Adding Mixed Numbers worksheets - Free Printable

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

1. Convert mixed numbers to improper fractions (if necessary).
2. Find a common denominator for the fractions.
3. Add the fractions.
4. Simplify the result and convert back to a mixed number if needed.

Let's solve each problem step by step.

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

#### Step 1: Simplify the mixed numbers
- \( 4 \frac{6}{2} = 4 + \frac{6}{2} = 4 + 3 = 7 \)
- \( 7 \frac{2}{4} = 7 + \frac{2}{4} = 7 + \frac{1}{2} = 7 \frac{1}{2} \)

#### Step 2: Add the simplified numbers
- \( 7 + 7 \frac{1}{2} = 14 \frac{1}{2} \)

#### Final Answer:
\[ \boxed{14 \frac{1}{2}} \]

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

#### Step 1: Simplify the mixed numbers
- \( 4 \frac{2}{2} = 4 + \frac{2}{2} = 4 + 1 = 5 \)
- \( 5 \frac{5}{2} = 5 + \frac{5}{2} = 5 + 2 \frac{1}{2} = 7 \frac{1}{2} \)

#### Step 2: Add the simplified numbers
- \( 5 + 7 \frac{1}{2} = 12 \frac{1}{2} \)

#### Final Answer:
\[ \boxed{12 \frac{1}{2}} \]

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Problem 3: \( 4 \frac{8}{10} + 3 \frac{7}{1} \)

#### Step 1: Simplify the mixed numbers
- \( 4 \frac{8}{10} = 4 + \frac{8}{10} = 4 + \frac{4}{5} = 4 \frac{4}{5} \)
- \( 3 \frac{7}{1} = 3 + 7 = 10 \)

#### Step 2: Add the simplified numbers
- \( 4 \frac{4}{5} + 10 = 14 \frac{4}{5} \)

#### Final Answer:
\[ \boxed{14 \frac{4}{5}} \]

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

#### Step 1: Convert to improper fractions
- \( 2 \frac{5}{2} = 2 + \frac{5}{2} = \frac{4}{2} + \frac{5}{2} = \frac{9}{2} \)
- \( 4 \frac{7}{3} = 4 + \frac{7}{3} = \frac{12}{3} + \frac{7}{3} = \frac{19}{3} \)

#### Step 2: Find a common denominator (LCM of 2 and 3 is 6)
- \( \frac{9}{2} = \frac{9 \times 3}{2 \times 3} = \frac{27}{6} \)
- \( \frac{19}{3} = \frac{19 \times 2}{3 \times 2} = \frac{38}{6} \)

#### Step 3: Add the fractions
- \( \frac{27}{6} + \frac{38}{6} = \frac{65}{6} \)

#### Step 4: Convert back to a mixed number
- \( \frac{65}{6} = 10 \frac{5}{6} \)

#### Final Answer:
\[ \boxed{10 \frac{5}{6}} \]

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

#### Step 1: Simplify the mixed numbers
- \( 4 \frac{5}{10} = 4 + \frac{5}{10} = 4 + \frac{1}{2} = 4 \frac{1}{2} \)
- \( 2 \frac{4}{4} = 2 + 1 = 3 \)

#### Step 2: Add the simplified numbers
- \( 4 \frac{1}{2} + 3 = 7 \frac{1}{2} \)

#### Final Answer:
\[ \boxed{7 \frac{1}{2}} \]

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Problem 6: \( 7 \frac{7}{10} + 1 \frac{7}{1} \)

#### Step 1: Simplify the mixed numbers
- \( 7 \frac{7}{10} = 7 + \frac{7}{10} \)
- \( 1 \frac{7}{1} = 1 + 7 = 8 \)

#### Step 2: Add the simplified numbers
- \( 7 \frac{7}{10} + 8 = 15 \frac{7}{10} \)

#### Final Answer:
\[ \boxed{15 \frac{7}{10}} \]

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Problem 7: \( 6 \frac{9}{8} + 2 \frac{2}{1} \)

#### Step 1: Simplify the mixed numbers
- \( 6 \frac{9}{8} = 6 + \frac{9}{8} = 6 + 1 \frac{1}{8} = 7 \frac{1}{8} \)
- \( 2 \frac{2}{1} = 2 + 2 = 4 \)

#### Step 2: Add the simplified numbers
- \( 7 \frac{1}{8} + 4 = 11 \frac{1}{8} \)

#### Final Answer:
\[ \boxed{11 \frac{1}{8}} \]

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Problem 8: \( 2 \frac{3}{5} + 6 \frac{6}{1} \)

#### Step 1: Simplify the mixed numbers
- \( 2 \frac{3}{5} = 2 + \frac{3}{5} \)
- \( 6 \frac{6}{1} = 6 + 6 = 12 \)

#### Step 2: Add the simplified numbers
- \( 2 \frac{3}{5} + 12 = 14 \frac{3}{5} \)

#### Final Answer:
\[ \boxed{14 \frac{3}{5}} \]

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

#### Step 1: Simplify the mixed numbers
- \( 1 \frac{8}{8} = 1 + 1 = 2 \)
- \( 1 \frac{4}{7} = 1 + \frac{4}{7} \)

#### Step 2: Add the simplified numbers
- \( 2 + 1 \frac{4}{7} = 3 \frac{4}{7} \)

#### Final Answer:
\[ \boxed{3 \frac{4}{7}} \]

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Problem 10: \( 6 \frac{3}{10} + 8 \frac{6}{5} \)

#### Step 1: Simplify the mixed numbers
- \( 6 \frac{3}{10} = 6 + \frac{3}{10} \)
- \( 8 \frac{6}{5} = 8 + \frac{6}{5} = 8 + 1 \frac{1}{5} = 9 \frac{1}{5} \)

#### Step 2: Add the simplified numbers
- \( 6 \frac{3}{10} + 9 \frac{1}{5} \)

#### Step 3: Convert \( \frac{1}{5} \) to a fraction with denominator 10
- \( \frac{1}{5} = \frac{2}{10} \)

#### Step 4: Add the fractions
- \( 6 \frac{3}{10} + 9 \frac{2}{10} = 15 \frac{5}{10} = 15 \frac{1}{2} \)

#### Final Answer:
\[ \boxed{15 \frac{1}{2}} \]

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Final Answers for All Problems

1. \( \boxed{14 \frac{1}{2}} \)
2. \( \boxed{12 \frac{1}{2}} \)
3. \( \boxed{14 \frac{4}{5}} \)
4. \( \boxed{10 \frac{5}{6}} \)
5. \( \boxed{7 \frac{1}{2}} \)
6. \( \boxed{15 \frac{7}{10}} \)
7. \( \boxed{11 \frac{1}{8}} \)
8. \( \boxed{14 \frac{3}{5}} \)
9. \( \boxed{3 \frac{4}{7}} \)
10. \( \boxed{15 \frac{1}{2}} \)
11. \( \boxed{7 \frac{1}{5}} \)
12. \( \boxed{11 \frac{5}{6}} \)
13. \( \boxed{11 \frac{1}{2}} \)
14. \( \boxed{12} \)
15. \( \boxed{4 \frac{3}{7}} \)
16. \( \boxed{6 \frac{3}{8}} \)
17. \( \boxed{6 \frac{1}{3}} \)
18. \( \boxed{6 \frac{4}{7}} \)
19. \( \boxed{9 \frac{1}{2}} \)
20. \( \boxed{7 \frac{17}{30}} \)
21. \( \boxed{7 \frac{5}{4}} \)
22. \( \boxed{9 \frac{1}{6}} \)

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Final Boxed Answers:
\[
\boxed{
\begin{array}{ll}
1. & 14 \frac{1}{2} \\
2. & 12 \frac{1}{2} \\
3. & 14 \frac{4}{5} \\
4. & 10 \frac{5}{6} \\
5. & 7 \frac{1}{2} \\
6. & 15 \frac{7}{10} \\
7. & 11 \frac{1}{8} \\
8. & 14 \frac{3}{5} \\
9. & 3 \frac{4}{7} \\
10. & 15 \frac{1}{2} \\
11. & 7 \frac{1}{5} \\
12. & 11 \frac{5}{6} \\
13. & 11 \frac{1}{2} \\
14. & 12 \\
15. & 4 \frac{3}{7} \\
16. & 6 \frac{3}{8} \\
17. & 6 \frac{1}{3} \\
18. & 6 \frac{4}{7} \\
19. & 9 \frac{1}{2} \\
20. & 7 \frac{17}{30} \\
21. & 7 \frac{5}{4} \\
22. & 9 \frac{1}{6} \\
\end{array}
}
\]