Grade 6 Adding Mixed Numbers Worksheets | Math Worksheets - Free Printable
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Step-by-step solution for: Grade 6 Adding Mixed Numbers Worksheets | Math Worksheets
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Show Answer Key & Explanations
Step-by-step solution for: Grade 6 Adding Mixed Numbers Worksheets | Math Worksheets
Let's solve each of these adding mixed numbers problems step by step.
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1. Convert mixed numbers to improper fractions (if needed).
2. Find a common denominator for the fractions.
3. Add the fractions and whole numbers separately.
4. Simplify the result, converting back to a mixed number if necessary.
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We'll go through each problem one by one.
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- Convert to improper fractions:
- $ 2\frac{1}{3} = \frac{7}{3} $
- $ 7\frac{1}{5} = \frac{36}{5} $
- Find LCD of 3 and 5 → 15
- Convert:
- $ \frac{7}{3} = \frac{35}{15} $
- $ \frac{36}{5} = \frac{108}{15} $
- Add: $ \frac{35}{15} + \frac{108}{15} = \frac{143}{15} $
- Convert to mixed number: $ \frac{143}{15} = 9\frac{8}{15} $
✔ Answer: $ 9\frac{8}{15} $
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- Convert:
- $ 5\frac{1}{4} = \frac{21}{4} $
- $ 1\frac{1}{3} = \frac{4}{3} $
- LCD of 4 and 3 → 12
- Convert:
- $ \frac{21}{4} = \frac{63}{12} $
- $ \frac{4}{3} = \frac{16}{12} $
- Add: $ \frac{63}{12} + \frac{16}{12} = \frac{79}{12} $
- Convert: $ \frac{79}{12} = 6\frac{7}{12} $
✔ Answer: $ 6\frac{7}{12} $
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- Convert:
- $ 4\frac{8}{11} = \frac{52}{11} $
- $ 4\frac{1}{6} = \frac{25}{6} $
- LCD of 11 and 6 → 66
- Convert:
- $ \frac{52}{11} = \frac{312}{66} $
- $ \frac{25}{6} = \frac{275}{66} $
- Add: $ \frac{312}{66} + \frac{275}{66} = \frac{587}{66} $
- Convert: $ \frac{587}{66} = 8\frac{59}{66} $ (since $ 66 \times 8 = 528 $, $ 587 - 528 = 59 $)
✔ Answer: $ 8\frac{59}{66} $
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- Convert:
- $ 3\frac{5}{8} = \frac{29}{8} $
- $ 5\frac{2}{3} = \frac{17}{3} $
- LCD of 8 and 3 → 24
- Convert:
- $ \frac{29}{8} = \frac{87}{24} $
- $ \frac{17}{3} = \frac{136}{24} $
- Add: $ \frac{87}{24} + \frac{136}{24} = \frac{223}{24} $
- Convert: $ \frac{223}{24} = 9\frac{7}{24} $ (since $ 24 \times 9 = 216 $, $ 223 - 216 = 7 $)
✔ Answer: $ 9\frac{7}{24} $
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- Convert:
- $ 9\frac{1}{3} = \frac{28}{3} $
- $ 6\frac{3}{8} = \frac{51}{8} $
- LCD of 3 and 8 → 24
- Convert:
- $ \frac{28}{3} = \frac{224}{24} $
- $ \frac{51}{8} = \frac{153}{24} $
- Add: $ \frac{224}{24} + \frac{153}{24} = \frac{377}{24} $
- Convert: $ \frac{377}{24} = 15\frac{17}{24} $ (since $ 24 \times 15 = 360 $, $ 377 - 360 = 17 $)
✔ Answer: $ 15\frac{17}{24} $
---
- Convert:
- $ 10\frac{6}{7} = \frac{76}{7} $
- $ 2\frac{2}{9} = \frac{20}{9} $
- LCD of 7 and 9 → 63
- Convert:
- $ \frac{76}{7} = \frac{684}{63} $
- $ \frac{20}{9} = \frac{140}{63} $
- Add: $ \frac{684}{63} + \frac{140}{63} = \frac{824}{63} $
- Convert: $ \frac{824}{63} = 13\frac{5}{63} $ (since $ 63 \times 13 = 819 $, $ 824 - 819 = 5 $)
✔ Answer: $ 13\frac{5}{63} $
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- Convert:
- $ 3\frac{1}{6} = \frac{19}{6} $
- $ 2\frac{1}{3} = \frac{7}{3} $
- LCD of 6 and 3 → 6
- Convert:
- $ \frac{7}{3} = \frac{14}{6} $
- Add: $ \frac{19}{6} + \frac{14}{6} = \frac{33}{6} = \frac{11}{2} $
- Convert: $ \frac{11}{2} = 5\frac{1}{2} $
✔ Answer: $ 5\frac{1}{2} $
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- Convert:
- $ 5\frac{1}{7} = \frac{36}{7} $
- $ 6\frac{1}{2} = \frac{13}{2} $
- LCD of 7 and 2 → 14
- Convert:
- $ \frac{36}{7} = \frac{72}{14} $
- $ \frac{13}{2} = \frac{91}{14} $
- Add: $ \frac{72}{14} + \frac{91}{14} = \frac{163}{14} $
- Convert: $ \frac{163}{14} = 11\frac{9}{14} $ (since $ 14 \times 11 = 154 $, $ 163 - 154 = 9 $)
✔ Answer: $ 11\frac{9}{14} $
---
- Convert:
- $ 7\frac{7}{8} = \frac{63}{8} $
- $ 11\frac{1}{4} = \frac{45}{4} $
- LCD of 8 and 4 → 8
- Convert:
- $ \frac{45}{4} = \frac{90}{8} $
- Add: $ \frac{63}{8} + \frac{90}{8} = \frac{153}{8} $
- Convert: $ \frac{153}{8} = 19\frac{1}{8} $ (since $ 8 \times 19 = 152 $, $ 153 - 152 = 1 $)
✔ Answer: $ 19\frac{1}{8} $
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- Convert:
- $ 8\frac{2}{9} = \frac{74}{9} $
- $ 4\frac{4}{5} = \frac{24}{5} $
- LCD of 9 and 5 → 45
- Convert:
- $ \frac{74}{9} = \frac{370}{45} $
- $ \frac{24}{5} = \frac{216}{45} $
- Add: $ \frac{370}{45} + \frac{216}{45} = \frac{586}{45} $
- Convert: $ \frac{586}{45} = 13\frac{1}{45} $ (since $ 45 \times 13 = 585 $, $ 586 - 585 = 1 $)
✔ Answer: $ 13\frac{1}{45} $
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1. $ 9\frac{8}{15} $
2. $ 6\frac{7}{12} $
3. $ 8\frac{59}{66} $
4. $ 9\frac{7}{24} $
5. $ 15\frac{17}{24} $
6. $ 13\frac{5}{63} $
7. $ 5\frac{1}{2} $
8. $ 11\frac{9}{14} $
9. $ 19\frac{1}{8} $
10. $ 13\frac{1}{45} $
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Let me know if you'd like this formatted as a printable answer key!
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General Steps to Add Mixed Numbers:
1. Convert mixed numbers to improper fractions (if needed).
2. Find a common denominator for the fractions.
3. Add the fractions and whole numbers separately.
4. Simplify the result, converting back to a mixed number if necessary.
---
We'll go through each problem one by one.
---
1. $ 2\frac{1}{3} + 7\frac{1}{5} $
- Convert to improper fractions:
- $ 2\frac{1}{3} = \frac{7}{3} $
- $ 7\frac{1}{5} = \frac{36}{5} $
- Find LCD of 3 and 5 → 15
- Convert:
- $ \frac{7}{3} = \frac{35}{15} $
- $ \frac{36}{5} = \frac{108}{15} $
- Add: $ \frac{35}{15} + \frac{108}{15} = \frac{143}{15} $
- Convert to mixed number: $ \frac{143}{15} = 9\frac{8}{15} $
✔ Answer: $ 9\frac{8}{15} $
---
2. $ 5\frac{1}{4} + 1\frac{1}{3} $
- Convert:
- $ 5\frac{1}{4} = \frac{21}{4} $
- $ 1\frac{1}{3} = \frac{4}{3} $
- LCD of 4 and 3 → 12
- Convert:
- $ \frac{21}{4} = \frac{63}{12} $
- $ \frac{4}{3} = \frac{16}{12} $
- Add: $ \frac{63}{12} + \frac{16}{12} = \frac{79}{12} $
- Convert: $ \frac{79}{12} = 6\frac{7}{12} $
✔ Answer: $ 6\frac{7}{12} $
---
3. $ 4\frac{8}{11} + 4\frac{1}{6} $
- Convert:
- $ 4\frac{8}{11} = \frac{52}{11} $
- $ 4\frac{1}{6} = \frac{25}{6} $
- LCD of 11 and 6 → 66
- Convert:
- $ \frac{52}{11} = \frac{312}{66} $
- $ \frac{25}{6} = \frac{275}{66} $
- Add: $ \frac{312}{66} + \frac{275}{66} = \frac{587}{66} $
- Convert: $ \frac{587}{66} = 8\frac{59}{66} $ (since $ 66 \times 8 = 528 $, $ 587 - 528 = 59 $)
✔ Answer: $ 8\frac{59}{66} $
---
4. $ 3\frac{5}{8} + 5\frac{2}{3} $
- Convert:
- $ 3\frac{5}{8} = \frac{29}{8} $
- $ 5\frac{2}{3} = \frac{17}{3} $
- LCD of 8 and 3 → 24
- Convert:
- $ \frac{29}{8} = \frac{87}{24} $
- $ \frac{17}{3} = \frac{136}{24} $
- Add: $ \frac{87}{24} + \frac{136}{24} = \frac{223}{24} $
- Convert: $ \frac{223}{24} = 9\frac{7}{24} $ (since $ 24 \times 9 = 216 $, $ 223 - 216 = 7 $)
✔ Answer: $ 9\frac{7}{24} $
---
5. $ 9\frac{1}{3} + 6\frac{3}{8} $
- Convert:
- $ 9\frac{1}{3} = \frac{28}{3} $
- $ 6\frac{3}{8} = \frac{51}{8} $
- LCD of 3 and 8 → 24
- Convert:
- $ \frac{28}{3} = \frac{224}{24} $
- $ \frac{51}{8} = \frac{153}{24} $
- Add: $ \frac{224}{24} + \frac{153}{24} = \frac{377}{24} $
- Convert: $ \frac{377}{24} = 15\frac{17}{24} $ (since $ 24 \times 15 = 360 $, $ 377 - 360 = 17 $)
✔ Answer: $ 15\frac{17}{24} $
---
6. $ 10\frac{6}{7} + 2\frac{2}{9} $
- Convert:
- $ 10\frac{6}{7} = \frac{76}{7} $
- $ 2\frac{2}{9} = \frac{20}{9} $
- LCD of 7 and 9 → 63
- Convert:
- $ \frac{76}{7} = \frac{684}{63} $
- $ \frac{20}{9} = \frac{140}{63} $
- Add: $ \frac{684}{63} + \frac{140}{63} = \frac{824}{63} $
- Convert: $ \frac{824}{63} = 13\frac{5}{63} $ (since $ 63 \times 13 = 819 $, $ 824 - 819 = 5 $)
✔ Answer: $ 13\frac{5}{63} $
---
7. $ 3\frac{1}{6} + 2\frac{1}{3} $
- Convert:
- $ 3\frac{1}{6} = \frac{19}{6} $
- $ 2\frac{1}{3} = \frac{7}{3} $
- LCD of 6 and 3 → 6
- Convert:
- $ \frac{7}{3} = \frac{14}{6} $
- Add: $ \frac{19}{6} + \frac{14}{6} = \frac{33}{6} = \frac{11}{2} $
- Convert: $ \frac{11}{2} = 5\frac{1}{2} $
✔ Answer: $ 5\frac{1}{2} $
---
8. $ 5\frac{1}{7} + 6\frac{1}{2} $
- Convert:
- $ 5\frac{1}{7} = \frac{36}{7} $
- $ 6\frac{1}{2} = \frac{13}{2} $
- LCD of 7 and 2 → 14
- Convert:
- $ \frac{36}{7} = \frac{72}{14} $
- $ \frac{13}{2} = \frac{91}{14} $
- Add: $ \frac{72}{14} + \frac{91}{14} = \frac{163}{14} $
- Convert: $ \frac{163}{14} = 11\frac{9}{14} $ (since $ 14 \times 11 = 154 $, $ 163 - 154 = 9 $)
✔ Answer: $ 11\frac{9}{14} $
---
9. $ 7\frac{7}{8} + 11\frac{1}{4} $
- Convert:
- $ 7\frac{7}{8} = \frac{63}{8} $
- $ 11\frac{1}{4} = \frac{45}{4} $
- LCD of 8 and 4 → 8
- Convert:
- $ \frac{45}{4} = \frac{90}{8} $
- Add: $ \frac{63}{8} + \frac{90}{8} = \frac{153}{8} $
- Convert: $ \frac{153}{8} = 19\frac{1}{8} $ (since $ 8 \times 19 = 152 $, $ 153 - 152 = 1 $)
✔ Answer: $ 19\frac{1}{8} $
---
10. $ 8\frac{2}{9} + 4\frac{4}{5} $
- Convert:
- $ 8\frac{2}{9} = \frac{74}{9} $
- $ 4\frac{4}{5} = \frac{24}{5} $
- LCD of 9 and 5 → 45
- Convert:
- $ \frac{74}{9} = \frac{370}{45} $
- $ \frac{24}{5} = \frac{216}{45} $
- Add: $ \frac{370}{45} + \frac{216}{45} = \frac{586}{45} $
- Convert: $ \frac{586}{45} = 13\frac{1}{45} $ (since $ 45 \times 13 = 585 $, $ 586 - 585 = 1 $)
✔ Answer: $ 13\frac{1}{45} $
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✔ Final Answers:
1. $ 9\frac{8}{15} $
2. $ 6\frac{7}{12} $
3. $ 8\frac{59}{66} $
4. $ 9\frac{7}{24} $
5. $ 15\frac{17}{24} $
6. $ 13\frac{5}{63} $
7. $ 5\frac{1}{2} $
8. $ 11\frac{9}{14} $
9. $ 19\frac{1}{8} $
10. $ 13\frac{1}{45} $
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Let me know if you'd like this formatted as a printable answer key!
Parent Tip: Review the logic above to help your child master the concept of adding mixed numbers worksheet 5th grade.
