Find the sum of mixed numbers in this math worksheet.

Let's solve each of these mixed number addition problems step by step. We'll convert the mixed numbers to improper fractions, find a common denominator if needed, add them, and then simplify or convert back to mixed numbers.

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1. $ 3\frac{1}{4} + 3\frac{5}{8} $

- Convert to improper fractions:
- $ 3\frac{1}{4} = \frac{13}{4} $
- $ 3\frac{5}{8} = \frac{29}{8} $
- Find common denominator: LCD of 4 and 8 is 8
- $ \frac{13}{4} = \frac{26}{8} $
- Add: $ \frac{26}{8} + \frac{29}{8} = \frac{55}{8} $
- Convert to mixed number: $ \frac{55}{8} = 6\frac{7}{8} $

✔ Answer: $ 6\frac{7}{8} $

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2. $ 9\frac{9}{10} + 2\frac{3}{5} $

- Convert:
- $ 9\frac{9}{10} = \frac{99}{10} $
- $ 2\frac{3}{5} = \frac{13}{5} $
- Common denominator: 10
- $ \frac{13}{5} = \frac{26}{10} $
- Add: $ \frac{99}{10} + \frac{26}{10} = \frac{125}{10} = \frac{25}{2} $
- Convert: $ \frac{25}{2} = 12\frac{1}{2} $

✔ Answer: $ 12\frac{1}{2} $

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3. $ 3\frac{5}{11} + 7\frac{2}{3} $

- Convert:
- $ 3\frac{5}{11} = \frac{38}{11} $
- $ 7\frac{2}{3} = \frac{23}{3} $
- LCD of 11 and 3 is 33
- $ \frac{38}{11} = \frac{114}{33} $
- $ \frac{23}{3} = \frac{253}{33} $
- Add: $ \frac{114 + 253}{33} = \frac{367}{33} $
- Convert: $ \frac{367}{33} = 11\frac{4}{33} $

✔ Answer: $ 11\frac{4}{33} $

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4. $ 5\frac{2}{8} + 2\frac{4}{10} $

Simplify first:
- $ 5\frac{2}{8} = 5\frac{1}{4} $
- $ 2\frac{4}{10} = 2\frac{2}{5} $

Now:
- $ 5\frac{1}{4} = \frac{21}{4} $
- $ 2\frac{2}{5} = \frac{12}{5} $
- LCD of 4 and 5 is 20
- $ \frac{21}{4} = \frac{105}{20} $
- $ \frac{12}{5} = \frac{48}{20} $
- Add: $ \frac{153}{20} = 7\frac{13}{20} $

✔ Answer: $ 7\frac{13}{20} $

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5. $ 8\frac{7}{9} + 5\frac{9}{11} $

- $ 8\frac{7}{9} = \frac{85}{9} $
- $ 5\frac{9}{11} = \frac{64}{11} $
- LCD of 9 and 11 is 99
- $ \frac{85}{9} = \frac{935}{99} $
- $ \frac{64}{11} = \frac{576}{99} $
- Add: $ \frac{1511}{99} $
- Divide: $ 1511 ÷ 99 = 15 $ remainder $ 1511 - 15×99 = 1511 - 1485 = 26 $
- So: $ 15\frac{26}{99} $

✔ Answer: $ 15\frac{26}{99} $

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6. $ 6\frac{2}{7} + 7\frac{1}{2} $

- $ 6\frac{2}{7} = \frac{44}{7} $
- $ 7\frac{1}{2} = \frac{15}{2} $
- LCD of 7 and 2 is 14
- $ \frac{44}{7} = \frac{88}{14} $
- $ \frac{15}{2} = \frac{105}{14} $
- Add: $ \frac{193}{14} = 13\frac{11}{14} $

✔ Answer: $ 13\frac{11}{14} $

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7. $ 5\frac{1}{2} + 8\frac{3}{4} $

- $ 5\frac{1}{2} = \frac{11}{2} $
- $ 8\frac{3}{4} = \frac{35}{4} $
- LCD of 2 and 4 is 4
- $ \frac{11}{2} = \frac{22}{4} $
- Add: $ \frac{22 + 35}{4} = \frac{57}{4} = 14\frac{1}{4} $

✔ Answer: $ 14\frac{1}{4} $

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8. $ 10\frac{2}{3} + 7\frac{1}{7} $

- $ 10\frac{2}{3} = \frac{32}{3} $
- $ 7\frac{1}{7} = \frac{50}{7} $
- LCD of 3 and 7 is 21
- $ \frac{32}{3} = \frac{224}{21} $
- $ \frac{50}{7} = \frac{150}{21} $
- Add: $ \frac{374}{21} = 17\frac{17}{21} $

✔ Answer: $ 17\frac{17}{21} $

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9. $ 10\frac{8}{10} + 9\frac{7}{12} $

Simplify:
- $ 10\frac{8}{10} = 10\frac{4}{5} = \frac{54}{5} $
- $ 9\frac{7}{12} = \frac{115}{12} $
- LCD of 5 and 12 is 60
- $ \frac{54}{5} = \frac{648}{60} $
- $ \frac{115}{12} = \frac{575}{60} $
- Add: $ \frac{1223}{60} = 20\frac{23}{60} $

✔ Answer: $ 20\frac{23}{60} $

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10. $ 3\frac{7}{8} + 3\frac{1}{3} $

- $ 3\frac{7}{8} = \frac{31}{8} $
- $ 3\frac{1}{3} = \frac{10}{3} $
- LCD of 8 and 3 is 24
- $ \frac{31}{8} = \frac{93}{24} $
- $ \frac{10}{3} = \frac{80}{24} $
- Add: $ \frac{173}{24} = 7\frac{5}{24} $

✔ Answer: $ 7\frac{5}{24} $

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11. $ 4\frac{3}{7} + 6\frac{1}{5} $

- $ 4\frac{3}{7} = \frac{31}{7} $
- $ 6\frac{1}{5} = \frac{31}{5} $
- LCD of 7 and 5 is 35
- $ \frac{31}{7} = \frac{155}{35} $
- $ \frac{31}{5} = \frac{217}{35} $
- Add: $ \frac{372}{35} = 10\frac{22}{35} $

✔ Answer: $ 10\frac{22}{35} $

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12. $ 1\frac{4}{6} + 9\frac{3}{8} $

Simplify:
- $ 1\frac{4}{6} = 1\frac{2}{3} = \frac{5}{3} $
- $ 9\frac{3}{8} = \frac{75}{8} $
- LCD of 3 and 8 is 24
- $ \frac{5}{3} = \frac{40}{24} $
- $ \frac{75}{8} = \frac{225}{24} $
- Add: $ \frac{265}{24} = 11\frac{1}{24} $

✔ Answer: $ 11\frac{1}{24} $

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13. $ 4\frac{8}{10} + 5\frac{2}{6} $

Simplify:
- $ 4\frac{8}{10} = 4\frac{4}{5} = \frac{24}{5} $
- $ 5\frac{2}{6} = 5\frac{1}{3} = \frac{16}{3} $
- LCD of 5 and 3 is 15
- $ \frac{24}{5} = \frac{72}{15} $
- $ \frac{16}{3} = \frac{80}{15} $
- Add: $ \frac{152}{15} = 10\frac{2}{15} $

✔ Answer: $ 10\frac{2}{15} $

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14. $ 3\frac{3}{9} + 7\frac{6}{11} $

Simplify:
- $ 3\frac{3}{9} = 3\frac{1}{3} = \frac{10}{3} $
- $ 7\frac{6}{11} = \frac{83}{11} $
- LCD of 3 and 11 is 33
- $ \frac{10}{3} = \frac{110}{33} $
- $ \frac{83}{11} = \frac{249}{33} $
- Add: $ \frac{359}{33} = 10\frac{29}{33} $

✔ Answer: $ 10\frac{29}{33} $

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✔ Final Answers:

1. $ 6\frac{7}{8} $
2. $ 12\frac{1}{2} $
3. $ 11\frac{4}{33} $
4. $ 7\frac{13}{20} $
5. $ 15\frac{26}{99} $
6. $ 13\frac{11}{14} $
7. $ 14\frac{1}{4} $
8. $ 17\frac{17}{21} $
9. $ 20\frac{23}{60} $
10. $ 7\frac{5}{24} $
11. $ 10\frac{22}{35} $
12. $ 11\frac{1}{24} $
13. $ 10\frac{2}{15} $
14. $ 10\frac{29}{33} $

Let me know if you'd like this as a printable sheet or with visual steps!