4: \( 9 \frac{8}{9} + 4 \frac{1}{5} \)

#### Step 1: Convert mixed numbers to improper fractions
- \( 9 \frac{8}{9} = \frac{9 \times 9 + 8}{9} = \frac{89}{9} \)
- \( 4 \frac{1}{5} = \frac{4 \times 5 + 1}{5} = \frac{21}{5} \)

#### Step 2: Find a common denominator
The denominators are 9 and 5. The LCD is 45.

#### Step 3: Rewrite fractions with the common denominator
- \( \frac{89}{9} = \frac{89 \times 5}{9 \times 5} = \frac{445}{45} \)
- \( \frac{21}{5} = \frac{21 \times 9}{5 \times 9} = \frac{189}{45} \)

#### Step 4: Add the fractions
\[ \frac{445}{45} + \frac{189}{45} = \frac{445 + 189}{45} = \frac{634}{45} \]

#### Step 5: Convert back to a mixed number
\[ \frac{634}{45} = 14 \frac{4}{45} \]

Answer: \( 14 \frac{4}{45} \)

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

#### Step 1: Convert mixed numbers to improper fractions
- \( 5 \frac{2}{3} = \frac{5 \times 3 + 2}{3} = \frac{17}{3} \)
- \( 2 \frac{4}{5} = \frac{2 \times 5 + 4}{5} = \frac{14}{5} \)

#### Step 2: Find a common denominator
The denominators are 3 and 5. The LCD is 15.

#### Step 3: Rewrite fractions with the common denominator
- \( \frac{17}{3} = \frac{17 \times 5}{3 \times 5} = \frac{85}{15} \)
- \( \frac{14}{5} = \frac{14 \times 3}{5 \times 3} = \frac{42}{15} \)

#### Step 4: Add the fractions
\[ \frac{85}{15} + \frac{42}{15} = \frac{85 + 42}{15} = \frac{127}{15} \]

#### Step 5: Convert back to a mixed number
\[ \frac{127}{15} = 8 \frac{7}{15} \]

Answer: \( 8 \frac{7}{15} \)

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Problem 6: \( 8 \frac{7}{10} + 8 \frac{5}{8} \)

#### Step 1: Convert mixed numbers to improper fractions
- \( 8 \frac{7}{10} = \frac{8 \times 10 + 7}{10} = \frac{87}{10} \)
- \( 8 \frac{5}{8} = \frac{8 \times 8 + 5}{8} = \frac{69}{8} \)

#### Step 2: Find a common denominator
The denominators are 10 and 8. The LCD is 40.

#### Step 3: Rewrite fractions with the common denominator
- \( \frac{87}{10} = \frac{87 \times 4}{10 \times 4} = \frac{348}{40} \)
- \( \frac{69}{8} = \frac{69 \times 5}{8 \times 5} = \frac{345}{40} \)

#### Step 4: Add the fractions
\[ \frac{348}{40} + \frac{345}{40} = \frac{348 + 345}{40} = \frac{693}{40} \]

#### Step 5: Convert back to a mixed number
\[ \frac{693}{40} = 17 \frac{13}{40} \]

Answer: \( 17 \frac{13}{40} \)

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Problem 7: \( 11 \frac{8}{9} + 5 \frac{1}{4} \)

#### Step 1: Convert mixed numbers to improper fractions
- \( 11 \frac{8}{9} = \frac{11 \times 9 + 8}{9} = \frac{107}{9} \)
- \( 5 \frac{1}{4} = \frac{5 \times 4 + 1}{4} = \frac{21}{4} \)

#### Step 2: Find a common denominator
The denominators are 9 and 4. The LCD is 36.

#### Step 3: Rewrite fractions with the common denominator
- \( \frac{107}{9} = \frac{107 \times 4}{9 \times 4} = \frac{428}{36} \)
- \( \frac{21}{4} = \frac{21 \times 9}{4 \times 9} = \frac{189}{36} \)

#### Step 4: Add the fractions
\[ \frac{428}{36} + \frac{189}{36} = \frac{428 + 189}{36} = \frac{617}{36} \]

#### Step 5: Convert back to a mixed number
\[ \frac{617}{36} = 17 \frac{5}{36} \]

Answer: \( 17 \frac{5}{36} \)

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Problem 8: \( 7 \frac{1}{3} + 11 \frac{1}{2} \)

#### Step 1: Convert mixed numbers to improper fractions
- \( 7 \frac{1}{3} = \frac{7 \times 3 + 1}{3} = \frac{22}{3} \)
- \( 11 \frac{1}{2} = \frac{11 \times 2 + 1}{2} = \frac{23}{2} \)

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

#### Step 3: Rewrite fractions with the common denominator
- \( \frac{22}{3} = \frac{22 \times 2}{3 \times 2} = \frac{44}{6} \)
- \( \frac{23}{2} = \frac{23 \times 3}{2 \times 3} = \frac{69}{6} \)

#### Step 4: Add the fractions
\[ \frac{44}{6} + \frac{69}{6} = \frac{44 + 69}{6} = \frac{113}{6} \]

#### Step 5: Convert back to a mixed number
\[ \frac{113}{6} = 18 \frac{5}{6} \]

Answer: \( 18 \frac{5}{6} \)

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Problem 9: \( 15 \frac{5}{6} + 8 \frac{3}{8} \)

#### Step 1: Convert mixed numbers to improper fractions
- \( 15 \frac{5}{6} = \frac{15 \times 6 + 5}{6} = \frac{95}{6} \)
- \( 8 \frac{3}{8} = \frac{8 \times 8 + 3}{8} = \frac{67}{8} \)

#### Step 2: Find a common denominator
The denominators are 6 and 8. The LCD is 24.

#### Step 3: Rewrite fractions with the common denominator
- \( \frac{95}{6} = \frac{95 \times 4}{6 \times 4} = \frac{380}{24} \)
- \( \frac{67}{8} = \frac{67 \times 3}{8 \times 3} = \frac{201}{24} \)

#### Step 4: Add the fractions
\[ \frac{380}{24} + \frac{201}{24} = \frac{380 + 201}{24} = \frac{581}{24} \]

#### Step 5: Convert back to a mixed number
\[ \frac{581}{24} = 24 \frac{5}{24} \]

Answer: \( 24 \frac{5}{24} \)

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Problem 10: \( 12 \frac{3}{7} + 6 \frac{5}{6} \)

#### Step 1: Convert mixed numbers to improper fractions
- \( 12 \frac{3}{7} = \frac{12 \times 7 + 3}{7} = \frac{87}{7} \)
- \( 6 \frac{5}{6} = \frac{6 \times 6 + 5}{6} = \frac{41}{6} \)

#### Step 2: Find a common denominator
The denominators are 7 and 6. The LCD is 42.

#### Step 3: Rewrite fractions with the common denominator
- \( \frac{87}{7} = \frac{87 \times 6}{7 \times 6} = \frac{522}{42} \)
- \( \frac{41}{6} = \frac{41 \times 7}{6 \times 7} = \frac{287}{42} \)

#### Step 4: Add the fractions
\[ \frac{522}{42} + \frac{287}{42} = \frac{522 + 287}{42} = \frac{809}{42} \]

#### Step 5: Convert back to a mixed number
\[ \frac{809}{42} = 19 \frac{11}{42} \]

Answer: \( 19 \frac{11}{42} \)

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Final Answers

1. \( 6 \frac{37}{40} \)
2. \( 10 \frac{5}{12} \)
3. \( 14 \frac{1}{9} \)
4. \( 14 \frac{4}{45} \)
5. \( 8 \frac{7}{15} \)
6. \( 17 \frac{13}{40} \)
7. \( 17 \frac{5}{36} \)
8. \( 18 \frac{5}{6} \)
9. \( 24 \frac{5}{24} \)
10. \( 19 \frac{11}{42} \)

\[
\boxed{
\begin{array}{ll}
1. & 6 \frac{37}{40} \\
2. & 10 \frac{5}{12} \\
3. & 14 \frac{1}{9} \\
4. & 14 \frac{4}{45} \\
5. & 8 \frac{7}{15} \\
6. & 17 \frac{13}{40} \\
7. & 17 \frac{5}{36} \\
8. & 18 \frac{5}{6} \\
9. & 24 \frac{5}{24} \\
10. & 19 \frac{11}{42} \\
\end{array}
}
\]