Grade 6 Adding Mixed Numbers Worksheets | Math Worksheets - Free Printable
Educational worksheet: Grade 6 Adding Mixed Numbers Worksheets | Math Worksheets. Download and print for classroom or home learning activities.
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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 subtracting mixed numbers problems step by step. We'll convert the mixed numbers to improper fractions, find a common denominator, subtract, and then simplify or convert back to mixed numbers as needed.
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- Convert to improper fractions:
- $ 2\frac{4}{9} = \frac{2 \times 9 + 4}{9} = \frac{18 + 4}{9} = \frac{22}{9} $
- $ 1\frac{4}{6} = \frac{1 \times 6 + 4}{6} = \frac{10}{6} $
- Simplify $ \frac{10}{6} = \frac{5}{3} $
- Find common denominator: LCM of 9 and 3 is 9
- $ \frac{5}{3} = \frac{15}{9} $
- Subtract: $ \frac{22}{9} - \frac{15}{9} = \frac{7}{9} $
✔ Answer: $ \frac{7}{9} $
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- Convert:
- $ 9\frac{1}{2} = \frac{19}{2} $
- $ 5\frac{1}{4} = \frac{21}{4} $
- Common denominator: LCM of 2 and 4 is 4
- $ \frac{19}{2} = \frac{38}{4} $
- Subtract: $ \frac{38}{4} - \frac{21}{4} = \frac{17}{4} $
- Convert to mixed number: $ \frac{17}{4} = 4\frac{1}{4} $
✔ Answer: $ 4\frac{1}{4} $
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- Convert:
- $ 7\frac{1}{3} = \frac{22}{3} $
- $ 4\frac{1}{6} = \frac{25}{6} $
- Common denominator: LCM of 3 and 6 is 6
- $ \frac{22}{3} = \frac{44}{6} $
- Subtract: $ \frac{44}{6} - \frac{25}{6} = \frac{19}{6} $
- Convert: $ \frac{19}{6} = 3\frac{1}{6} $
✔ Answer: $ 3\frac{1}{6} $
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- Convert:
- $ 7\frac{1}{2} = \frac{15}{2} $
- $ 3\frac{5}{6} = \frac{23}{6} $
- Common denominator: LCM of 2 and 6 is 6
- $ \frac{15}{2} = \frac{45}{6} $
- Subtract: $ \frac{45}{6} - \frac{23}{6} = \frac{22}{6} = \frac{11}{3} $
- Convert: $ \frac{11}{3} = 3\frac{2}{3} $
✔ Answer: $ 3\frac{2}{3} $
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- Same denominators, so subtract whole numbers and fractions:
- $ 11 - 5 = 6 $
- $ \frac{3}{4} - \frac{1}{4} = \frac{2}{4} = \frac{1}{2} $
✔ Answer: $ 6\frac{1}{2} $
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- Simplify $ \frac{2}{4} = \frac{1}{2} $
- So: $ 8\frac{1}{2} - 2\frac{3}{20} $
- Convert:
- $ 8\frac{1}{2} = \frac{17}{2} $
- $ 2\frac{3}{20} = \frac{43}{20} $
- Common denominator: LCM of 2 and 20 is 20
- $ \frac{17}{2} = \frac{170}{20} $
- Subtract: $ \frac{170}{20} - \frac{43}{20} = \frac{127}{20} $
- Convert: $ \frac{127}{20} = 6\frac{7}{20} $
✔ Answer: $ 6\frac{7}{20} $
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- Simplify $ \frac{3}{6} = \frac{1}{2} $
- So: $ 12\frac{2}{3} - 4\frac{1}{2} $
- Convert:
- $ 12\frac{2}{3} = \frac{38}{3} $
- $ 4\frac{1}{2} = \frac{9}{2} $
- Common denominator: LCM of 3 and 2 is 6
- $ \frac{38}{3} = \frac{76}{6} $
- $ \frac{9}{2} = \frac{27}{6} $
- Subtract: $ \frac{76}{6} - \frac{27}{6} = \frac{49}{6} $
- Convert: $ \frac{49}{6} = 8\frac{1}{6} $
✔ Answer: $ 8\frac{1}{6} $
---
- Convert:
- $ 5\frac{2}{5} = \frac{27}{5} $
- $ 4\frac{1}{6} = \frac{25}{6} $
- Common denominator: LCM of 5 and 6 is 30
- $ \frac{27}{5} = \frac{162}{30} $
- $ \frac{25}{6} = \frac{125}{30} $
- Subtract: $ \frac{162}{30} - \frac{125}{30} = \frac{37}{30} $
- Convert: $ \frac{37}{30} = 1\frac{7}{30} $
✔ Answer: $ 1\frac{7}{30} $
---
- Convert:
- $ 6\frac{4}{5} = \frac{34}{5} $
- $ 3\frac{3}{8} = \frac{27}{8} $
- Common denominator: LCM of 5 and 8 is 40
- $ \frac{34}{5} = \frac{272}{40} $
- $ \frac{27}{8} = \frac{135}{40} $
- Subtract: $ \frac{272}{40} - \frac{135}{40} = \frac{137}{40} $
- Convert: $ \frac{137}{40} = 3\frac{17}{40} $
✔ Answer: $ 3\frac{17}{40} $
---
- Convert:
- $ 9\frac{2}{3} = \frac{29}{3} $
- $ 6\frac{1}{11} = \frac{67}{11} $
- Common denominator: LCM of 3 and 11 is 33
- $ \frac{29}{3} = \frac{319}{33} $
- $ \frac{67}{11} = \frac{201}{33} $
- Subtract: $ \frac{319}{33} - \frac{201}{33} = \frac{118}{33} $
- Convert: $ \frac{118}{33} = 3\frac{19}{33} $
✔ Answer: $ 3\frac{19}{33} $
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1. $ \frac{7}{9} $
2. $ 4\frac{1}{4} $
3. $ 3\frac{1}{6} $
4. $ 3\frac{2}{3} $
5. $ 6\frac{1}{2} $
6. $ 6\frac{7}{20} $
7. $ 8\frac{1}{6} $
8. $ 1\frac{7}{30} $
9. $ 3\frac{17}{40} $
10. $ 3\frac{19}{33} $
Let me know if you'd like a printable version or explanations with visual models!
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1. $ 2\frac{4}{9} - 1\frac{4}{6} $
- Convert to improper fractions:
- $ 2\frac{4}{9} = \frac{2 \times 9 + 4}{9} = \frac{18 + 4}{9} = \frac{22}{9} $
- $ 1\frac{4}{6} = \frac{1 \times 6 + 4}{6} = \frac{10}{6} $
- Simplify $ \frac{10}{6} = \frac{5}{3} $
- Find common denominator: LCM of 9 and 3 is 9
- $ \frac{5}{3} = \frac{15}{9} $
- Subtract: $ \frac{22}{9} - \frac{15}{9} = \frac{7}{9} $
✔ Answer: $ \frac{7}{9} $
---
2. $ 9\frac{1}{2} - 5\frac{1}{4} $
- Convert:
- $ 9\frac{1}{2} = \frac{19}{2} $
- $ 5\frac{1}{4} = \frac{21}{4} $
- Common denominator: LCM of 2 and 4 is 4
- $ \frac{19}{2} = \frac{38}{4} $
- Subtract: $ \frac{38}{4} - \frac{21}{4} = \frac{17}{4} $
- Convert to mixed number: $ \frac{17}{4} = 4\frac{1}{4} $
✔ Answer: $ 4\frac{1}{4} $
---
3. $ 7\frac{1}{3} - 4\frac{1}{6} $
- Convert:
- $ 7\frac{1}{3} = \frac{22}{3} $
- $ 4\frac{1}{6} = \frac{25}{6} $
- Common denominator: LCM of 3 and 6 is 6
- $ \frac{22}{3} = \frac{44}{6} $
- Subtract: $ \frac{44}{6} - \frac{25}{6} = \frac{19}{6} $
- Convert: $ \frac{19}{6} = 3\frac{1}{6} $
✔ Answer: $ 3\frac{1}{6} $
---
4. $ 7\frac{1}{2} - 3\frac{5}{6} $
- Convert:
- $ 7\frac{1}{2} = \frac{15}{2} $
- $ 3\frac{5}{6} = \frac{23}{6} $
- Common denominator: LCM of 2 and 6 is 6
- $ \frac{15}{2} = \frac{45}{6} $
- Subtract: $ \frac{45}{6} - \frac{23}{6} = \frac{22}{6} = \frac{11}{3} $
- Convert: $ \frac{11}{3} = 3\frac{2}{3} $
✔ Answer: $ 3\frac{2}{3} $
---
5. $ 11\frac{3}{4} - 5\frac{1}{4} $
- Same denominators, so subtract whole numbers and fractions:
- $ 11 - 5 = 6 $
- $ \frac{3}{4} - \frac{1}{4} = \frac{2}{4} = \frac{1}{2} $
✔ Answer: $ 6\frac{1}{2} $
---
6. $ 8\frac{2}{4} - 2\frac{3}{20} $
- Simplify $ \frac{2}{4} = \frac{1}{2} $
- So: $ 8\frac{1}{2} - 2\frac{3}{20} $
- Convert:
- $ 8\frac{1}{2} = \frac{17}{2} $
- $ 2\frac{3}{20} = \frac{43}{20} $
- Common denominator: LCM of 2 and 20 is 20
- $ \frac{17}{2} = \frac{170}{20} $
- Subtract: $ \frac{170}{20} - \frac{43}{20} = \frac{127}{20} $
- Convert: $ \frac{127}{20} = 6\frac{7}{20} $
✔ Answer: $ 6\frac{7}{20} $
---
7. $ 12\frac{2}{3} - 4\frac{3}{6} $
- Simplify $ \frac{3}{6} = \frac{1}{2} $
- So: $ 12\frac{2}{3} - 4\frac{1}{2} $
- Convert:
- $ 12\frac{2}{3} = \frac{38}{3} $
- $ 4\frac{1}{2} = \frac{9}{2} $
- Common denominator: LCM of 3 and 2 is 6
- $ \frac{38}{3} = \frac{76}{6} $
- $ \frac{9}{2} = \frac{27}{6} $
- Subtract: $ \frac{76}{6} - \frac{27}{6} = \frac{49}{6} $
- Convert: $ \frac{49}{6} = 8\frac{1}{6} $
✔ Answer: $ 8\frac{1}{6} $
---
8. $ 5\frac{2}{5} - 4\frac{1}{6} $
- Convert:
- $ 5\frac{2}{5} = \frac{27}{5} $
- $ 4\frac{1}{6} = \frac{25}{6} $
- Common denominator: LCM of 5 and 6 is 30
- $ \frac{27}{5} = \frac{162}{30} $
- $ \frac{25}{6} = \frac{125}{30} $
- Subtract: $ \frac{162}{30} - \frac{125}{30} = \frac{37}{30} $
- Convert: $ \frac{37}{30} = 1\frac{7}{30} $
✔ Answer: $ 1\frac{7}{30} $
---
9. $ 6\frac{4}{5} - 3\frac{3}{8} $
- Convert:
- $ 6\frac{4}{5} = \frac{34}{5} $
- $ 3\frac{3}{8} = \frac{27}{8} $
- Common denominator: LCM of 5 and 8 is 40
- $ \frac{34}{5} = \frac{272}{40} $
- $ \frac{27}{8} = \frac{135}{40} $
- Subtract: $ \frac{272}{40} - \frac{135}{40} = \frac{137}{40} $
- Convert: $ \frac{137}{40} = 3\frac{17}{40} $
✔ Answer: $ 3\frac{17}{40} $
---
10. $ 9\frac{2}{3} - 6\frac{1}{11} $
- Convert:
- $ 9\frac{2}{3} = \frac{29}{3} $
- $ 6\frac{1}{11} = \frac{67}{11} $
- Common denominator: LCM of 3 and 11 is 33
- $ \frac{29}{3} = \frac{319}{33} $
- $ \frac{67}{11} = \frac{201}{33} $
- Subtract: $ \frac{319}{33} - \frac{201}{33} = \frac{118}{33} $
- Convert: $ \frac{118}{33} = 3\frac{19}{33} $
✔ Answer: $ 3\frac{19}{33} $
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✔ Final Answers:
1. $ \frac{7}{9} $
2. $ 4\frac{1}{4} $
3. $ 3\frac{1}{6} $
4. $ 3\frac{2}{3} $
5. $ 6\frac{1}{2} $
6. $ 6\frac{7}{20} $
7. $ 8\frac{1}{6} $
8. $ 1\frac{7}{30} $
9. $ 3\frac{17}{40} $
10. $ 3\frac{19}{33} $
Let me know if you'd like a printable version or explanations with visual models!
Parent Tip: Review the logic above to help your child master the concept of adding and subtracting mixed numbers with unlike denominators worksheet pdf.
