Subtracting Mixed Numbers with Different Denominators (Grades 5-6 ... - Free Printable

Let's solve each of these mixed number subtraction problems step by step. We'll subtract the mixed numbers and reduce the answers to lowest terms.

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Key Steps for Subtracting Mixed Numbers with Different Denominators:

1. Convert mixed numbers to improper fractions.
2. Find a common denominator.
3. Subtract the fractions.
4. Convert back to a mixed number if needed.
5. Simplify (reduce) to lowest terms.

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Let’s go through each problem:

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1. $ 5\frac{5}{6} - 4\frac{1}{3} $

- Convert:
- $ 5\frac{5}{6} = \frac{35}{6} $
- $ 4\frac{1}{3} = \frac{13}{3} = \frac{26}{6} $
- Subtract: $ \frac{35}{6} - \frac{26}{6} = \frac{9}{6} = \frac{3}{2} = 1\frac{1}{2} $

✔ Answer: $ 1\frac{1}{2} $

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2. $ 3\frac{1}{3} - 2\frac{1}{4} $

- Convert:
- $ 3\frac{1}{3} = \frac{10}{3} $
- $ 2\frac{1}{4} = \frac{9}{4} $
- LCD of 3 and 4 is 12.
- $ \frac{10}{3} = \frac{40}{12} $
- $ \frac{9}{4} = \frac{27}{12} $
- Subtract: $ \frac{40}{12} - \frac{27}{12} = \frac{13}{12} = 1\frac{1}{12} $

✔ Answer: $ 1\frac{1}{12} $

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3. $ 2\frac{1}{4} - 1\frac{1}{3} $

- Convert:
- $ 2\frac{1}{4} = \frac{9}{4} $
- $ 1\frac{1}{3} = \frac{4}{3} $
- LCD of 4 and 3 is 12.
- $ \frac{9}{4} = \frac{27}{12} $
- $ \frac{4}{3} = \frac{16}{12} $
- Subtract: $ \frac{27}{12} - \frac{16}{12} = \frac{11}{12} $

✔ Answer: $ \frac{11}{12} $

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

- Convert:
- $ 8\frac{1}{3} = \frac{25}{3} $
- $ 5\frac{2}{5} = \frac{27}{5} $
- LCD of 3 and 5 is 15.
- $ \frac{25}{3} = \frac{125}{15} $
- $ \frac{27}{5} = \frac{81}{15} $
- Subtract: $ \frac{125}{15} - \frac{81}{15} = \frac{44}{15} = 2\frac{14}{15} $

✔ Answer: $ 2\frac{14}{15} $

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5. $ 1\frac{1}{2} - 1\frac{1}{3} $

- Convert:
- $ 1\frac{1}{2} = \frac{3}{2} $
- $ 1\frac{1}{3} = \frac{4}{3} $
- LCD of 2 and 3 is 6.
- $ \frac{3}{2} = \frac{9}{6} $
- $ \frac{4}{3} = \frac{8}{6} $
- Subtract: $ \frac{9}{6} - \frac{8}{6} = \frac{1}{6} $

✔ Answer: $ \frac{1}{6} $

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6. $ 4\frac{1}{4} - 2\frac{1}{2} $

- Convert:
- $ 4\frac{1}{4} = \frac{17}{4} $
- $ 2\frac{1}{2} = \frac{5}{2} = \frac{10}{4} $
- Subtract: $ \frac{17}{4} - \frac{10}{4} = \frac{7}{4} = 1\frac{3}{4} $

✔ Answer: $ 1\frac{3}{4} $

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7. $ 9\frac{1}{3} - 6\frac{3}{10} $

- Convert:
- $ 9\frac{1}{3} = \frac{28}{3} $
- $ 6\frac{3}{10} = \frac{63}{10} $
- LCD of 3 and 10 is 30.
- $ \frac{28}{3} = \frac{280}{30} $
- $ \frac{63}{10} = \frac{189}{30} $
- Subtract: $ \frac{280}{30} - \frac{189}{30} = \frac{91}{30} = 3\frac{1}{30} $

✔ Answer: $ 3\frac{1}{30} $

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8. $ 6\frac{1}{5} - 3\frac{3}{8} $

- Convert:
- $ 6\frac{1}{5} = \frac{31}{5} $
- $ 3\frac{3}{8} = \frac{27}{8} $
- LCD of 5 and 8 is 40.
- $ \frac{31}{5} = \frac{248}{40} $
- $ \frac{27}{8} = \frac{135}{40} $
- Subtract: $ \frac{248}{40} - \frac{135}{40} = \frac{113}{40} = 2\frac{33}{40} $

✔ Answer: $ 2\frac{33}{40} $

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9. $ 4\frac{3}{8} - 2\frac{1}{16} $

- Convert:
- $ 4\frac{3}{8} = \frac{35}{8} $
- $ 2\frac{1}{16} = \frac{33}{16} $
- LCD of 8 and 16 is 16.
- $ \frac{35}{8} = \frac{70}{16} $
- Subtract: $ \frac{70}{16} - \frac{33}{16} = \frac{37}{16} = 2\frac{5}{16} $

✔ Answer: $ 2\frac{5}{16} $

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10. $ 1\frac{1}{4} - 1\frac{1}{5} $

- Convert:
- $ 1\frac{1}{4} = \frac{5}{4} $
- $ 1\frac{1}{5} = \frac{6}{5} $
- LCD of 4 and 5 is 20.
- $ \frac{5}{4} = \frac{25}{20} $
- $ \frac{6}{5} = \frac{24}{20} $
- Subtract: $ \frac{25}{20} - \frac{24}{20} = \frac{1}{20} $

✔ Answer: $ \frac{1}{20} $

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11. $ 8\frac{1}{6} - 7\frac{2}{3} $

- Convert:
- $ 8\frac{1}{6} = \frac{49}{6} $
- $ 7\frac{2}{3} = \frac{23}{3} = \frac{46}{6} $
- Subtract: $ \frac{49}{6} - \frac{46}{6} = \frac{3}{6} = \frac{1}{2} $

✔ Answer: $ \frac{1}{2} $

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12. $ 5\frac{1}{2} - 3\frac{4}{5} $

- Convert:
- $ 5\frac{1}{2} = \frac{11}{2} $
- $ 3\frac{4}{5} = \frac{19}{5} $
- LCD of 2 and 5 is 10.
- $ \frac{11}{2} = \frac{55}{10} $
- $ \frac{19}{5} = \frac{38}{10} $
- Subtract: $ \frac{55}{10} - \frac{38}{10} = \frac{17}{10} = 1\frac{7}{10} $

✔ Answer: $ 1\frac{7}{10} $

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13. $ 3\frac{1}{2} - 2\frac{1}{4} $

- Convert:
- $ 3\frac{1}{2} = \frac{7}{2} $
- $ 2\frac{1}{4} = \frac{9}{4} $
- LCD of 2 and 4 is 4.
- $ \frac{7}{2} = \frac{14}{4} $
- Subtract: $ \frac{14}{4} - \frac{9}{4} = \frac{5}{4} = 1\frac{1}{4} $

✔ Answer: $ 1\frac{1}{4} $

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14. $ 2\frac{2}{3} - 1\frac{1}{4} $

- Convert:
- $ 2\frac{2}{3} = \frac{8}{3} $
- $ 1\frac{1}{4} = \frac{5}{4} $
- LCD of 3 and 4 is 12.
- $ \frac{8}{3} = \frac{32}{12} $
- $ \frac{5}{4} = \frac{15}{12} $
- Subtract: $ \frac{32}{12} - \frac{15}{12} = \frac{17}{12} = 1\frac{5}{12} $

✔ Answer: $ 1\frac{5}{12} $

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✔ Final Answers:

1. $ 1\frac{1}{2} $
2. $ 1\frac{1}{12} $
3. $ \frac{11}{12} $
4. $ 2\frac{14}{15} $
5. $ \frac{1}{6} $
6. $ 1\frac{3}{4} $
7. $ 3\frac{1}{30} $
8. $ 2\frac{33}{40} $
9. $ 2\frac{5}{16} $
10. $ \frac{1}{20} $
11. $ \frac{1}{2} $
12. $ 1\frac{7}{10} $
13. $ 1\frac{1}{4} $
14. $ 1\frac{5}{12} $

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